Modeling Complex Phenomena Using Multiscale Time Sequences

DTIC Science & Technology

2009-08-24

measures based on Hurst and Holder exponents , auto-regressive methods and Fourier and wavelet decomposition methods. The applications for this technology...relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and Holder exponents , auto-regressive...different scales and how these scales relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and

Wavelet and Fractal Analysis of Remotely Sensed Surface Temperature with Applications to Estimation of Surface Sensible Heat Flux Density

NASA Technical Reports Server (NTRS)

Schieldge, John

2000-01-01

Wavelet and fractal analyses have been used successfully to analyze one-dimensional data sets such as time series of financial, physical, and biological parameters. These techniques have been applied to two-dimensional problems in some instances, including the analysis of remote sensing imagery. In this respect, these techniques have not been widely used by the remote sensing community, and their overall capabilities as analytical tools for use on satellite and aircraft data sets is not well known. Wavelet and fractal analyses have the potential to provide fresh insight into the characterization of surface properties such as temperature and emissivity distributions, and surface processes such as the heat and water vapor exchange between the surface and the lower atmosphere. In particular, the variation of sensible heat flux density as a function of the change In scale of surface properties Is difficult to estimate, but - in general - wavelets and fractals have proved useful in determining the way a parameter varies with changes in scale. We present the results of a limited study on the relationship between spatial variations in surface temperature distribution and sensible heat flux distribution as determined by separate wavelet and fractal analyses. We analyzed aircraft imagery obtained in the thermal infrared (IR) bands from the multispectral TIMS and hyperspectral MASTER airborne sensors. The thermal IR data allows us to estimate the surface kinetic temperature distribution for a number of sites in the Midwestern and Southwestern United States (viz., San Pedro River Basin, Arizona; El Reno, Oklahoma; Jornada, New Mexico). The ground spatial resolution of the aircraft data varied from 5 to 15 meters. All sites were instrumented with meteorological and hydrological equipment including surface layer flux measuring stations such as Bowen Ratio systems and sonic anemometers. The ground and aircraft data sets provided the inputs for the wavelet and fractal analyses, and the validation of the results.

Multifractal modeling, segmentation, prediction, and statistical validation of posterior fossa tumors

NASA Astrophysics Data System (ADS)

Islam, Atiq; Iftekharuddin, Khan M.; Ogg, Robert J.; Laningham, Fred H.; Sivakumar, Bhuvaneswari

2008-03-01

In this paper, we characterize the tumor texture in pediatric brain magnetic resonance images (MRIs) and exploit these features for automatic segmentation of posterior fossa (PF) tumors. We focus on PF tumor because of the prevalence of such tumor in pediatric patients. Due to varying appearance in MRI, we propose to model the tumor texture with a multi-fractal process, such as a multi-fractional Brownian motion (mBm). In mBm, the time-varying Holder exponent provides flexibility in modeling irregular tumor texture. We develop a detailed mathematical framework for mBm in two-dimension and propose a novel algorithm to estimate the multi-fractal structure of tissue texture in brain MRI based on wavelet coefficients. This wavelet based multi-fractal feature along with MR image intensity and a regular fractal feature obtained using our existing piecewise-triangular-prism-surface-area (PTPSA) method, are fused in segmenting PF tumor and non-tumor regions in brain T1, T2, and FLAIR MR images respectively. We also demonstrate a non-patient-specific automated tumor prediction scheme based on these image features. We experimentally show the tumor discriminating power of our novel multi-fractal texture along with intensity and fractal features in automated tumor segmentation and statistical prediction. To evaluate the performance of our tumor prediction scheme, we obtain ROCs and demonstrate how sharply the curves reach the specificity of 1.0 sacrificing minimal sensitivity. Experimental results show the effectiveness of our proposed techniques in automatic detection of PF tumors in pediatric MRIs.

Multispectral image fusion based on fractal features

NASA Astrophysics Data System (ADS)

Tian, Jie; Chen, Jie; Zhang, Chunhua

2004-01-01

Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the composition of source pyramid images. So this fusion scheme is a multi-resolution analysis. The wavelet decomposition of image can be actually considered as special pyramid decomposition. According to wavelet decomposition theories, the approximation of image (formula available in paper) at resolution 2j+1 equal to its orthogonal projection in space , that is, where Ajf is the low-frequency approximation of image f(x, y) at resolution 2j and , , represent the vertical, horizontal and diagonal wavelet coefficients respectively at resolution 2j. These coefficients describe the high-frequency information of image at direction of vertical, horizontal and diagonal respectively. Ajf, , and are independent and can be considered as images. In this paper J is set to be 1, so the source image is decomposed to produce the son-images Af, D1f, D2f and D3f. To solve the problem of detecting artifacts, the concepts of vertical fractal dimension FD1, horizontal fractal dimension FD2 and diagonal fractal dimension FD3 are proposed in this paper. The vertical fractal dimension FD1 corresponds to the vertical wavelet coefficients image after the wavelet decomposition of source image, the horizontal fractal dimension FD2 corresponds to the horizontal wavelet coefficients and the diagonal fractal dimension FD3 the diagonal one. These definitions enrich the illustration of source images. Therefore they are helpful to classify the targets. Then the detection of artifacts in the decomposed images is a problem of pattern recognition in 4-D space. The combination of FD0, FD1, FD2 and FD3 make a vector of (FD0, FD1, FD2, FD3), which can be considered as a united feature vector of the studied image. All the parts of the images are classified in the 4-D pattern space created by the vector of (FD0, FD1, FD2, FD3) so that the area that contains man-made objects could be detected. This detection can be considered as a coarse recognition, and then the significant areas in each son-images are signed so that they can be dealt with special rules. There has been various fusion rules developed with each one aiming at a special problem. These rules have different performance, so it is very important to select an appropriate rule during the design of an image fusion system. Recent research denotes that the rule should be adjustable so that it is always suitable to extrude the features of targets and to preserve the pixels of useful information. In this paper, owing to the consideration that fractal dimension is one of the main features to distinguish man-made targets from natural objects, the fusion rule was defined that if the studied region of image contains man-made target, the pixels of the source image whose fractal dimension is minimal are saved to be the pixels of the fused image, otherwise, a weighted average operator is adopted to avoid loss of information. The main idea of this rule is to store the pixels with low fractal dimensions, so it can be named Minimal Fractal dimensions (MFD) fusion rule. This fractal-based algorithm is compared with a common weighted average fusion algorithm. An objective assessment is taken to the two fusion results. The criteria of Entropy, Cross-Entropy, Peak Signal-to-Noise Ratio (PSNR) and Standard Gray Scale Difference are defined in this paper. Reversely to the idea of constructing an ideal image as the assessing reference, the source images are selected to be the reference in this paper. It can be deemed that this assessment is to calculate how much the image quality has been enhanced and the quantity of information has been increased when the fused image is compared with the source images. The experimental results imply that the fractal-based multi-spectral fusion algorithm can effectively preserve the information of man-made objects with a high contrast. It is proved that this algorithm could well preserve features of military targets because that battlefield targets are most man-made objects and in common their images differ from fractal models obviously. Furthermore, the fractal features are not sensitive to the imaging conditions and the movement of targets, so this fractal-based algorithm may be very practical.

Diesel Engine Valve Clearance Fault Diagnosis Based on Features Extraction Techniques and FastICA-SVM

NASA Astrophysics Data System (ADS)

Jing, Ya-Bing; Liu, Chang-Wen; Bi, Feng-Rong; Bi, Xiao-Yang; Wang, Xia; Shao, Kang

2017-07-01

Numerous vibration-based techniques are rarely used in diesel engines fault diagnosis in a direct way, due to the surface vibration signals of diesel engines with the complex non-stationary and nonlinear time-varying features. To investigate the fault diagnosis of diesel engines, fractal correlation dimension, wavelet energy and entropy as features reflecting the diesel engine fault fractal and energy characteristics are extracted from the decomposed signals through analyzing vibration acceleration signals derived from the cylinder head in seven different states of valve train. An intelligent fault detector FastICA-SVM is applied for diesel engine fault diagnosis and classification. The results demonstrate that FastICA-SVM achieves higher classification accuracy and makes better generalization performance in small samples recognition. Besides, the fractal correlation dimension and wavelet energy and entropy as the special features of diesel engine vibration signal are considered as input vectors of classifier FastICA-SVM and could produce the excellent classification results. The proposed methodology improves the accuracy of feature extraction and the fault diagnosis of diesel engines.

Polarimetric Wavelet Fractal Remote Sensing Principles for Space Materials (Preprint)

DTIC Science & Technology

2012-06-04

previously introduced 9-10, 28. The combination of polarimetry and wavelet-fractal analysis yields enhanced knowledge of the spatial-temporal-frequency...applications in situations that require analysis over very short time durations or where information is localized, and have been combined with polarimetry ...and D.B. Chenault, “Near Infrared Imaging Polarimetry ”, Proc. SPIE 4481, pp. 30-31, 2001. [8] A.B. Mahler, P. Smith, R. Chipman, G. Smith, N

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the ``Chaos Game Representation'' (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene- coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent ``sub-periods'' in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration. This work examines the model's behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system ``information dynamics'' correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed.

Non-stationary dynamics in the bouncing ball: A wavelet perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

Fractal Signals & Space-Time Cartoons

NASA Astrophysics Data System (ADS)

Oetama, H. C. Jakob; Maksoed, W. H.

2016-03-01

In ``Theory of Scale Relativity'', 1991- L. Nottale states whereas ``scale relativity is a geometrical & fractal space-time theory''. It took in comparisons to ``a unified, wavelet based framework for efficiently synthetizing, analyzing ∖7 processing several broad classes of fractal signals''-Gregory W. Wornell:``Signal Processing with Fractals'', 1995. Furthers, in Fig 1.1. a simple waveform from statistically scale-invariant random process [ibid.,h 3 ]. Accompanying RLE Technical Report 566 ``Synthesis, Analysis & Processing of Fractal Signals'' as well as from Wornell, Oct 1991 herewith intended to deducts =a Δt + (1 - β Δ t) ...in Petersen, et.al: ``Scale invariant properties of public debt growth'',2010 h. 38006p2 to [1/{1- (2 α (λ) /3 π) ln (λ/r)}depicts in Laurent Nottale,1991, h 24. Acknowledgment devotes to theLates HE. Mr. BrigadierGeneral-TNI[rtd].Prof. Ir. HANDOJO.

A new set of wavelet- and fractals-based features for Gleason grading of prostate cancer histopathology images

NASA Astrophysics Data System (ADS)

Mosquera Lopez, Clara; Agaian, Sos

2013-02-01

Prostate cancer detection and staging is an important step towards patient treatment selection. Advancements in digital pathology allow the application of new quantitative image analysis algorithms for computer-assisted diagnosis (CAD) on digitized histopathology images. In this paper, we introduce a new set of features to automatically grade pathological images using the well-known Gleason grading system. The goal of this study is to classify biopsy images belonging to Gleason patterns 3, 4, and 5 by using a combination of wavelet and fractal features. For image classification we use pairwise coupling Support Vector Machine (SVM) classifiers. The accuracy of the system, which is close to 97%, is estimated through three different cross-validation schemes. The proposed system offers the potential for automating classification of histological images and supporting prostate cancer diagnosis.

Automatic brain tumor detection in MRI: methodology and statistical validation

NASA Astrophysics Data System (ADS)

Iftekharuddin, Khan M.; Islam, Mohammad A.; Shaik, Jahangheer; Parra, Carlos; Ogg, Robert

2005-04-01

Automated brain tumor segmentation and detection are immensely important in medical diagnostics because it provides information associated to anatomical structures as well as potential abnormal tissue necessary to delineate appropriate surgical planning. In this work, we propose a novel automated brain tumor segmentation technique based on multiresolution texture information that combines fractal Brownian motion (fBm) and wavelet multiresolution analysis. Our wavelet-fractal technique combines the excellent multiresolution localization property of wavelets to texture extraction of fractal. We prove the efficacy of our technique by successfully segmenting pediatric brain MR images (MRIs) from St. Jude Children"s Research Hospital. We use self-organizing map (SOM) as our clustering tool wherein we exploit both pixel intensity and multiresolution texture features to obtain segmented tumor. Our test results show that our technique successfully segments abnormal brain tissues in a set of T1 images. In the next step, we design a classifier using Feed-Forward (FF) neural network to statistically validate the presence of tumor in MRI using both the multiresolution texture and the pixel intensity features. We estimate the corresponding receiver operating curve (ROC) based on the findings of true positive fractions and false positive fractions estimated from our classifier at different threshold values. An ROC, which can be considered as a gold standard to prove the competence of a classifier, is obtained to ascertain the sensitivity and specificity of our classifier. We observe that at threshold 0.4 we achieve true positive value of 1.0 (100%) sacrificing only 0.16 (16%) false positive value for the set of 50 T1 MRI analyzed in this experiment.

Micromorphological characterization of zinc/silver particle composite coatings.

PubMed

Méndez, Alia; Reyes, Yolanda; Trejo, Gabriel; StĘpień, Krzysztof; Ţălu, Ştefan

2015-12-01

The aim of this study was to evaluate the three-dimensional (3D) surface micromorphology of zinc/silver particles (Zn/AgPs) composite coatings with antibacterial activity prepared using an electrodeposition technique. These 3D nanostructures were investigated over square areas of 5 μm × 5 μm by atomic force microscopy (AFM), fractal, and wavelet analysis. The fractal analysis of 3D surface roughness revealed that (Zn/AgPs) composite coatings have fractal geometry. Triangulation method, based on the linear interpolation type, applied for AFM data was employed in order to characterise the surfaces topographically (in amplitude, spatial distribution and pattern of surface characteristics). The surface fractal dimension Df , as well as height values distribution have been determined for the 3D nanostructure surfaces. © 2015 The Authors published by Wiley Periodicals, Inc.

Nonlinear analysis of EEG in major depression with fractal dimensions.

PubMed

Akar, Saime A; Kara, Sadik; Agambayev, Sumeyra; Bilgic, Vedat

2015-01-01

Major depressive disorder (MDD) is a psychiatric mood disorder characterized by cognitive and functional impairments in attention, concentration, learning and memory. In order to investigate and understand its underlying neural activities and pathophysiology, EEG methodologies can be used. In this study, we estimated the nonlinearity features of EEG in MDD patients to assess the dynamical properties underlying the frontal and parietal brain activity. EEG data were obtained from 16 patients and 15 matched healthy controls. A wavelet-chaos methodology was used for data analysis. First, EEGs of subjects were decomposed into 5 EEG sub-bands by discrete wavelet transform. Then, both the Katz's and Higuchi's fractal dimensions (KFD and HFD) were calculated as complexity measures for full-band and sub-bands EEGs. Last, two-way analyses of variances were used to test EEG complexity differences on each fractality measures. As a result, a significantly increased complexity was found in both parietal and frontal regions of MDD patients. This significantly increased complexity was observed not only in full-band activity but also in beta and gamma sub-bands of EEG. The findings of the present study indicate the possibility of using the wavelet-chaos methodology to discriminate the EEGs of MDD patients from healthy controls.

Micromorphological characterization of zinc/silver particle composite coatings

PubMed Central

Méndez, Alia; Reyes, Yolanda; Trejo, Gabriel; StĘpień, Krzysztof

2015-01-01

ABSTRACT The aim of this study was to evaluate the three‐dimensional (3D) surface micromorphology of zinc/silver particles (Zn/AgPs) composite coatings with antibacterial activity prepared using an electrodeposition technique. These 3D nanostructures were investigated over square areas of 5 μm × 5 μm by atomic force microscopy (AFM), fractal, and wavelet analysis. The fractal analysis of 3D surface roughness revealed that (Zn/AgPs) composite coatings have fractal geometry. Triangulation method, based on the linear interpolation type, applied for AFM data was employed in order to characterise the surfaces topographically (in amplitude, spatial distribution and pattern of surface characteristics). The surface fractal dimension D f, as well as height values distribution have been determined for the 3D nanostructure surfaces. Microsc. Res. Tech. 78:1082–1089, 2015. © 2015 The Authors published by Wiley Periodicals, Inc. PMID:26500164

Image characterization by fractal descriptors in variational mode decomposition domain: Application to brain magnetic resonance

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2016-08-01

The main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi-resolution domains to characterize biomedical digital image texture. In this regard, three multi-resolution techniques are considered: the well-known discrete wavelet transform (DWT) and the empirical mode decomposition (EMD), and; the newly introduced; variational mode decomposition mode (VMD). The original image is decomposed by the DWT, EMD, and VMD into different scales. Then, Fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image. The support vector machine (SVM) was used to perform supervised classification. The empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images (MRI) affected with Alzheimer disease (AD). Our results demonstrate that fractal descriptors estimated in VMD domain outperform those estimated in DWT and EMD domains; and also those directly estimated from the original image.

BOOK REVIEW: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

NASA Astrophysics Data System (ADS)

Ng, J.; Kingsbury, N. G.

2004-02-01

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies’ wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author’s own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.

Wavelets in Physics

NASA Astrophysics Data System (ADS)

van den Berg, J. C.

2004-03-01

A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.

Wavelets in Physics

NASA Astrophysics Data System (ADS)

van den Berg, J. C.

1999-08-01

A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.

Diagnostic methodology for incipient system disturbance based on a neural wavelet approach

NASA Astrophysics Data System (ADS)

Won, In-Ho

Since incipient system disturbances are easily mixed up with other events or noise sources, the signal from the system disturbance can be neglected or identified as noise. Thus, as available knowledge and information is obtained incompletely or inexactly from the measurements; an exploration into the use of artificial intelligence (AI) tools to overcome these uncertainties and limitations was done. A methodology integrating the feature extraction efficiency of the wavelet transform with the classification capabilities of neural networks is developed for signal classification in the context of detecting incipient system disturbances. The synergistic effects of wavelets and neural networks present more strength and less weakness than either technique taken alone. A wavelet feature extractor is developed to form concise feature vectors for neural network inputs. The feature vectors are calculated from wavelet coefficients to reduce redundancy and computational expense. During this procedure, the statistical features based on the fractal concept to the wavelet coefficients play a role as crucial key in the wavelet feature extractor. To verify the proposed methodology, two applications are investigated and successfully tested. The first involves pump cavitation detection using dynamic pressure sensor. The second pertains to incipient pump cavitation detection using signals obtained from a current sensor. Also, through comparisons between three proposed feature vectors and with statistical techniques, it is shown that the variance feature extractor provides a better approach in the performed applications.

Visual information processing II; Proceedings of the Meeting, Orlando, FL, Apr. 14-16, 1993

NASA Technical Reports Server (NTRS)

Huck, Friedrich O. (Editor); Juday, Richard D. (Editor)

1993-01-01

Various papers on visual information processing are presented. Individual topics addressed include: aliasing as noise, satellite image processing using a hammering neural network, edge-detetion method using visual perception, adaptive vector median filters, design of a reading test for low-vision image warping, spatial transformation architectures, automatic image-enhancement method, redundancy reduction in image coding, lossless gray-scale image compression by predictive GDF, information efficiency in visual communication, optimizing JPEG quantization matrices for different applications, use of forward error correction to maintain image fidelity, effect of peanoscanning on image compression. Also discussed are: computer vision for autonomous robotics in space, optical processor for zero-crossing edge detection, fractal-based image edge detection, simulation of the neon spreading effect by bandpass filtering, wavelet transform (WT) on parallel SIMD architectures, nonseparable 2D wavelet image representation, adaptive image halftoning based on WT, wavelet analysis of global warming, use of the WT for signal detection, perfect reconstruction two-channel rational filter banks, N-wavelet coding for pattern classification, simulation of image of natural objects, number-theoretic coding for iconic systems.

Influence of pansharpening techniques in obtaining accurate vegetation thematic maps

NASA Astrophysics Data System (ADS)

Ibarrola-Ulzurrun, Edurne; Gonzalo-Martin, Consuelo; Marcello-Ruiz, Javier

2016-10-01

In last decades, there have been a decline in natural resources, becoming important to develop reliable methodologies for their management. The appearance of very high resolution sensors has offered a practical and cost-effective means for a good environmental management. In this context, improvements are needed for obtaining higher quality of the information available in order to get reliable classified images. Thus, pansharpening enhances the spatial resolution of the multispectral band by incorporating information from the panchromatic image. The main goal in the study is to implement pixel and object-based classification techniques applied to the fused imagery using different pansharpening algorithms and the evaluation of thematic maps generated that serve to obtain accurate information for the conservation of natural resources. A vulnerable heterogenic ecosystem from Canary Islands (Spain) was chosen, Teide National Park, and Worldview-2 high resolution imagery was employed. The classes considered of interest were set by the National Park conservation managers. 7 pansharpening techniques (GS, FIHS, HCS, MTF based, Wavelet `à trous' and Weighted Wavelet `à trous' through Fractal Dimension Maps) were chosen in order to improve the data quality with the goal to analyze the vegetation classes. Next, different classification algorithms were applied at pixel-based and object-based approach, moreover, an accuracy assessment of the different thematic maps obtained were performed. The highest classification accuracy was obtained applying Support Vector Machine classifier at object-based approach in the Weighted Wavelet `à trous' through Fractal Dimension Maps fused image. Finally, highlight the difficulty of the classification in Teide ecosystem due to the heterogeneity and the small size of the species. Thus, it is important to obtain accurate thematic maps for further studies in the management and conservation of natural resources.

Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

NASA Astrophysics Data System (ADS)

Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir

2012-10-01

Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

Continuous EEG signal analysis for asynchronous BCI application.

PubMed

Hsu, Wei-Yen

2011-08-01

In this study, we propose a two-stage recognition system for continuous analysis of electroencephalogram (EEG) signals. An independent component analysis (ICA) and correlation coefficient are used to automatically eliminate the electrooculography (EOG) artifacts. Based on the continuous wavelet transform (CWT) and Student's two-sample t-statistics, active segment selection then detects the location of active segment in the time-frequency domain. Next, multiresolution fractal feature vectors (MFFVs) are extracted with the proposed modified fractal dimension from wavelet data. Finally, the support vector machine (SVM) is adopted for the robust classification of MFFVs. The EEG signals are continuously analyzed in 1-s segments, and every 0.5 second moves forward to simulate asynchronous BCI works in the two-stage recognition architecture. The segment is first recognized as lifted or not in the first stage, and then is classified as left or right finger lifting at stage two if the segment is recognized as lifting in the first stage. Several statistical analyses are used to evaluate the performance of the proposed system. The results indicate that it is a promising system in the applications of asynchronous BCI work.

Multifractality in Cardiac Dynamics

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Rosenblum, Misha; Stanley, H. Eugene; Havlin, Shlomo; Goldberger, Ary

1997-03-01

Wavelet decomposition is used to analyze the fractal scaling properties of heart beat time series. The singularity spectrum D(h) of the variations in the beat-to-beat intervals is obtained from the wavelet transform modulus maxima which contain information on the hierarchical distribution of the singularities in the signal. Multifractal behavior is observed for healthy cardiac dynamics while pathologies are associated with loss of support in the singularity spectrum.

A comparative analysis of spectral exponent estimation techniques for 1/fβ processes with applications to the analysis of stride interval time series

PubMed Central

Schaefer, Alexander; Brach, Jennifer S.; Perera, Subashan; Sejdić, Ervin

2013-01-01

Background The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f) = 1/fβ. The scaling exponent β is thus often interpreted as a “biomarker” of relative health and decline. New Method This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. Results The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Comparison with Existing Methods: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. Conclusions The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. PMID:24200509

A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series.

PubMed

Schaefer, Alexander; Brach, Jennifer S; Perera, Subashan; Sejdić, Ervin

2014-01-30

The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline. This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. Copyright © 2013 Elsevier B.V. All rights reserved.

Fractal density modeling of crustal heterogeneity from the KTB deep hole

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2017-03-01

Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

Continuous wavelet transform based time-scale and multifractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nurujjaman, Md.; Narayanan, Ramesh; Iyengar, A. N. Sekar

2009-10-15

Continuous wavelet transform (CWT) based time-scale and multifractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift), which is a typical nonlinear behavior, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multifractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed tomore » become a monofractal for periodic signals. These multifractal spectra were also used to estimate different quantities such as the correlation and fractal dimension, degree of multifractality, and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Espinosa-Paredes, Gilberto; Prieto-Guerrero, Alfonso; Nunez-Carrera, Alejandro

This paper introduces a wavelet-based method to analyze instability events in a boiling water reactor (BWR) during transient phenomena. The methodology to analyze BWR signals includes the following: (a) the short-time Fourier transform (STFT) analysis, (b) decomposition using the continuous wavelet transform (CWT), and (c) application of multiresolution analysis (MRA) using discrete wavelet transform (DWT). STFT analysis permits the study, in time, of the spectral content of analyzed signals. The CWT provides information about ruptures, discontinuities, and fractal behavior. To detect these important features in the signal, a mother wavelet has to be chosen and applied at several scales tomore » obtain optimum results. MRA allows fast implementation of the DWT. Features like important frequencies, discontinuities, and transients can be detected with analysis at different levels of detail coefficients. The STFT was used to provide a comparison between a classic method and the wavelet-based method. The damping ratio, which is an important stability parameter, was calculated as a function of time. The transient behavior can be detected by analyzing the maximum contained in detail coefficients at different levels in the signal decomposition. This method allows analysis of both stationary signals and highly nonstationary signals in the timescale plane. This methodology has been tested with the benchmark power instability event of Laguna Verde nuclear power plant (NPP) Unit 1, which is a BWR-5 NPP.« less

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

NASA Technical Reports Server (NTRS)

Gollmer, Steven M.; Harshvardhan; Cahalan, Robert F.; Snider, Jack B.

1995-01-01

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models.

Textural characterization of histopathological images for oral sub-mucous fibrosis detection.

PubMed

Krishnan, M Muthu Rama; Shah, Pratik; Choudhary, Anirudh; Chakraborty, Chandan; Paul, Ranjan Rashmi; Ray, Ajoy K

2011-10-01

In the field of quantitative microscopy, textural information plays a significant role very often in tissue characterization and diagnosis, in addition to morphology and intensity. The aim of this work is to improve the classification accuracy based on textural features for the development of a computer assisted screening of oral sub-mucous fibrosis (OSF). In fact, a systematic approach is introduced in order to grade the histopathological tissue sections into normal, OSF without dysplasia and OSF with dysplasia, which would help the oral onco-pathologists to screen the subjects rapidly. In totality, 71 textural features are extracted from epithelial region of the tissue sections using various wavelet families, Gabor-wavelet, local binary pattern, fractal dimension and Brownian motion curve, followed by preprocessing and segmentation. Wavelet families contribute a common set of 9 features, out of which 8 are significant and other 61 out of 62 obtained from the rest of the extractors are also statistically significant (p<0.05) in discriminating the three stages. Based on mean distance criteria, the best wavelet family (i.e., biorthogonal3.1 (bior3.1)) is selected for classifier design. support vector machine (SVM) is trained by 146 samples based on 69 textural features and its classification accuracy is computed for each of the combinations of wavelet family and rest of the extractors. Finally, it has been investigated that bior3.1 wavelet coefficients leads to higher accuracy (88.38%) in combination with LBP and Gabor wavelet features through three-fold cross validation. Results are shown and discussed in detail. It is shown that combining more than one texture measure instead of using just one might improve the overall accuracy. Copyright © 2011 Elsevier Ltd. All rights reserved.

Fetal Heart Sounds Detection Using Wavelet Transform and Fractal Dimension

PubMed Central

Koutsiana, Elisavet; Hadjileontiadis, Leontios J.; Chouvarda, Ioanna; Khandoker, Ahsan H.

2017-01-01

Phonocardiography is a non-invasive technique for the detection of fetal heart sounds (fHSs). In this study, analysis of fetal phonocardiograph (fPCG) signals, in order to achieve fetal heartbeat segmentation, is proposed. The proposed approach (namely WT–FD) is a wavelet transform (WT)-based method that combines fractal dimension (FD) analysis in the WT domain for the extraction of fHSs from the underlying noise. Its adoption in this field stems from its successful use in the fields of lung and bowel sounds de-noising analysis. The efficiency of the WT–FD method in fHS extraction has been evaluated with 19 simulated fHS signals, created for the present study, with additive noise up to (3 dB), along with the simulated fPCGs database available at PhysioBank. Results have shown promising performance in the identification of the correct location and morphology of the fHSs, reaching an overall accuracy of 89% justifying the efficacy of the method. The WT–FD approach effectively extracts the fHS signals from the noisy background, paving the way for testing it in real fHSs and clearly contributing to better evaluation of the fetal heart functionality. PMID:28944222

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

NASA Technical Reports Server (NTRS)

Huck, Friedrich O. (Editor); Juday, Richard D. (Editor)

1992-01-01

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Frozen Fractals all Around: Solar flares, Ampere’s Law, and the Search for Units in Scale-Free Processes.

NASA Astrophysics Data System (ADS)

McAteer, R. T. James

2015-08-01

My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary key steps in identifying the nature of the mother wavelet to ensuring the viability of this powerful connection.

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

NASA Astrophysics Data System (ADS)

Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.

2018-02-01

River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

(Multi)fractality of Earthquakes by use of Wavelet Analysis

NASA Astrophysics Data System (ADS)

Enescu, B.; Ito, K.; Struzik, Z. R.

2002-12-01

The fractal character of earthquakes' occurrence, in time, space or energy, has by now been established beyond doubt and is in agreement with modern models of seismicity. Moreover, the cascade-like generation process of earthquakes -with one "main" shock followed by many aftershocks, having their own aftershocks- may well be described through multifractal analysis, well suited for dealing with such multiplicative processes. The (multi)fractal character of seismicity has been analysed so far by using traditional techniques, like the box-counting and correlation function algorithms. This work introduces a new approach for characterising the multifractal patterns of seismicity. The use of wavelet analysis, in particular of the wavelet transform modulus maxima, to multifractal analysis was pioneered by Arneodo et al. (1991, 1995) and applied successfully in diverse fields, such as the study of turbulence, the DNA sequences or the heart rate dynamics. The wavelets act like a microscope, revealing details about the analysed data at different times and scales. We introduce and perform such an analysis on the occurrence time of earthquakes and show its advantages. In particular, we analyse shallow seismicity, characterised by a high aftershock "productivity", as well as intermediate and deep seismic activity, known for its scarcity of aftershocks. We examine as well declustered (aftershocks removed) versions of seismic catalogues. Our preliminary results show some degree of multifractality for the undeclustered, shallow seismicity. On the other hand, at large scales, we detect a monofractal scaling behaviour, clearly put in evidence for the declustered, shallow seismic activity. Moreover, some of the declustered sequences show a long-range dependent (LRD) behaviour, characterised by a Hurst exponent, H > 0.5, in contrast with the memory-less, Poissonian model. We demonstrate that the LRD is a genuine characteristic and is not an effect of the time series probability distribution function. One of the most attractive features of wavelet analysis is its ability to determine a local Hurst exponent. We show that this feature together with the possibility of extending the analysis to spatial patterns may constitute a valuable approach to search for anomalous (precursory?) patterns of seismic activity.

Fractal dimension to classify the heart sound recordings with KNN and fuzzy c-mean clustering methods

NASA Astrophysics Data System (ADS)

Juniati, D.; Khotimah, C.; Wardani, D. E. K.; Budayasa, K.

2018-01-01

The heart abnormalities can be detected from heart sound. A heart sound can be heard directly with a stethoscope or indirectly by a phonocardiograph, a machine of the heart sound recording. This paper presents the implementation of fractal dimension theory to make a classification of phonocardiograms into a normal heart sound, a murmur, or an extrasystole. The main algorithm used to calculate the fractal dimension was Higuchi’s Algorithm. There were two steps to make a classification of phonocardiograms, feature extraction, and classification. For feature extraction, we used Discrete Wavelet Transform to decompose the signal of heart sound into several sub-bands depending on the selected level. After the decomposition process, the signal was processed using Fast Fourier Transform (FFT) to determine the spectral frequency. The fractal dimension of the FFT output was calculated using Higuchi Algorithm. The classification of fractal dimension of all phonocardiograms was done with KNN and Fuzzy c-mean clustering methods. Based on the research results, the best accuracy obtained was 86.17%, the feature extraction by DWT decomposition level 3 with the value of kmax 50, using 5-fold cross validation and the number of neighbors was 5 at K-NN algorithm. Meanwhile, for fuzzy c-mean clustering, the accuracy was 78.56%.

Multifractal spectrum of physiological signals: a mechanism-related approach

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Pavlova, Olga N.; Abdurashitov, Arkady S.; Arinushkin, Pavel A.; Runnova, Anastasiya E.; Semyachkina-Glushkovskaya, Oxana V.

2017-04-01

In this paper we discuss an approach for mechanism-related analysis of physiological signals performed with the wavelet-based multifractal formalism. This approach assumes estimation of the singularity spectrum for the band-pass filtered processes at different physiological conditions in order to provide explanation of the occurred changes in the Hölder exponents and the multi-fractality degree. We illustrate the considered approach using two examples, namely, the dynamics of the cerebral blood flow (CBF) and the electrical activity of the brain.

Characterization of the Hydrocarbon Potential and Non-Potential Zones Using Wavelet-Based Fractal Analysis

NASA Astrophysics Data System (ADS)

Mukherjee, Bappa; Roy, P. N. S.

The identification of prospective and dry zone is of major importance from well log data. Truthfulness in the identification of potential zone is a very crucial issue in hydrocarbon exploration. In this line, the problem has received considerable attention and many conventional techniques have been proposed. The purpose of this study is to recognize the hydrocarbon and non-hydrocarbon bearing portion within a reservoir by using the non-conventional technique. The wavelet based fractal analysis (WBFA) has been applied on the wire-line log data in order to obtain the pre-defined hydrocarbon (HC) and non-hydrocarbon (NHC) zones by their self-affine signal nature is demonstrated in this paper. The feasibility of the proposed technique is tested with the help of most commonly used logs, like self-potential, gamma ray, resistivity and porosity log responses. These logs are obtained from the industry to make out several HC and NHC zones of all wells in the study region belonging to the upper Assam basin. The results obtained in this study for a particular log response, where in the case of HC bearing zones, it is found that they are mainly situated in a variety of sandstones lithology which leads to the higher Hurst exponent. Further, the NHC zones found to be analogous to lithology with higher shale content having lower Hurst exponent. The above proposed technique can overcome the chance of miss interpretation in conventional reservoir characterization.

Paradigms of Complexity: Fractals and Structures in the Sciences

NASA Astrophysics Data System (ADS)

Novak, Miroslav M.

The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic Dynamics of Elastic-Plastic Beams * The Riemann Non-Differentiable Function and Identities for the Gaussian Sums * Revealing the Multifractal Nature of Failure Sequence * The Fractal Nature of wood Revealed by Drying * Squaring the Circle: Diffusion Volume and Acoustic Behaviour of a Fractal Structure * Relationship Between Acupuncture Holographic Units and Fetus Development; Fractal Features of Two Acupuncture Holographic Unit Systems * The Fractal Properties of the Large-Scale Magnetic Fields on the Sun * Fractal Analysis of Tide Gauge Data * Author Index

Signal-Noise Identification of Magnetotelluric Signals Using Fractal-Entropy and Clustering Algorithm for Targeted De-Noising

NASA Astrophysics Data System (ADS)

Li, Jin; Zhang, Xian; Gong, Jinzhe; Tang, Jingtian; Ren, Zhengyong; Li, Guang; Deng, Yanli; Cai, Jin

A new technique is proposed for signal-noise identification and targeted de-noising of Magnetotelluric (MT) signals. This method is based on fractal-entropy and clustering algorithm, which automatically identifies signal sections corrupted by common interference (square, triangle and pulse waves), enabling targeted de-noising and preventing the loss of useful information in filtering. To implement the technique, four characteristic parameters — fractal box dimension (FBD), higuchi fractal dimension (HFD), fuzzy entropy (FuEn) and approximate entropy (ApEn) — are extracted from MT time-series. The fuzzy c-means (FCM) clustering technique is used to analyze the characteristic parameters and automatically distinguish signals with strong interference from the rest. The wavelet threshold (WT) de-noising method is used only to suppress the identified strong interference in selected signal sections. The technique is validated through signal samples with known interference, before being applied to a set of field measured MT/Audio Magnetotelluric (AMT) data. Compared with the conventional de-noising strategy that blindly applies the filter to the overall dataset, the proposed method can automatically identify and purposefully suppress the intermittent interference in the MT/AMT signal. The resulted apparent resistivity-phase curve is more continuous and smooth, and the slow-change trend in the low-frequency range is more precisely reserved. Moreover, the characteristic of the target-filtered MT/AMT signal is close to the essential characteristic of the natural field, and the result more accurately reflects the inherent electrical structure information of the measured site.

Visual communications and image processing '92; Proceedings of the Meeting, Boston, MA, Nov. 18-20, 1992

NASA Astrophysics Data System (ADS)

Maragos, Petros

The topics discussed at the conference include hierarchical image coding, motion analysis, feature extraction and image restoration, video coding, and morphological and related nonlinear filtering. Attention is also given to vector quantization, morphological image processing, fractals and wavelets, architectures for image and video processing, image segmentation, biomedical image processing, and model-based analysis. Papers are presented on affine models for motion and shape recovery, filters for directly detecting surface orientation in an image, tracking of unresolved targets in infrared imagery using a projection-based method, adaptive-neighborhood image processing, and regularized multichannel restoration of color images using cross-validation. (For individual items see A93-20945 to A93-20951)

Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu

2001-03-01

We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.

The wavelet transform as an analysis tool for structure identification in molecular clouds

NASA Astrophysics Data System (ADS)

Gill, Arnold Gerald

1993-01-01

Of the many methods used to attempt to understand the complex structure of giant molecular clouds, perhaps the most commonly used are the autocorrelation functions (ACF), the structure function, and the power spectrum. However, these do not give unique interpretations of structure, as is shown by explicit examples compared to the Taurus Molecular Complex. Thus, another, independent method of analysis is indicated. Here, the wavelet transform is presented, a relatively new technique less than 10 years old. It can be thought of as a band-pass filter that identifies structures of specific sizes. In addition, its mathematical properties allow it to be used to identify fractal structures and accurately identify the scaling exponent. This is shown by the wavelet transform identifying the fractal dimension of a hierarchical rain cloud model first proposed by Frisch et al. (1978). A wavelet analysis is then carried out for a range of astronomical CO data, including the clouds Orion A and B and NGC 7538 (in (12)CO) and Orion A and B, Mon R2, and L1551 (in (13)CO). The data analyzed consists of the velocities of the fitted Gaussians to the individual spectra, the halfwidths and amplitude of these Gaussians, and the total area of the spectral line. For most of the clouds investigated, each of these data types showed a very high degree of scaling coherence over a wide range of scales, from down at the beam spacing up to the full size of the cloud. The analysis carried out uses both the scaling and structure identification strengths of the wavelet transform The fragmentation parameters used by Scalo (1985) and the parameters of the geometric molecular cloud description introduced by Henriksen (1986) are calculated for each cloud. These results are all consistent with previous observations of these and other molecular clouds, though they are obtained individually for each cloud investigated. It is found that the uncertainties are of a magnitude that the differentiation of various theories of molecular cloud structure is not possible. It is noted that the effects of projection and superposition strongly affect the values of some of these parameters, thus hampering a thorough understanding of the underlying physics. The strengths and weaknesses of the wavelet transform in the analysis of molecular cloud data are presented, as well as directions for future work.

An accurate sleep stages classification system using a new class of optimally time-frequency localized three-band wavelet filter bank.

PubMed

Sharma, Manish; Goyal, Deepanshu; Achuth, P V; Acharya, U Rajendra

2018-07-01

Sleep related disorder causes diminished quality of lives in human beings. Sleep scoring or sleep staging is the process of classifying various sleep stages which helps to detect the quality of sleep. The identification of sleep-stages using electroencephalogram (EEG) signals is an arduous task. Just by looking at an EEG signal, one cannot determine the sleep stages precisely. Sleep specialists may make errors in identifying sleep stages by visual inspection. To mitigate the erroneous identification and to reduce the burden on doctors, a computer-aided EEG based system can be deployed in the hospitals, which can help identify the sleep stages, correctly. Several automated systems based on the analysis of polysomnographic (PSG) signals have been proposed. A few sleep stage scoring systems using EEG signals have also been proposed. But, still there is a need for a robust and accurate portable system developed using huge dataset. In this study, we have developed a new single-channel EEG based sleep-stages identification system using a novel set of wavelet-based features extracted from a large EEG dataset. We employed a novel three-band time-frequency localized (TBTFL) wavelet filter bank (FB). The EEG signals are decomposed using three-level wavelet decomposition, yielding seven sub-bands (SBs). This is followed by the computation of discriminating features namely, log-energy (LE), signal-fractal-dimensions (SFD), and signal-sample-entropy (SSE) from all seven SBs. The extracted features are ranked and fed to the support vector machine (SVM) and other supervised learning classifiers. In this study, we have considered five different classification problems (CPs), (two-class (CP-1), three-class (CP-2), four-class (CP-3), five-class (CP-4) and six-class (CP-5)). The proposed system yielded accuracies of 98.3%, 93.9%, 92.1%, 91.7%, and 91.5% for CP-1 to CP-5, respectively, using 10-fold cross validation (CV) technique. Copyright © 2018 Elsevier Ltd. All rights reserved.

Analyzing gene expression time-courses based on multi-resolution shape mixture model.

PubMed

Li, Ying; He, Ye; Zhang, Yu

2016-11-01

Biological processes actually are a dynamic molecular process over time. Time course gene expression experiments provide opportunities to explore patterns of gene expression change over a time and understand the dynamic behavior of gene expression, which is crucial for study on development and progression of biology and disease. Analysis of the gene expression time-course profiles has not been fully exploited so far. It is still a challenge problem. We propose a novel shape-based mixture model clustering method for gene expression time-course profiles to explore the significant gene groups. Based on multi-resolution fractal features and mixture clustering model, we proposed a multi-resolution shape mixture model algorithm. Multi-resolution fractal features is computed by wavelet decomposition, which explore patterns of change over time of gene expression at different resolution. Our proposed multi-resolution shape mixture model algorithm is a probabilistic framework which offers a more natural and robust way of clustering time-course gene expression. We assessed the performance of our proposed algorithm using yeast time-course gene expression profiles compared with several popular clustering methods for gene expression profiles. The grouped genes identified by different methods are evaluated by enrichment analysis of biological pathways and known protein-protein interactions from experiment evidence. The grouped genes identified by our proposed algorithm have more strong biological significance. A novel multi-resolution shape mixture model algorithm based on multi-resolution fractal features is proposed. Our proposed model provides a novel horizons and an alternative tool for visualization and analysis of time-course gene expression profiles. The R and Matlab program is available upon the request. Copyright © 2016 Elsevier Inc. All rights reserved.

Détection des transitions lithologiques par l'analyse de la composante fractale des diagraphies par transformée continue en ondelettes

NASA Astrophysics Data System (ADS)

Zaourar, Naima; Hamoudi, Mohamed; Briqueu, Louis

2006-06-01

The frequency analysis of many log data permits to verify that their stochastic component show 'power-law-type' spectral densities, characteristic of 1/f noise. They can be modelled by fractional Brownian motions. Continuous Wavelet Transformation (CWT) provides us with very efficient methods to determine the local spectral exponents of these scaling laws. These new attributes are related to the local fractality of these signals. We first present some theoretical results and an application to a fractional Brownian motion. The second application concerns a dataset recorded in the MAR203 borehole. We show that clustering of these new pseudo-logs leads to a good resolution between different lithofacies. To cite this article: N. Zaourar et al., C. R. Geoscience 338 (2006).

Optimizing Complexity Measures for fMRI Data: Algorithm, Artifact, and Sensitivity

PubMed Central

Rubin, Denis; Fekete, Tomer; Mujica-Parodi, Lilianne R.

2013-01-01

Introduction Complexity in the brain has been well-documented at both neuronal and hemodynamic scales, with increasing evidence supporting its use in sensitively differentiating between mental states and disorders. However, application of complexity measures to fMRI time-series, which are short, sparse, and have low signal/noise, requires careful modality-specific optimization. Methods Here we use both simulated and real data to address two fundamental issues: choice of algorithm and degree/type of signal processing. Methods were evaluated with regard to resilience to acquisition artifacts common to fMRI as well as detection sensitivity. Detection sensitivity was quantified in terms of grey-white matter contrast and overlap with activation. We additionally investigated the variation of complexity with activation and emotional content, optimal task length, and the degree to which results scaled with scanner using the same paradigm with two 3T magnets made by different manufacturers. Methods for evaluating complexity were: power spectrum, structure function, wavelet decomposition, second derivative, rescaled range, Higuchi’s estimate of fractal dimension, aggregated variance, and detrended fluctuation analysis. To permit direct comparison across methods, all results were normalized to Hurst exponents. Results Power-spectrum, Higuchi’s fractal dimension, and generalized Hurst exponent based estimates were most successful by all criteria; the poorest-performing measures were wavelet, detrended fluctuation analysis, aggregated variance, and rescaled range. Conclusions Functional MRI data have artifacts that interact with complexity calculations in nontrivially distinct ways compared to other physiological data (such as EKG, EEG) for which these measures are typically used. Our results clearly demonstrate that decisions regarding choice of algorithm, signal processing, time-series length, and scanner have a significant impact on the reliability and sensitivity of complexity estimates. PMID:23700424

Segmentation of time series with long-range fractal correlations.

PubMed

Bernaola-Galván, P; Oliver, J L; Hackenberg, M; Coronado, A V; Ivanov, P Ch; Carpena, P

2012-06-01

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

Emotion Recognition from EEG Signals Using Multidimensional Information in EMD Domain.

PubMed

Zhuang, Ning; Zeng, Ying; Tong, Li; Zhang, Chi; Zhang, Hanming; Yan, Bin

2017-01-01

This paper introduces a method for feature extraction and emotion recognition based on empirical mode decomposition (EMD). By using EMD, EEG signals are decomposed into Intrinsic Mode Functions (IMFs) automatically. Multidimensional information of IMF is utilized as features, the first difference of time series, the first difference of phase, and the normalized energy. The performance of the proposed method is verified on a publicly available emotional database. The results show that the three features are effective for emotion recognition. The role of each IMF is inquired and we find that high frequency component IMF1 has significant effect on different emotional states detection. The informative electrodes based on EMD strategy are analyzed. In addition, the classification accuracy of the proposed method is compared with several classical techniques, including fractal dimension (FD), sample entropy, differential entropy, and discrete wavelet transform (DWT). Experiment results on DEAP datasets demonstrate that our method can improve emotion recognition performance.

Segmentation of time series with long-range fractal correlations

PubMed Central

Bernaola-Galván, P.; Oliver, J.L.; Hackenberg, M.; Coronado, A.V.; Ivanov, P.Ch.; Carpena, P.

2012-01-01

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome. PMID:23645997

Long-Range Temporal Correlations, Multifractality, and the Causal Relation between Neural Inputs and Movements

PubMed Central

Hu, Jing; Zheng, Yi; Gao, Jianbo

2013-01-01

Understanding the causal relation between neural inputs and movements is very important for the success of brain-machine interfaces (BMIs). In this study, we analyze 104 neurons’ firings using statistical, information theoretic, and fractal analysis. The latter include Fano factor analysis, multifractal adaptive fractal analysis (MF-AFA), and wavelet multifractal analysis. We find neuronal firings are highly non-stationary, and Fano factor analysis always indicates long-range correlations in neuronal firings, irrespective of whether those firings are correlated with movement trajectory or not, and thus does not reveal any actual correlations between neural inputs and movements. On the other hand, MF-AFA and wavelet multifractal analysis clearly indicate that when neuronal firings are not well correlated with movement trajectory, they do not have or only have weak temporal correlations. When neuronal firings are well correlated with movements, they are characterized by very strong temporal correlations, up to a time scale comparable to the average time between two successive reaching tasks. This suggests that neurons well correlated with hand trajectory experienced a “re-setting” effect at the start of each reaching task, in the sense that within the movement correlated neurons the spike trains’ long-range dependences persisted about the length of time the monkey used to switch between task executions. A new task execution re-sets their activity, making them only weakly correlated with their prior activities on longer time scales. We further discuss the significance of the coalition of those important neurons in executing cortical control of prostheses. PMID:24130549

Multi-scale variability and long-range memory in indoor Radon concentrations from Coimbra, Portugal

NASA Astrophysics Data System (ADS)

Donner, Reik V.; Potirakis, Stelios; Barbosa, Susana

2014-05-01

The presence or absence of long-range correlations in the variations of indoor Radon concentrations has recently attracted considerable interest. As a radioactive gas naturally emitted from the ground in certain geological settings, understanding environmental factors controlling Radon concentrations and their dynamics is important for estimating its effect on human health and the efficiency of possible measures for reducing the corresponding exposition. In this work, we re-analyze two high-resolution records of indoor Radon concentrations from Coimbra, Portugal, each of which spans several months of continuous measurements. In order to evaluate the presence of long-range correlations and fractal scaling, we utilize a multiplicity of complementary methods, including power spectral analysis, ARFIMA modeling, classical and multi-fractal detrended fluctuation analysis, and two different estimators of the signals' fractal dimensions. Power spectra and fluctuation functions reveal some complex behavior with qualitatively different properties on different time-scales: white noise in the high-frequency part, indications of some long-range correlated process dominating time scales of several hours to days, and pronounced low-frequency variability associated with tidal and/or meteorological forcing. In order to further decompose these different scales of variability, we apply two different approaches. On the one hand, applying multi-resolution analysis based on the discrete wavelet transform allows separately studying contributions on different time scales and characterize their specific correlation and scaling properties. On the other hand, singular system analysis (SSA) provides a reconstruction of the essential modes of variability. Specifically, by considering only the first leading SSA modes, we achieve an efficient de-noising of our environmental signals, highlighting the low-frequency variations together with some distinct scaling on sub-daily time-scales resembling the properties of a long-range correlated process.

Scaling analysis and model estimation of solar corona index

NASA Astrophysics Data System (ADS)

Ray, Samujjwal; Ray, Rajdeep; Khondekar, Mofazzal Hossain; Ghosh, Koushik

2018-04-01

A monthly average solar green coronal index time series for the period from January 1939 to December 2008 collected from NOAA (The National Oceanic and Atmospheric Administration) has been analysed in this paper in perspective of scaling analysis and modelling. Smoothed and de-noising have been done using suitable mother wavelet as a pre-requisite. The Finite Variance Scaling Method (FVSM), Higuchi method, rescaled range (R/S) and a generalized method have been applied to calculate the scaling exponents and fractal dimensions of the time series. Autocorrelation function (ACF) is used to find autoregressive (AR) process and Partial autocorrelation function (PACF) has been used to get the order of AR model. Finally a best fit model has been proposed using Yule-Walker Method with supporting results of goodness of fit and wavelet spectrum. The results reveal an anti-persistent, Short Range Dependent (SRD), self-similar property with signatures of non-causality, non-stationarity and nonlinearity in the data series. The model shows the best fit to the data under observation.

Wavelet versus detrended fluctuation analysis of multifractal structures

NASA Astrophysics Data System (ADS)

Oświȩcimka, Paweł; Kwapień, Jarosław; Drożdż, Stanisław

2006-07-01

We perform a comparative study of applicability of the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maxima (WTMM) method in proper detecting of monofractal and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Lévy flights, and different sorts of multifractal binomial cascades. Our results show that in the majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended. In particular, WTMM gives biased outcomes for the fractional Brownian motion with different values of Hurst exponent, indicating spurious multifractality. In some cases WTMM can also give different results if one applies different wavelets. We do not exclude using WTMM in real data analysis, but it occurs that while one may apply MFDFA in a more automatic fashion, WTMM must be applied with care. In the second part of our work, we perform an analogous analysis on empirical data coming from the American and from the German stock market. For this data both methods detect rich multifractality in terms of broad f(α) , but MFDFA suggests that this multifractality is poorer than in the case of WTMM.

Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series

NASA Astrophysics Data System (ADS)

Ghosh, Sayantan; Manimaran, P.; Panigrahi, Prasanta K.

2011-11-01

We make use of wavelet transform to study the multi-scale, self-similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scales. The fact that, the wavelets belonging to the Daubechies’ (Db) basis enables one to isolate local polynomial trends of different degrees, plays the key role in isolating fluctuations at different scales. One of the primary motivations of this work is to study the emergence of the k-3 behavior [X. Gabaix, P. Gopikrishnan, V. Plerou, H. Stanley, A theory of power law distributions in financial market fluctuations, Nature 423 (2003) 267-270] of the fluctuations starting with high frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series. The fluctuations reveal fat tail non-Gaussian behavior, unstable periodic modulations, at finer scales, from which the characteristic k-3 power law behavior emerges at sufficiently large scales. We further identify stable periodic behavior through the continuous Morlet wavelet.

Variability of Decimetre and Centimetre Scale Ice Surface Roughness and the Potential Consequences on the CryoSat Radar Altimeter Signal

NASA Astrophysics Data System (ADS)

Cawkwell, F. G.; Burgess, D. O.; Sharp, M. J.; Demuth, M.

2004-12-01

Snow and ice surface roughness affect the backscatter of the pulse emitted by a radar altimeter, and hence the accuracy of the surface elevation calculated from the waveform echo, but the influence of surface roughness has not been quantified. As part of the CryoSat calibration/validation field campaigns on the Devon Ice Cap in 2004, surface roughness measurements were made at 0.1-7km intervals along a 48km transect from near the summit to the southern margin. Measurements were made at the decimetre scale by surveying and at the centimetre scale using digital photography. The data collected were subjected to wavelet analysis to define characteristic roughness wavelengths, and the fractal dimension associated with each of these was calculated using the semi-variogram method. Vario functions were calculated for the photographic data. The survey results show that wavelength scales depend on orientation and distance from the ice cap summit, the fractal dimension depends on the wavelength scale and the orientation, and both are significantly affected by storm events. Profiles aligned with the easterly prevailing wind direction, and thus perpendicular to the predicted satellite track, proved to be more sensitive to meteorological events than those normal to the dominant winds. Wavelet and fractal analysis of the photographic data was less conclusive, potentially due to the `noisier' nature of the data at this scale, where `noise' is actually the superimposition of small scale wavelengths onto larger ones. Vario analysis showed the characteristic wavelengths at the centimetre scale to increase with distance from the summit, although the abrading effect of storm events caused a decrease in wavelength. The amplitude of the roughness also increases with distance from the summit, although following a period of calm this value is significantly decreased along the transect. Orientation with respect to the prevailing wind direction is also a significant factor. Analysis of the return waveforms acquired by an airborne radar altimeter concurrently with ground data will allow the impact of the different roughness scales and orientations to be assessed.

Mustiscaling Analysis applied to field Water Content through Distributed Fiber Optic Temperature sensing measurements

NASA Astrophysics Data System (ADS)

Benitez Buelga, Javier; Rodriguez-Sinobas, Leonor; Sanchez, Raul; Gil, Maria; Tarquis, Ana M.

2014-05-01

Soils can be seen as the result of spatial variation operating over several scales. This observation points to 'variability' as a key soil attribute that should be studied. Soil variability has often been considered to be composed of 'functional' (explained) variations plus random fluctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise. Geostatistical methods and, more recently, multifractal/wavelet techniques have been used to characterize scaling and heterogeneity of soil properties among others coming from complexity science. Multifractal formalism, first proposed by Mandelbrot (1982), is suitable for variables with self-similar distribution on a spatial domain (Kravchenko et al., 2002). Multifractal analysis can provide insight into spatial variability of crop or soil parameters (Vereecken et al., 2007). This technique has been used to characterize the scaling property of a variable measured along a transect as a mass distribution of a statistical measure on a spatial domain of the studied field (Zeleke and Si, 2004). To do this, it divides the transect into a number of self-similar segments. It identifies the differences among the subsets by using a wide range of statistical moments. Wavelets were developed in the 1980s for signal processing, and later introduced to soil science by Lark and Webster (1999). The wavelet transform decomposes a series; whether this be a time series (Whitcher, 1998; Percival and Walden, 2000), or as in our case a series of measurements made along a transect; into components (wavelet coefficients) which describe local variation in the series at different scale (or frequency) intervals, giving up only some resolution in space (Lark et al., 2003, 2004). Wavelet coefficients can be used to estimate scale specific components of variation and correlation. This allows us to see which scales contribute most to signal variation, or to see at which scales signals are most correlated. This can give us an insight into the dominant processes An alternative to both of the above methods has been described recently. Relative entropy and increments in relative entropy has been applied in soil images (Bird et al., 2006) and in soil transect data (Tarquis et al., 2008) to study scale effects localized in scale and provide the information that is complementary to the information about scale dependencies found across a range of scales. We will use them in this work to describe the spatial scaling properties of a set of field water content data measured in an extension of a corn field, in a plot of 500 m2 and an spatial resolution of 25 cm. These measurements are based on an optics cable (BruggSteal) buried on a ziz-zag deployment at 30cm depth. References Bird, N., M.C. Díaz, A. Saa, and A.M. Tarquis. 2006. A review of fractal and multifractal analysis of soil pore-scale images. J. Hydrol. 322:211-219. Kravchenko, A.N., R. Omonode, G.A. Bollero, and D.G. Bullock. 2002. Quantitative mapping of soil drainage classes using topographical data and soil electrical conductivity. Soil Sci. Soc. Am. J. 66:235-243. Lark, R.M., A.E. Milne, T.M. Addiscott, K.W.T. Goulding, C.P. Webster, and S. O'Flaherty. 2004. Scale- and location-dependent correlation of nitrous oxide emissions with soil properties: An analysis using wavelets. Eur. J. Soil Sci. 55:611-627. Lark, R.M., S.R. Kaffka, and D.L. Corwin. 2003. Multiresolution analysis of data on electrical conductivity of soil using wavelets. J. Hydrol. 272:276-290. Lark, R. M. and Webster, R. 1999. Analysis and elucidation of soil variation using wavelets. European J. of Soil Science, 50(2): 185-206. Mandelbrot, B.B. 1982. The fractal geometry of nature. W.H. Freeman, New York. Percival, D.B., and A.T. Walden. 2000. Wavelet methods for time series analysis. Cambridge Univ. Press, Cambridge, UK. Tarquis, A.M., N.R. Bird, A.P. Whitmore, M.C. Cartagena, and Y. Pachepsky. 2008. Multiscale analysis of soil transect data. Vadose Zone J. 7: 563-569. Vereecken, H., R. Kasteel, J. Vanderborght, and T. Harter. 2007. Upscaling hydraulic properties and soil water flow processes in heterogeneous soils: A review. Vadose Zone J. 6:1-28. Whitcher, B.J. 1998. Assessing nonstationary time series using wavelets. Ph.D. diss. Univ. of Washington, Seattle (Diss. Abstr. 9907961). Zeleke, T.B., and B.C. Si. 2004. Scaling properties of topographic indices and crop yield: Multifractal and joint multifractal approaches. Agron J., 96:1082-1090.

Crack orientation and depth estimation in a low-pressure turbine disc using a phased array ultrasonic transducer and an artificial neural network.

PubMed

Yang, Xiaoxia; Chen, Shili; Jin, Shijiu; Chang, Wenshuang

2013-09-13

Stress corrosion cracks (SCC) in low-pressure steam turbine discs are serious hidden dangers to production safety in the power plants, and knowing the orientation and depth of the initial cracks is essential for the evaluation of the crack growth rate, propagation direction and working life of the turbine disc. In this paper, a method based on phased array ultrasonic transducer and artificial neural network (ANN), is proposed to estimate both the depth and orientation of initial cracks in the turbine discs. Echo signals from cracks with different depths and orientations were collected by a phased array ultrasonic transducer, and the feature vectors were extracted by wavelet packet, fractal technology and peak amplitude methods. The radial basis function (RBF) neural network was investigated and used in this application. The final results demonstrated that the method presented was efficient in crack estimation tasks.

Crack Orientation and Depth Estimation in a Low-Pressure Turbine Disc Using a Phased Array Ultrasonic Transducer and an Artificial Neural Network

PubMed Central

Yang, Xiaoxia; Chen, Shili; Jin, Shijiu; Chang, Wenshuang

2013-01-01

Stress corrosion cracks (SCC) in low-pressure steam turbine discs are serious hidden dangers to production safety in the power plants, and knowing the orientation and depth of the initial cracks is essential for the evaluation of the crack growth rate, propagation direction and working life of the turbine disc. In this paper, a method based on phased array ultrasonic transducer and artificial neural network (ANN), is proposed to estimate both the depth and orientation of initial cracks in the turbine discs. Echo signals from cracks with different depths and orientations were collected by a phased array ultrasonic transducer, and the feature vectors were extracted by wavelet packet, fractal technology and peak amplitude methods. The radial basis function (RBF) neural network was investigated and used in this application. The final results demonstrated that the method presented was efficient in crack estimation tasks. PMID:24064602

Scale invariant texture descriptors for classifying celiac disease

PubMed Central

Hegenbart, Sebastian; Uhl, Andreas; Vécsei, Andreas; Wimmer, Georg

2013-01-01

Scale invariant texture recognition methods are applied for the computer assisted diagnosis of celiac disease. In particular, emphasis is given to techniques enhancing the scale invariance of multi-scale and multi-orientation wavelet transforms and methods based on fractal analysis. After fine-tuning to specific properties of our celiac disease imagery database, which consists of endoscopic images of the duodenum, some scale invariant (and often even viewpoint invariant) methods provide classification results improving the current state of the art. However, not each of the investigated scale invariant methods is applicable successfully to our dataset. Therefore, the scale invariance of the employed approaches is explicitly assessed and it is found that many of the analyzed methods are not as scale invariant as they theoretically should be. Results imply that scale invariance is not a key-feature required for successful classification of our celiac disease dataset. PMID:23481171

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

NASA Astrophysics Data System (ADS)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Fusion of High Resolution Multispectral Imagery in Vulnerable Coastal and Land Ecosystems.

PubMed

Ibarrola-Ulzurrun, Edurne; Gonzalo-Martin, Consuelo; Marcello-Ruiz, Javier; Garcia-Pedrero, Angel; Rodriguez-Esparragon, Dionisio

2017-01-25

Ecosystems provide a wide variety of useful resources that enhance human welfare, but these resources are declining due to climate change and anthropogenic pressure. In this work, three vulnerable ecosystems, including shrublands, coastal areas with dunes systems and areas of shallow water, are studied. As far as these resources' reduction is concerned, remote sensing and image processing techniques could contribute to the management of these natural resources in a practical and cost-effective way, although some improvements are needed for obtaining a higher quality of the information available. An important quality improvement is the fusion at the pixel level. Hence, the objective of this work is to assess which pansharpening technique provides the best fused image for the different types of ecosystems. After a preliminary evaluation of twelve classic and novel fusion algorithms, a total of four pansharpening algorithms was analyzed using six quality indices. The quality assessment was implemented not only for the whole set of multispectral bands, but also for the subset of spectral bands covered by the wavelength range of the panchromatic image and outside of it. A better quality result is observed in the fused image using only the bands covered by the panchromatic band range. It is important to highlight the use of these techniques not only in land and urban areas, but a novel analysis in areas of shallow water ecosystems. Although the algorithms do not show a high difference in land and coastal areas, coastal ecosystems require simpler algorithms, such as fast intensity hue saturation, whereas more heterogeneous ecosystems need advanced algorithms, as weighted wavelet ' à trous ' through fractal dimension maps for shrublands and mixed ecosystems. Moreover, quality map analysis was carried out in order to study the fusion result in each band at the local level. Finally, to demonstrate the performance of these pansharpening techniques, advanced Object-Based (OBIA) support vector machine classification was applied, and a thematic map for the shrubland ecosystem was obtained, which corroborates wavelet ' à trous ' through fractal dimension maps as the best fusion algorithm for this ecosystem.

Fusion of High Resolution Multispectral Imagery in Vulnerable Coastal and Land Ecosystems

PubMed Central

Ibarrola-Ulzurrun, Edurne; Gonzalo-Martin, Consuelo; Marcello-Ruiz, Javier; Garcia-Pedrero, Angel; Rodriguez-Esparragon, Dionisio

2017-01-01

Ecosystems provide a wide variety of useful resources that enhance human welfare, but these resources are declining due to climate change and anthropogenic pressure. In this work, three vulnerable ecosystems, including shrublands, coastal areas with dunes systems and areas of shallow water, are studied. As far as these resources’ reduction is concerned, remote sensing and image processing techniques could contribute to the management of these natural resources in a practical and cost-effective way, although some improvements are needed for obtaining a higher quality of the information available. An important quality improvement is the fusion at the pixel level. Hence, the objective of this work is to assess which pansharpening technique provides the best fused image for the different types of ecosystems. After a preliminary evaluation of twelve classic and novel fusion algorithms, a total of four pansharpening algorithms was analyzed using six quality indices. The quality assessment was implemented not only for the whole set of multispectral bands, but also for the subset of spectral bands covered by the wavelength range of the panchromatic image and outside of it. A better quality result is observed in the fused image using only the bands covered by the panchromatic band range. It is important to highlight the use of these techniques not only in land and urban areas, but a novel analysis in areas of shallow water ecosystems. Although the algorithms do not show a high difference in land and coastal areas, coastal ecosystems require simpler algorithms, such as fast intensity hue saturation, whereas more heterogeneous ecosystems need advanced algorithms, as weighted wavelet ‘à trous’ through fractal dimension maps for shrublands and mixed ecosystems. Moreover, quality map analysis was carried out in order to study the fusion result in each band at the local level. Finally, to demonstrate the performance of these pansharpening techniques, advanced Object-Based (OBIA) support vector machine classification was applied, and a thematic map for the shrubland ecosystem was obtained, which corroborates wavelet ‘à trous’ through fractal dimension maps as the best fusion algorithm for this ecosystem. PMID:28125055

Assessment of features for automatic CTG analysis based on expert annotation.

PubMed

Chudácek, Vacláv; Spilka, Jirí; Lhotská, Lenka; Janku, Petr; Koucký, Michal; Huptych, Michal; Bursa, Miroslav

2011-01-01

Cardiotocography (CTG) is the monitoring of fetal heart rate (FHR) and uterine contractions (TOCO) since 1960's used routinely by obstetricians to detect fetal hypoxia. The evaluation of the FHR in clinical settings is based on an evaluation of macroscopic morphological features and so far has managed to avoid adopting any achievements from the HRV research field. In this work, most of the ever-used features utilized for FHR characterization, including FIGO, HRV, nonlinear, wavelet, and time and frequency domain features, are investigated and the features are assessed based on their statistical significance in the task of distinguishing the FHR into three FIGO classes. Annotation derived from the panel of experts instead of the commonly utilized pH values was used for evaluation of the features on a large data set (552 records). We conclude the paper by presenting the best uncorrelated features and their individual rank of importance according to the meta-analysis of three different ranking methods. Number of acceleration and deceleration, interval index, as well as Lempel-Ziv complexity and Higuchi's fractal dimension are among the top five features.

Dynamical complexity detection in geomagnetic activity indices using wavelet transforms and Tsallis entropy

NASA Astrophysics Data System (ADS)

Balasis, G.; Daglis, I. A.; Papadimitriou, C.; Kalimeri, M.; Anastasiadis, A.; Eftaxias, K.

2008-12-01

Dynamical complexity detection for output time series of complex systems is one of the foremost problems in physics, biology, engineering, and economic sciences. Especially in magnetospheric physics, accurate detection of the dissimilarity between normal and abnormal states (e.g. pre-storm activity and magnetic storms) can vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. Herein, we examine the fractal spectral properties of the Dst data using a wavelet analysis technique. We show that distinct changes in associated scaling parameters occur (i.e., transition from anti- persistent to persistent behavior) as an intense magnetic storm approaches. We then analyze Dst time series by introducing the non-extensive Tsallis entropy, Sq, as an appropriate complexity measure. The Tsallis entropy sensitively shows the complexity dissimilarity among different "physiological" (normal) and "pathological" states (intense magnetic storms). The Tsallis entropy implies the emergence of two distinct patterns: (i) a pattern associated with the intense magnetic storms, which is characterized by a higher degree of organization, and (ii) a pattern associated with normal periods, which is characterized by a lower degree of organization.

Enhancing seismic P phase arrival picking based on wavelet denoising and kurtosis picker

NASA Astrophysics Data System (ADS)

Shang, Xueyi; Li, Xibing; Weng, Lei

2018-01-01

P phase arrival picking of weak signals is still challenging in seismology. A wavelet denoising is proposed to enhance seismic P phase arrival picking, and the kurtosis picker is applied on the wavelet-denoised signal to identify P phase arrival. It has been called the WD-K picker. The WD-K picker, which is different from those traditional wavelet-based pickers on the basis of a single wavelet component or certain main wavelet components, takes full advantage of the reconstruction of main detail wavelet components and the approximate wavelet component. The proposed WD-K picker considers more wavelet components and presents a better P phase arrival feature. The WD-K picker has been evaluated on 500 micro-seismic signals recorded in the Chinese Yongshaba mine. The comparison between the WD-K pickings and manual pickings shows the good picking accuracy of the WD-K picker. Furthermore, the WD-K picking performance has been compared with the main detail wavelet component combining-based kurtosis (WDC-K) picker, the single wavelet component-based kurtosis (SW-K) picker, and certain main wavelet component-based maximum kurtosis (MMW-K) picker. The comparison has demonstrated that the WD-K picker has better picking accuracy than the other three-wavelet and kurtosis-based pickers, thus showing the enhanced ability of wavelet denoising.

Scaling properties and symmetrical patterns in the epidemiology of rotavirus infection.

PubMed Central

José, Marco V; Bishop, Ruth F

2003-01-01

The rich epidemiological database of the incidence of rotavirus, as a cause of severe diarrhoea in young children, coupled with knowledge of the natural history of the infection, can make this virus a paradigm for studies of epidemic dynamics. The cyclic recurrence of childhood rotavirus epidemics in unvaccinated populations provides one of the best documented phenomena in population dynamics. This paper makes use of epidemiological data on rotavirus infection in young children admitted to hospital in Melbourne, Australia from 1977 to 2000. Several mathematical methods were used to characterize the overall dynamics of rotavirus infections as a whole and individually as serotypes G1, G2, G3, G4 and G9. These mathematical methods are as follows: seasonal autoregressive integrated moving-average (SARIMA) models, power spectral density (PSD), higher-order spectral analysis (HOSA) (bispectrum estimation and quadratic phase coupling (QPC)), detrended fluctuation analysis (DFA), wavelet analysis (WA) and a surrogate data analysis technique. Each of these techniques revealed different dynamic aspects of rotavirus epidemiology. In particular, we confirm the existence of an annual, biannual and a quinquennial period but additionally we found other embedded cycles (e.g. ca. 3 years). There seems to be an overall unique geometric and dynamic structure of the data despite the apparent changes in the dynamics of the last years. The inherent dynamics seems to be conserved regardless of the emergence of new serotypes, the re-emergence of old serotypes or the transient disappearance of a particular serotype. More importantly, the dynamics of all serotypes is multiple synchronized so that they behave as a single entity at the epidemic level. Overall, the whole dynamics follow a scale-free power-law fractal scaling behaviour. We found that there are three different scaling regions in the time-series, suggesting that processes influencing the epidemic dynamics of rotavirus over less than 12 months differ from those that operate between 1 and ca. 3 years, as well as those between 3 and ca. 5 years. To discard the possibility that the observed patterns could be due to artefacts, we applied a surrogate data analysis technique which enabled us to discern if only random components or linear features of the incidence of rotavirus contribute to its dynamics. The global dynamics of the epidemic is portrayed by wavelet-based incidence analysis. The resulting wavelet transform of the incidence of rotavirus crisply reveals a repeating pattern over time that looks similar on many scales (a property called self-similarity). Both the self-similar behaviour and the absence of a single characteristic scale of the power-law fractal-like scaling of the incidence of rotavirus infection imply that there is not a universal inherently more virulent serotype to which severe gastroenteritis can uniquely be ascribed. PMID:14561323

Automatic lithofacies segmentation from well-logs data. A comparative study between the Self-Organizing Map (SOM) and Walsh transform

NASA Astrophysics Data System (ADS)

Aliouane, Leila; Ouadfeul, Sid-Ali; Rabhi, Abdessalem; Rouina, Fouzi; Benaissa, Zahia; Boudella, Amar

2013-04-01

The main goal of this work is to realize a comparison between two lithofacies segmentation techniques of reservoir interval. The first one is based on the Kohonen's Self-Organizing Map neural network machine. The second technique is based on the Walsh transform decomposition. Application to real well-logs data of two boreholes located in the Algerian Sahara shows that the Self-organizing map is able to provide more lithological details that the obtained lithofacies model given by the Walsh decomposition. Keywords: Comparison, Lithofacies, SOM, Walsh References: 1)Aliouane, L., Ouadfeul, S., Boudella, A., 2011, Fractal analysis based on the continuous wavelet transform and lithofacies classification from well-logs data using the self-organizing map neural network, Arabian Journal of geosciences, doi: 10.1007/s12517-011-0459-4 2) Aliouane, L., Ouadfeul, S., Djarfour, N., Boudella, A., 2012, Petrophysical Parameters Estimation from Well-Logs Data Using Multilayer Perceptron and Radial Basis Function Neural Networks, Lecture Notes in Computer Science Volume 7667, 2012, pp 730-736, doi : 10.1007/978-3-642-34500-5_86 3)Ouadfeul, S. and Aliouane., L., 2011, Multifractal analysis revisited by the continuous wavelet transform applied in lithofacies segmentation from well-logs data, International journal of applied physics and mathematics, Vol01 N01. 4) Ouadfeul, S., Aliouane, L., 2012, Lithofacies Classification Using the Multilayer Perceptron and the Self-organizing Neural Networks, Lecture Notes in Computer Science Volume 7667, 2012, pp 737-744, doi : 10.1007/978-3-642-34500-5_87 5) Weisstein, Eric W. "Fast Walsh Transform." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FastWalshTransform.html

Segmentation of singularity maps in the context of soil porosity

NASA Astrophysics Data System (ADS)

Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

2016-04-01

Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in porphyry Cu deposits by fractal concentration-volume modeling. Journal of Geochemical Exploration, 108, 220-232. Martín-Sotoca, J. J., Tarquis, A. M., Saa-Requejo, A. and Grau, J. B. (2015). Pore detection in Computed Tomography (CT) soil images through singularity map analysis. Oral Presentation in PedoFract VIII Congress (June, La Coruña - Spain).

Automatic evaluation of intrapartum fetal heart rate recordings: a comprehensive analysis of useful features.

PubMed

Chudáček, V; Spilka, J; Janků, P; Koucký, M; Lhotská, L; Huptych, M

2011-08-01

Cardiotocography is the monitoring of fetal heart rate (FHR) and uterine contractions (TOCO), used routinely since the 1960s by obstetricians to detect fetal hypoxia. The evaluation of the FHR in clinical settings is based on an evaluation of macroscopic morphological features and so far has managed to avoid adopting any achievements from the HRV research field. In this work, most of the features utilized for FHR characterization, including FIGO, HRV, nonlinear, wavelet, and time and frequency domain features, are investigated and assessed based on their statistical significance in the task of distinguishing the FHR into three FIGO classes. We assess the features on a large data set (552 records) and unlike in other published papers we use three-class expert evaluation of the records instead of the pH values. We conclude the paper by presenting the best uncorrelated features and their individual rank of importance according to the meta-analysis of three different ranking methods. The number of accelerations and decelerations, interval index, as well as Lempel-Ziv complexity and Higuchi's fractal dimension are among the top five features.

High-performance wavelet engine

NASA Astrophysics Data System (ADS)

Taylor, Fred J.; Mellot, Jonathon D.; Strom, Erik; Koren, Iztok; Lewis, Michael P.

1993-11-01

Wavelet processing has shown great promise for a variety of image and signal processing applications. Wavelets are also among the most computationally expensive techniques in signal processing. It is demonstrated that a wavelet engine constructed with residue number system arithmetic elements offers significant advantages over commercially available wavelet accelerators based upon conventional arithmetic elements. Analysis is presented predicting the dynamic range requirements of the reported residue number system based wavelet accelerator.

Dependence and risk assessment for oil prices and exchange rate portfolios: A wavelet based approach

NASA Astrophysics Data System (ADS)

Aloui, Chaker; Jammazi, Rania

2015-10-01

In this article, we propose a wavelet-based approach to accommodate the stylized facts and complex structure of financial data, caused by frequent and abrupt changes of markets and noises. Specifically, we show how the combination of both continuous and discrete wavelet transforms with traditional financial models helps improve portfolio's market risk assessment. In the empirical stage, three wavelet-based models (wavelet-EGARCH with dynamic conditional correlations, wavelet-copula, and wavelet-extreme value) are considered and applied to crude oil price and US dollar exchange rate data. Our findings show that the wavelet-based approach provides an effective and powerful tool for detecting extreme moments and improving the accuracy of VaR and Expected Shortfall estimates of oil-exchange rate portfolios after noise is removed from the original data.

Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets

NASA Astrophysics Data System (ADS)

Cifter, Atilla

2011-06-01

This paper introduces wavelet-based extreme value theory (EVT) for univariate value-at-risk estimation. Wavelets and EVT are combined for volatility forecasting to estimate a hybrid model. In the first stage, wavelets are used as a threshold in generalized Pareto distribution, and in the second stage, EVT is applied with a wavelet-based threshold. This new model is applied to two major emerging stock markets: the Istanbul Stock Exchange (ISE) and the Budapest Stock Exchange (BUX). The relative performance of wavelet-based EVT is benchmarked against the Riskmetrics-EWMA, ARMA-GARCH, generalized Pareto distribution, and conditional generalized Pareto distribution models. The empirical results show that the wavelet-based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail-loss tests. The superior forecasting performance of the wavelet-based EVT model is also consistent with Basel II requirements, and this new model can be used by financial institutions as well.

Wavelet based free-form deformations for nonrigid registration

NASA Astrophysics Data System (ADS)

Sun, Wei; Niessen, Wiro J.; Klein, Stefan

2014-03-01

In nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have been proposed as a signal representation suitable for multi-scale problems. Wavelet analysis leads to a unique decomposition of a signal into its coarse- and fine-scale components. Potentially, this could therefore be useful for image registration. In this work, we investigate whether a wavelet-based FFD model has advantages for nonrigid image registration. We use a B-splines based wavelet, as defined by Cai and Wang.1 This wavelet is expressed as a linear combination of B-spline basis functions. Derived from the original B-spline function, this wavelet is smooth, differentiable, and compactly supported. The basis functions of this wavelet are orthogonal across scales in Sobolev space. This wavelet was previously used for registration in computer vision, in 2D optical flow problems,2 but it was not compared with the conventional B-spline FFD in medical image registration problems. An advantage of choosing this B-splines based wavelet model is that the space of allowable deformation is exactly equivalent to that of the traditional B-spline. The wavelet transformation is essentially a (linear) reparameterization of the B-spline transformation model. Experiments on 10 CT lung and 18 T1-weighted MRI brain datasets show that wavelet based registration leads to smoother deformation fields than traditional B-splines based registration, while achieving better accuracy.

Wavelet analysis techniques applied to removing varying spectroscopic background in calibration model for pear sugar content

NASA Astrophysics Data System (ADS)

Liu, Yande; Ying, Yibin; Lu, Huishan; Fu, Xiaping

2005-11-01

A new method is proposed to eliminate the varying background and noise simultaneously for multivariate calibration of Fourier transform near infrared (FT-NIR) spectral signals. An ideal spectrum signal prototype was constructed based on the FT-NIR spectrum of fruit sugar content measurement. The performances of wavelet based threshold de-noising approaches via different combinations of wavelet base functions were compared. Three families of wavelet base function (Daubechies, Symlets and Coiflets) were applied to estimate the performance of those wavelet bases and threshold selection rules by a series of experiments. The experimental results show that the best de-noising performance is reached via the combinations of Daubechies 4 or Symlet 4 wavelet base function. Based on the optimization parameter, wavelet regression models for sugar content of pear were also developed and result in a smaller prediction error than a traditional Partial Least Squares Regression (PLSR) mode.

Wavelet transforms with discrete-time continuous-dilation wavelets

NASA Astrophysics Data System (ADS)

Zhao, Wei; Rao, Raghuveer M.

1999-03-01

Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.

Pre-Service Teachers' Concept Images on Fractal Dimension

ERIC Educational Resources Information Center

Karakus, Fatih

2016-01-01

The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

Editorial

NASA Astrophysics Data System (ADS)

Liu, Shuai

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation.

A shift to randomness of brain oscillations in people with autism.

PubMed

Lai, Meng-Chuan; Lombardo, Michael V; Chakrabarti, Bhismadev; Sadek, Susan A; Pasco, Greg; Wheelwright, Sally J; Bullmore, Edward T; Baron-Cohen, Simon; Suckling, John

2010-12-15

Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions. Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism. Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex. Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions. Copyright © 2010 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Optimal spinneret layout in Von Koch curves of fractal theory based needleless electrospinning process

NASA Astrophysics Data System (ADS)

Yang, Wenxiu; Liu, Yanbo; Zhang, Ligai; Cao, Hong; Wang, Yang; Yao, Jinbo

2016-06-01

Needleless electrospinning technology is considered as a better avenue to produce nanofibrous materials at large scale, and electric field intensity and its distribution play an important role in controlling nanofiber diameter and quality of the nanofibrous web during electrospinning. In the current study, a novel needleless electrospinning method was proposed based on Von Koch curves of Fractal configuration, simulation and analysis on electric field intensity and distribution in the new electrospinning process were performed with Finite element analysis software, Comsol Multiphysics 4.4, based on linear and nonlinear Von Koch fractal curves (hereafter called fractal models). The result of simulation and analysis indicated that Second level fractal structure is the optimal linear electrospinning spinneret in terms of field intensity and uniformity. Further simulation and analysis showed that the circular type of Fractal spinneret has better field intensity and distribution compared to spiral type of Fractal spinneret in the nonlinear Fractal electrospinning technology. The electrospinning apparatus with the optimal Von Koch fractal spinneret was set up to verify the theoretical analysis results from Comsol simulation, achieving more uniform electric field distribution and lower energy cost, compared to the current needle and needleless electrospinning technologies.

PULSAR SIGNAL DENOISING METHOD BASED ON LAPLACE DISTRIBUTION IN NO-SUBSAMPLING WAVELET PACKET DOMAIN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wenbo, Wang; Yanchao, Zhao; Xiangli, Wang

2016-11-01

In order to improve the denoising effect of the pulsar signal, a new denoising method is proposed in the no-subsampling wavelet packet domain based on the local Laplace prior model. First, we count the true noise-free pulsar signal’s wavelet packet coefficient distribution characteristics and construct the true signal wavelet packet coefficients’ Laplace probability density function model. Then, we estimate the denosied wavelet packet coefficients by using the noisy pulsar wavelet coefficients based on maximum a posteriori criteria. Finally, we obtain the denoisied pulsar signal through no-subsampling wavelet packet reconstruction of the estimated coefficients. The experimental results show that the proposed method performs better when calculating the pulsar time of arrival than the translation-invariant wavelet denoising method.

Multifractal analysis of a GCM climate

NASA Astrophysics Data System (ADS)

Carl, P.

2003-04-01

Multifractal analysis using the Wavelet Transform Modulus Maxima (WTMM) approach is being applied to the climate of a Mintz--Arakawa type, coarse resolution, two--layer AGCM. The model shows a backwards running period multiplication scenario throughout the northern summer, subsequent to a 'hard', subcritical Hopf bifurcation late in spring. This 'route out of chaos' (seen in cross sections of a toroidal phase space structure) is born in the planetary monsoon system which inflates the seasonal 'cycle' into these higher order structures and is blamed for the pronounced intraseasonal--to--centennial model climate variability. Previous analyses of the latter using advanced modal decompositions showed regularity based patterns in the time--frequency plane which are qualitatively similar to those obtained from the real world. The closer look here at the singularity structures, as a fundamental diagnostic supplement, aims at both more complete understanding (and quantification) of the model's qualitative dynamics and search for further tools of model intercomparison and verification in this respect. Analysing wavelet is the 10th derivative of the Gaussian which might suffice to suppress regular patterns in the data. Intraseasonal attractors, studied in time series of model precipitation over Central India, show shifting and braodening singularity spectra towards both more violent extreme events (premonsoon--monsoon transition) and weaker events (late summer to postmonsoon transition). Hints at a fractal basin boundary are found close to transition from period--2 to period--1 in the monsoon activity cycle. Interannual analyses are provided for runs with varied solar constants. To address the (in--)stationarity issue, first results are presented with a windowed multifractal analysis of longer--term runs ("singularity spectrogram").

Unification of two fractal families

NASA Astrophysics Data System (ADS)

Liu, Ying

1995-06-01

Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

Wavelet-based 3-D inversion for frequency-domain airborne EM data

NASA Astrophysics Data System (ADS)

Liu, Yunhe; Farquharson, Colin G.; Yin, Changchun; Baranwal, Vikas C.

2018-04-01

In this paper, we propose a new wavelet-based 3-D inversion method for frequency-domain airborne electromagnetic (FDAEM) data. Instead of inverting the model in the space domain using a smoothing constraint, this new method recovers the model in the wavelet domain based on a sparsity constraint. In the wavelet domain, the model is represented by two types of coefficients, which contain both large- and fine-scale informations of the model, meaning the wavelet-domain inversion has inherent multiresolution. In order to accomplish a sparsity constraint, we minimize an L1-norm measure in the wavelet domain that mostly gives a sparse solution. The final inversion system is solved by an iteratively reweighted least-squares method. We investigate different orders of Daubechies wavelets to accomplish our inversion algorithm, and test them on synthetic frequency-domain AEM data set. The results show that higher order wavelets having larger vanishing moments and regularity can deliver a more stable inversion process and give better local resolution, while the lower order wavelets are simpler and less smooth, and thus capable of recovering sharp discontinuities if the model is simple. At last, we test this new inversion algorithm on a frequency-domain helicopter EM (HEM) field data set acquired in Byneset, Norway. Wavelet-based 3-D inversion of HEM data is compared to L2-norm-based 3-D inversion's result to further investigate the features of the new method.

Study on Conversion Between Momentum and Contrarian Based on Fractal Game

NASA Astrophysics Data System (ADS)

Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

2015-06-01

Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

Optimal wavelets for biomedical signal compression.

PubMed

Nielsen, Mogens; Kamavuako, Ernest Nlandu; Andersen, Michael Midtgaard; Lucas, Marie-Françoise; Farina, Dario

2006-07-01

Signal compression is gaining importance in biomedical engineering due to the potential applications in telemedicine. In this work, we propose a novel scheme of signal compression based on signal-dependent wavelets. To adapt the mother wavelet to the signal for the purpose of compression, it is necessary to define (1) a family of wavelets that depend on a set of parameters and (2) a quality criterion for wavelet selection (i.e., wavelet parameter optimization). We propose the use of an unconstrained parameterization of the wavelet for wavelet optimization. A natural performance criterion for compression is the minimization of the signal distortion rate given the desired compression rate. For coding the wavelet coefficients, we adopted the embedded zerotree wavelet coding algorithm, although any coding scheme may be used with the proposed wavelet optimization. As a representative example of application, the coding/encoding scheme was applied to surface electromyographic signals recorded from ten subjects. The distortion rate strongly depended on the mother wavelet (for example, for 50% compression rate, optimal wavelet, mean+/-SD, 5.46+/-1.01%; worst wavelet 12.76+/-2.73%). Thus, optimization significantly improved performance with respect to previous approaches based on classic wavelets. The algorithm can be applied to any signal type since the optimal wavelet is selected on a signal-by-signal basis. Examples of application to ECG and EEG signals are also reported.

Investigation into How 8th Grade Students Define Fractals

ERIC Educational Resources Information Center

Karakus, Fatih

2015-01-01

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

Order-fractal transitions in abstract paintings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calleja, E.M. de la, E-mail: elsama79@gmail.com; Cervantes, F.; Calleja, J. de la

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

Iterated oversampled filter banks and wavelet frames

NASA Astrophysics Data System (ADS)

Selesnick, Ivan W.; Sendur, Levent

2000-12-01

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and tow distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform is nearly shift-invariant, and can be used to improve denoising. Because the associated time- frequency lattice preserves the dyadic structure of the critically sampled DWT it can be used with tree-based denoising algorithms that exploit parent-child correlation.

EEG analysis using wavelet-based information tools.

PubMed

Rosso, O A; Martin, M T; Figliola, A; Keller, K; Plastino, A

2006-06-15

Wavelet-based informational tools for quantitative electroencephalogram (EEG) record analysis are reviewed. Relative wavelet energies, wavelet entropies and wavelet statistical complexities are used in the characterization of scalp EEG records corresponding to secondary generalized tonic-clonic epileptic seizures. In particular, we show that the epileptic recruitment rhythm observed during seizure development is well described in terms of the relative wavelet energies. In addition, during the concomitant time-period the entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus, for this kind of seizures, triggers a self-organized brain state characterized by both order and maximal complexity.

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

A new wavelet transform to sparsely represent cortical current densities for EEG/MEG inverse problems.

PubMed

Liao, Ke; Zhu, Min; Ding, Lei

2013-08-01

The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Fault Diagnosis for Micro-Gas Turbine Engine Sensors via Wavelet Entropy

PubMed Central

Yu, Bing; Liu, Dongdong; Zhang, Tianhong

2011-01-01

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can’t be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (IWEE) and instantaneous wavelet singular entropy (IWSE) are defined based on the previous wavelet entropy theory. Subsequently, a fault diagnosis method for gas turbine sensors is proposed based on the results of a numerically simulated example. Then, experiments on this method are carried out on a real micro gas turbine engine. In the experiment, four types of faults with different magnitudes are presented. The experimental results show that the proposed method for sensor fault diagnosis is efficient. PMID:22163734

Fault diagnosis for micro-gas turbine engine sensors via wavelet entropy.

PubMed

Yu, Bing; Liu, Dongdong; Zhang, Tianhong

2011-01-01

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can't be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (IWEE) and instantaneous wavelet singular entropy (IWSE) are defined based on the previous wavelet entropy theory. Subsequently, a fault diagnosis method for gas turbine sensors is proposed based on the results of a numerically simulated example. Then, experiments on this method are carried out on a real micro gas turbine engine. In the experiment, four types of faults with different magnitudes are presented. The experimental results show that the proposed method for sensor fault diagnosis is efficient.

a Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

NASA Astrophysics Data System (ADS)

Lu, Hong-Lin; Zhang, Ji-Jun; Tan, Xiao-Hua; Li, Xiao-Ping; Zhao, Jia-Hui

Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions Df and the capillary tortuosity fractal dimensions DT have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

Daily water level forecasting using wavelet decomposition and artificial intelligence techniques

NASA Astrophysics Data System (ADS)

Seo, Youngmin; Kim, Sungwon; Kisi, Ozgur; Singh, Vijay P.

2015-01-01

Reliable water level forecasting for reservoir inflow is essential for reservoir operation. The objective of this paper is to develop and apply two hybrid models for daily water level forecasting and investigate their accuracy. These two hybrid models are wavelet-based artificial neural network (WANN) and wavelet-based adaptive neuro-fuzzy inference system (WANFIS). Wavelet decomposition is employed to decompose an input time series into approximation and detail components. The decomposed time series are used as inputs to artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) for WANN and WANFIS models, respectively. Based on statistical performance indexes, the WANN and WANFIS models are found to produce better efficiency than the ANN and ANFIS models. WANFIS7-sym10 yields the best performance among all other models. It is found that wavelet decomposition improves the accuracy of ANN and ANFIS. This study evaluates the accuracy of the WANN and WANFIS models for different mother wavelets, including Daubechies, Symmlet and Coiflet wavelets. It is found that the model performance is dependent on input sets and mother wavelets, and the wavelet decomposition using mother wavelet, db10, can further improve the efficiency of ANN and ANFIS models. Results obtained from this study indicate that the conjunction of wavelet decomposition and artificial intelligence models can be a useful tool for accurate forecasting daily water level and can yield better efficiency than the conventional forecasting models.

Estimation of Hurst Exponent for the Financial Time Series

NASA Astrophysics Data System (ADS)

Kumar, J.; Manchanda, P.

2009-07-01

Till recently statistical methods and Fourier analysis were employed to study fluctuations in stock markets in general and Indian stock market in particular. However current trend is to apply the concepts of wavelet methodology and Hurst exponent, see for example the work of Manchanda, J. Kumar and Siddiqi, Journal of the Frankline Institute 144 (2007), 613-636 and paper of Cajueiro and B. M. Tabak. Cajueiro and Tabak, Physica A, 2003, have checked the efficiency of emerging markets by computing Hurst component over a time window of 4 years of data. Our goal in the present paper is to understand the dynamics of the Indian stock market. We look for the persistency in the stock market through Hurst exponent and fractal dimension of time series data of BSE 100 and NIFTY 50.

Digital video technologies and their network requirements

DOE Office of Scientific and Technical Information (OSTI.GOV)

R. P. Tsang; H. Y. Chen; J. M. Brandt

1999-11-01

Coded digital video signals are considered to be one of the most difficult data types to transport due to their real-time requirements and high bit rate variability. In this study, the authors discuss the coding mechanisms incorporated by the major compression standards bodies, i.e., JPEG and MPEG, as well as more advanced coding mechanisms such as wavelet and fractal techniques. The relationship between the applications which use these coding schemes and their network requirements are the major focus of this study. Specifically, the authors relate network latency, channel transmission reliability, random access speed, buffering and network bandwidth with the variousmore » coding techniques as a function of the applications which use them. Such applications include High-Definition Television, Video Conferencing, Computer-Supported Collaborative Work (CSCW), and Medical Imaging.« less

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

PubMed

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

Segmentation-based wavelet transform for still-image compression

NASA Astrophysics Data System (ADS)

Mozelle, Gerard; Seghier, Abdellatif; Preteux, Francoise J.

1996-10-01

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

Band structures in fractal grading porous phononic crystals

NASA Astrophysics Data System (ADS)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2014-05-01

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

A wavelet-based Gaussian method for energy dispersive X-ray fluorescence spectrum.

PubMed

Liu, Pan; Deng, Xiaoyan; Tang, Xin; Shen, Shijian

2017-05-01

This paper presents a wavelet-based Gaussian method (WGM) for the peak intensity estimation of energy dispersive X-ray fluorescence (EDXRF). The relationship between the parameters of Gaussian curve and the wavelet coefficients of Gaussian peak point is firstly established based on the Mexican hat wavelet. It is found that the Gaussian parameters can be accurately calculated by any two wavelet coefficients at the peak point which has to be known. This fact leads to a local Gaussian estimation method for spectral peaks, which estimates the Gaussian parameters based on the detail wavelet coefficients of Gaussian peak point. The proposed method is tested via simulated and measured spectra from an energy X-ray spectrometer, and compared with some existing methods. The results prove that the proposed method can directly estimate the peak intensity of EDXRF free from the background information, and also effectively distinguish overlap peaks in EDXRF spectrum.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

Surface Fractal Analysis for Estimating the Fracture Energy Absorption of Nanoparticle Reinforced Composites

PubMed Central

Pramanik, Brahmananda; Tadepalli, Tezeswi; Mantena, P. Raju

2012-01-01

In this study, the fractal dimensions of failure surfaces of vinyl ester based nanocomposites are estimated using two classical methods, Vertical Section Method (VSM) and Slit Island Method (SIM), based on the processing of 3D digital microscopic images. Self-affine fractal geometry has been observed in the experimentally obtained failure surfaces of graphite platelet reinforced nanocomposites subjected to quasi-static uniaxial tensile and low velocity punch-shear loading. Fracture energy and fracture toughness are estimated analytically from the surface fractal dimensionality. Sensitivity studies show an exponential dependency of fracture energy and fracture toughness on the fractal dimensionality. Contribution of fracture energy to the total energy absorption of these nanoparticle reinforced composites is demonstrated. For the graphite platelet reinforced nanocomposites investigated, surface fractal analysis has depicted the probable ductile or brittle fracture propagation mechanism, depending upon the rate of loading. PMID:28817017

Wavelet-based compression of pathological images for telemedicine applications

NASA Astrophysics Data System (ADS)

Chen, Chang W.; Jiang, Jianfei; Zheng, Zhiyong; Wu, Xue G.; Yu, Lun

2000-05-01

In this paper, we present the performance evaluation of wavelet-based coding techniques as applied to the compression of pathological images for application in an Internet-based telemedicine system. We first study how well suited the wavelet-based coding is as it applies to the compression of pathological images, since these images often contain fine textures that are often critical to the diagnosis of potential diseases. We compare the wavelet-based compression with the DCT-based JPEG compression in the DICOM standard for medical imaging applications. Both objective and subjective measures have been studied in the evaluation of compression performance. These studies are performed in close collaboration with expert pathologists who have conducted the evaluation of the compressed pathological images and communication engineers and information scientists who designed the proposed telemedicine system. These performance evaluations have shown that the wavelet-based coding is suitable for the compression of various pathological images and can be integrated well with the Internet-based telemedicine systems. A prototype of the proposed telemedicine system has been developed in which the wavelet-based coding is adopted for the compression to achieve bandwidth efficient transmission and therefore speed up the communications between the remote terminal and the central server of the telemedicine system.

Comparison between deterministic and statistical wavelet estimation methods through predictive deconvolution: Seismic to well tie example from the North Sea

NASA Astrophysics Data System (ADS)

de Macedo, Isadora A. S.; da Silva, Carolina B.; de Figueiredo, J. J. S.; Omoboya, Bode

2017-01-01

Wavelet estimation as well as seismic-to-well tie procedures are at the core of every seismic interpretation workflow. In this paper we perform a comparative study of wavelet estimation methods for seismic-to-well tie. Two approaches to wavelet estimation are discussed: a deterministic estimation, based on both seismic and well log data, and a statistical estimation, based on predictive deconvolution and the classical assumptions of the convolutional model, which provides a minimum-phase wavelet. Our algorithms, for both wavelet estimation methods introduce a semi-automatic approach to determine the optimum parameters of deterministic wavelet estimation and statistical wavelet estimation and, further, to estimate the optimum seismic wavelets by searching for the highest correlation coefficient between the recorded trace and the synthetic trace, when the time-depth relationship is accurate. Tests with numerical data show some qualitative conclusions, which are probably useful for seismic inversion and interpretation of field data, by comparing deterministic wavelet estimation and statistical wavelet estimation in detail, especially for field data example. The feasibility of this approach is verified on real seismic and well data from Viking Graben field, North Sea, Norway. Our results also show the influence of the washout zones on well log data on the quality of the well to seismic tie.

A system framework of inter-enterprise machining quality control based on fractal theory

NASA Astrophysics Data System (ADS)

Zhao, Liping; Qin, Yongtao; Yao, Yiyong; Yan, Peng

2014-03-01

In order to meet the quality control requirement of dynamic and complicated product machining processes among enterprises, a system framework of inter-enterprise machining quality control based on fractal was proposed. In this system framework, the fractal-specific characteristic of inter-enterprise machining quality control function was analysed, and the model of inter-enterprise machining quality control was constructed by the nature of fractal structures. Furthermore, the goal-driven strategy of inter-enterprise quality control and the dynamic organisation strategy of inter-enterprise quality improvement were constructed by the characteristic analysis on this model. In addition, the architecture of inter-enterprise machining quality control based on fractal was established by means of Web service. Finally, a case study for application was presented. The result showed that the proposed method was available, and could provide guidance for quality control and support for product reliability in inter-enterprise machining processes.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

NASA Astrophysics Data System (ADS)

Tan, X.-H.; Liu, C.-Y.; Li, X.-P.; Wang, H.-Q.; Deng, H.

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster DcTσ become bigger with an increase of stress. However, the pore fractal dimension of solid cluster Dcfσ and capillary bundle Dpfσ remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Adjusting Wavelet-based Multiresolution Analysis Boundary Conditions for Robust Long-term Streamflow Forecasting Model

NASA Astrophysics Data System (ADS)

Maslova, I.; Ticlavilca, A. M.; McKee, M.

2012-12-01

There has been an increased interest in wavelet-based streamflow forecasting models in recent years. Often overlooked in this approach are the circularity assumptions of the wavelet transform. We propose a novel technique for minimizing the wavelet decomposition boundary condition effect to produce long-term, up to 12 months ahead, forecasts of streamflow. A simulation study is performed to evaluate the effects of different wavelet boundary rules using synthetic and real streamflow data. A hybrid wavelet-multivariate relevance vector machine model is developed for forecasting the streamflow in real-time for Yellowstone River, Uinta Basin, Utah, USA. The inputs of the model utilize only the past monthly streamflow records. They are decomposed into components formulated in terms of wavelet multiresolution analysis. It is shown that the model model accuracy can be increased by using the wavelet boundary rule introduced in this study. This long-term streamflow modeling and forecasting methodology would enable better decision-making and managing water availability risk.

The 4D hyperspherical diffusion wavelet: A new method for the detection of localized anatomical variation.

PubMed

Hosseinbor, Ameer Pasha; Kim, Won Hwa; Adluru, Nagesh; Acharya, Amit; Vorperian, Houri K; Chung, Moo K

2014-01-01

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links Hyper-SPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multiscale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the first-ever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM.

The 4D Hyperspherical Diffusion Wavelet: A New Method for the Detection of Localized Anatomical Variation

PubMed Central

Hosseinbor, A. Pasha; Kim, Won Hwa; Adluru, Nagesh; Acharya, Amit; Vorperian, Houri K.; Chung, Moo K.

2014-01-01

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links HyperSPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multiscale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the firstever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM. PMID:25320783

Fractal-Based Image Analysis In Radiological Applications

NASA Astrophysics Data System (ADS)

Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.

1987-10-01

We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

[Recent progress of research and applications of fractal and its theories in medicine].

PubMed

Cai, Congbo; Wang, Ping

2014-10-01

Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

Passenger flow analysis of Beijing urban rail transit network using fractal approach

NASA Astrophysics Data System (ADS)

Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

2018-04-01

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

EnvironmentalWaveletTool: Continuous and discrete wavelet analysis and filtering for environmental time series

NASA Astrophysics Data System (ADS)

Galiana-Merino, J. J.; Pla, C.; Fernandez-Cortes, A.; Cuezva, S.; Ortiz, J.; Benavente, D.

2014-10-01

A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of several environmental time series, particularly focused on the analyses of cave monitoring data. The continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform have been implemented to provide a fast and precise time-period examination of the time series at different period bands. Moreover, statistic methods to examine the relation between two signals have been included. Finally, the entropy of curves and splines based methods have also been developed for segmenting and modeling the analyzed time series. All these methods together provide a user-friendly and fast program for the environmental signal analysis, with useful, practical and understandable results.

Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

NASA Astrophysics Data System (ADS)

Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui

2016-03-01

Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.

On the Daubechies-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of vanishing moments of the associated wavelet. It is illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small-scale structure is present.

Speckle noise reduction in quantitative optical metrology techniques by application of the discrete wavelet transformation

NASA Astrophysics Data System (ADS)

Furlong, Cosme; Pryputniewicz, Ryszard J.

2002-06-01

Effective suppression of speckle noise content in interferometric data images can help in improving accuracy and resolution of the results obtained with interferometric optical metrology techniques. In this paper, novel speckle noise reduction algorithms based on the discrete wavelet transformation are presented. The algorithms proceed by: (a) estimating the noise level contained in the interferograms of interest, (b) selecting wavelet families, (c) applying the wavelet transformation using the selected families, (d) wavelet thresholding, and (e) applying the inverse wavelet transformation, producing denoised interferograms. The algorithms are applied to the different stages of the processing procedures utilized for generation of quantitative speckle correlation interferometry data of fiber-optic based opto-electronic holography (FOBOEH) techniques, allowing identification of optimal processing conditions. It is shown that wavelet algorithms are effective for speckle noise reduction while preserving image features otherwise faded with other algorithms.

Target Detection and Classification Using Seismic and PIR Sensors

DTIC Science & Technology

2012-06-01

time series analysis via wavelet - based partitioning,” Signal Process...regard, this paper presents a wavelet - based method for target detection and classification. The proposed method has been validated on data sets of...The work reported in this paper makes use of a wavelet - based feature extraction method , called Symbolic Dynamic Filtering (SDF) [12]–[14]. The

Wavelet Types Comparison for Extracting Iris Feature Based on Energy Compaction

NASA Astrophysics Data System (ADS)

Rizal Isnanto, R.

2015-06-01

Human iris has a very unique pattern which is possible to be used as a biometric recognition. To identify texture in an image, texture analysis method can be used. One of method is wavelet that extract the image feature based on energy. Wavelet transforms used are Haar, Daubechies, Coiflets, Symlets, and Biorthogonal. In the research, iris recognition based on five mentioned wavelets was done and then comparison analysis was conducted for which some conclusions taken. Some steps have to be done in the research. First, the iris image is segmented from eye image then enhanced with histogram equalization. The features obtained is energy value. The next step is recognition using normalized Euclidean distance. Comparison analysis is done based on recognition rate percentage with two samples stored in database for reference images. After finding the recognition rate, some tests are conducted using Energy Compaction for all five types of wavelets above. As the result, the highest recognition rate is achieved using Haar, whereas for coefficients cutting for C(i) < 0.1, Haar wavelet has a highest percentage, therefore the retention rate or significan coefficient retained for Haaris lower than other wavelet types (db5, coif3, sym4, and bior2.4)

Wavelet tree structure based speckle noise removal for optical coherence tomography

NASA Astrophysics Data System (ADS)

Yuan, Xin; Liu, Xuan; Liu, Yang

2018-02-01

We report a new speckle noise removal algorithm in optical coherence tomography (OCT). Though wavelet domain thresholding algorithms have demonstrated superior advantages in suppressing noise magnitude and preserving image sharpness in OCT, the wavelet tree structure has not been investigated in previous applications. In this work, we propose an adaptive wavelet thresholding algorithm via exploiting the tree structure in wavelet coefficients to remove the speckle noise in OCT images. The threshold for each wavelet band is adaptively selected following a special rule to retain the structure of the image across different wavelet layers. Our results demonstrate that the proposed algorithm outperforms conventional wavelet thresholding, with significant advantages in preserving image features.

Spatially adaptive bases in wavelet-based coding of semi-regular meshes

NASA Astrophysics Data System (ADS)

Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter

2010-05-01

In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.

[Lithology feature extraction of CASI hyperspectral data based on fractal signal algorithm].

PubMed

Tang, Chao; Chen, Jian-Ping; Cui, Jing; Wen, Bo-Tao

2014-05-01

Hyperspectral data is characterized by combination of image and spectrum and large data volume dimension reduction is the main research direction. Band selection and feature extraction is the primary method used for this objective. In the present article, the authors tested methods applied for the lithology feature extraction from hyperspectral data. Based on the self-similarity of hyperspectral data, the authors explored the application of fractal algorithm to lithology feature extraction from CASI hyperspectral data. The "carpet method" was corrected and then applied to calculate the fractal value of every pixel in the hyperspectral data. The results show that fractal information highlights the exposed bedrock lithology better than the original hyperspectral data The fractal signal and characterized scale are influenced by the spectral curve shape, the initial scale selection and iteration step. At present, research on the fractal signal of spectral curve is rare, implying the necessity of further quantitative analysis and investigation of its physical implications.

Fractal-Based Analysis of the Influence of Music on Human Respiration

NASA Astrophysics Data System (ADS)

Reza Namazi, H.

An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Watermarking on 3D mesh based on spherical wavelet transform.

PubMed

Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng

2004-03-01

In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.

A lung sound classification system based on the rational dilation wavelet transform.

PubMed

Ulukaya, Sezer; Serbes, Gorkem; Sen, Ipek; Kahya, Yasemin P

2016-08-01

In this work, a wavelet based classification system that aims to discriminate crackle, normal and wheeze lung sounds is presented. While the previous works related with this problem use constant low Q-factor wavelets, which have limited frequency resolution and can not cope with oscillatory signals, in the proposed system, the Rational Dilation Wavelet Transform, whose Q-factors can be tuned, is employed. Proposed system yields an accuracy of 95 % for crackle, 97 % for wheeze, 93.50 % for normal and 95.17 % for total sound signal types using energy feature subset and proposed approach is superior to conventional low Q-factor wavelet analysis.

Undergraduate Experiment with Fractal Diffraction Gratings

ERIC Educational Resources Information Center

Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

Spherical 3D isotropic wavelets

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2012-04-01

Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

NASA Astrophysics Data System (ADS)

Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

2018-05-01

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

A New Algorithm with Plane Waves and Wavelets for Random Velocity Fields with Many Spatial Scales

NASA Astrophysics Data System (ADS)

Elliott, Frank W.; Majda, Andrew J.

1995-03-01

A new Monte Carlo algorithm for constructing and sampling stationary isotropic Gaussian random fields with power-law energy spectrum, infrared divergence, and fractal self-similar scaling is developed here. The theoretical basis for this algorithm involves the fact that such a random field is well approximated by a superposition of random one-dimensional plane waves involving a fixed finite number of directions. In general each one-dimensional plane wave is the sum of a random shear layer and a random acoustical wave. These one-dimensional random plane waves are then simulated by a wavelet Monte Carlo method for a single space variable developed recently by the authors. The computational results reported in this paper demonstrate remarkable low variance and economical representation of such Gaussian random fields through this new algorithm. In particular, the velocity structure function for an imcorepressible isotropic Gaussian random field in two space dimensions with the Kolmogoroff spectrum can be simulated accurately over 12 decades with only 100 realizations of the algorithm with the scaling exponent accurate to 1.1% and the constant prefactor accurate to 6%; in fact, the exponent of the velocity structure function can be computed over 12 decades within 3.3% with only 10 realizations. Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.

Multiscale rescaled range analysis of EEG recordings in sevoflurane anesthesia.

PubMed

Liang, Zhenhu; Li, Duan; Ouyang, Gaoxiang; Wang, Yinghua; Voss, Logan J; Sleigh, Jamie W; Li, Xiaoli

2012-04-01

The Hurst exponent (HE) is a nonlinear method measuring the smoothness of a fractal time series. In this study we applied the HE index, extracted from electroencephalographic (EEG) recordings, as a measure of anesthetic drug effects on brain activity. In 19 adult patients undergoing sevoflurane general anesthesia, we calculated the HE of the raw EEG; comparing the maximal overlap discrete wavelet transform (MODWT) with the traditional rescaled range (R/S) analysis techniques, and with a commercial index of depth of anesthesia - the response entropy (RE). We analyzed each wavelet-decomposed sub-band as well as the combined low frequency bands (HEOLFBs). The methods were compared in regard to pharmacokinetic/pharmacodynamic (PK/PD) modeling, and prediction probability. All the low frequency band HE indices decreased when anesthesia deepened. However the HEOLFB was the best index because: it was less sensitive to artifacts, most closely tracked the exact point of loss of consciousness, showed a better prediction probability in separating the awake and unconscious states, and tracked sevoflurane concentration better - as estimated by the PK/PD models. The HE is a useful measure for estimating the depth of anesthesia. It was noted that HEOLFB showed the best performance for tracking drug effect. The HEOLFB could be used as an index for accurately estimating the effect of anesthesia on brain activity. Copyright © 2011 International Federation of Clinical Neurophysiology. All rights reserved.

Fundamental Fractal Antenna Design Process

NASA Astrophysics Data System (ADS)

Zhu, L. P.; Kim, T. C.; Kakas, G. D.

2017-12-01

Antenna designers are always looking to come up with new ideas to push the envelope for new antennas, using a smaller volume while striving for higher bandwidth, wider bandwidth, and antenna gain. One proposed method of increasing bandwidth or shrinking antenna size is via the use of fractal geometry, which gives rise to fractal antennas. Fractals are those fun shapes that if one zooms in or zoom out, the structure is always the same. Design a new type of antenna based on fractal antenna design by utilize the Design of Experiment (DOE) will be shown in fractal antenna design process. Investigate conformal fractal antenna design for patterns, dimensions, and size, of the antenna but maintaining or improving the antenna performance. Research shows an antenna designer how to create basic requirements of the fractal antenna through a step by step process, and provides how to optimize the antenna design with the model prediction, lab measurement, and actual results from the compact range measurement on the antenna patterns.

[Recognition of landscape characteristic scale based on two-dimension wavelet analysis].

PubMed

Gao, Yan-Ni; Chen, Wei; He, Xing-Yuan; Li, Xiao-Yu

2010-06-01

Three wavelet bases, i. e., Haar, Daubechies, and Symlet, were chosen to analyze the validity of two-dimension wavelet analysis in recognizing the characteristic scales of the urban, peri-urban, and rural landscapes of Shenyang. Owing to the transform scale of two-dimension wavelet must be the integer power of 2, some characteristic scales cannot be accurately recognized. Therefore, the pixel resolution of images was resampled to 3, 3.5, 4, and 4.5 m to densify the scale in analysis. It was shown that two-dimension wavelet analysis worked effectively in checking characteristic scale. Haar, Daubechies, and Symle were the optimal wavelet bases to the peri-urban landscape, urban landscape, and rural landscape, respectively. Both Haar basis and Symlet basis played good roles in recognizing the fine characteristic scale of rural landscape and in detecting the boundary of peri-urban landscape. Daubechies basis and Symlet basis could be also used to detect the boundary of urban landscape and rural landscape, respectively.

Efficacy Evaluation of Different Wavelet Feature Extraction Methods on Brain MRI Tumor Detection

NASA Astrophysics Data System (ADS)

Nabizadeh, Nooshin; John, Nigel; Kubat, Miroslav

2014-03-01

Automated Magnetic Resonance Imaging brain tumor detection and segmentation is a challenging task. Among different available methods, feature-based methods are very dominant. While many feature extraction techniques have been employed, it is still not quite clear which of feature extraction methods should be preferred. To help improve the situation, we present the results of a study in which we evaluate the efficiency of using different wavelet transform features extraction methods in brain MRI abnormality detection. Applying T1-weighted brain image, Discrete Wavelet Transform (DWT), Discrete Wavelet Packet Transform (DWPT), Dual Tree Complex Wavelet Transform (DTCWT), and Complex Morlet Wavelet Transform (CMWT) methods are applied to construct the feature pool. Three various classifiers as Support Vector Machine, K Nearest Neighborhood, and Sparse Representation-Based Classifier are applied and compared for classifying the selected features. The results show that DTCWT and CMWT features classified with SVM, result in the highest classification accuracy, proving of capability of wavelet transform features to be informative in this application.

Extracting fingerprint of wireless devices based on phase noise and multiple level wavelet decomposition

NASA Astrophysics Data System (ADS)

Zhao, Weichen; Sun, Zhuo; Kong, Song

2016-10-01

Wireless devices can be identified by the fingerprint extracted from the signal transmitted, which is useful in wireless communication security and other fields. This paper presents a method that extracts fingerprint based on phase noise of signal and multiple level wavelet decomposition. The phase of signal will be extracted first and then decomposed by multiple level wavelet decomposition. The statistic value of each wavelet coefficient vector is utilized for constructing fingerprint. Besides, the relationship between wavelet decomposition level and recognition accuracy is simulated. And advertised decomposition level is revealed as well. Compared with previous methods, our method is simpler and the accuracy of recognition remains high when Signal Noise Ratio (SNR) is low.

Fractal symmetry of protein interior: what have we learned?

PubMed

Banerji, Anirban; Ghosh, Indira

2011-08-01

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.

P-adic model of transport in porous disordered media

NASA Astrophysics Data System (ADS)

Khrennikov, Adrei Yu.; Oleschko, Klaudia

2014-05-01

The soil porosity and permeability are the most important quantitative indicators of soil dynamics under the land-use change. The main problema in the modeling of this dynamic is still poor correlation between the real measuring data and the mathematical and computer simulation models. In order to overpassed this deep divorce we have designed a new technique, able to compare the data arised from the multiscale image analices and time series of the basic physical properties dynamics in porous media studied in time and space. We present a model of the diffusion reaction type describing transport in disordered porous media, e.g., water or oil flow in a complex network of pores. Our model is based on p-adic representation of such networks. This is a kind of fractal representation. We explore advantages of p- adic representation, namely, the possibility to endow p-adic trees with an algebraic structure and ultrametric topology and, hence, to apply analysis which have (at least some) similarities with ordinary real analysis on the straight line. We present the system of two diffusion reaction equations describing propagation of particles in networks of pores in disordered media. As an application, one can consider water transport through the soil pore Networks, or oil flow through capillaries nets. Under some restrictions on potentials and rate coefficients we found the stationary regime corresponding to water content or concentration of oil in a cluster of capillaries. Usage of p-adic analysis (in particular, p-adic wavelets) gives a possibility to find the stationary solution in the analytic form which makes possible to present a clear pedological or geological picture of the process. The mathematical model elaborated in this paper (Khrennikov, 2013) can be applied to variety of problems from water concentration in aquifers to the problem of formation of oil reservoirs in disordered media with porous structures. Another possible application may have real practical output. In fact, our system of diffusion-reaction equations can be used to model the process of extraction of water or oil from an extended network of capillaries (Khrennikov et al., 2013). The accomplished analyses show that the time series of water content/pressure dynamics in saturated/unsaturated conditions reflect the fractal structure of pores separated by familias base don the seven geometric descriptors which we used for the soils multiscale images (Oleschko et al., 2012). The similar models were applied to the porous media behind the oil flow from wells. These results motivate usage of the fractal and, in particular, p-adic methods of modeling.

Skin image retrieval using Gabor wavelet texture feature.

PubMed

Ou, X; Pan, W; Zhang, X; Xiao, P

2016-12-01

Skin imaging plays a key role in many clinical studies. We have used many skin imaging techniques, including the recently developed capacitive contact skin imaging based on fingerprint sensors. The aim of this study was to develop an effective skin image retrieval technique using Gabor wavelet transform, which can be used on different types of skin images, but with a special focus on skin capacitive contact images. Content-based image retrieval (CBIR) is a useful technology to retrieve stored images from database by supplying query images. In a typical CBIR, images are retrieved based on colour, shape, texture, etc. In this study, texture feature is used for retrieving skin images, and Gabor wavelet transform is used for texture feature description and extraction. The results show that the Gabor wavelet texture features can work efficiently on different types of skin images. Although Gabor wavelet transform is slower compared with other image retrieval techniques, such as principal component analysis (PCA) and grey-level co-occurrence matrix (GLCM), Gabor wavelet transform is the best for retrieving skin capacitive contact images and facial images with different orientations. Gabor wavelet transform can also work well on facial images with different expressions and skin cancer/disease images. We have developed an effective skin image retrieval method based on Gabor wavelet transform, that it is useful for retrieving different types of images, namely digital colour face images, digital colour skin cancer and skin disease images, and particularly greyscale skin capacitive contact images. Gabor wavelet transform can also be potentially useful for face recognition (with different orientation and expressions) and skin cancer/disease diagnosis. © 2016 Society of Cosmetic Scientists and the Société Française de Cosmétologie.

Wavelet transforms as solutions of partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zweig, G.

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuousmore » wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.« less

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

NASA Astrophysics Data System (ADS)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset.

PubMed

Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro

2017-12-01

Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.

Running wavelet archetype aids the determination of heart rate from the video photoplethysmogram during motion.

PubMed

Addison, Paul S; Foo, David M H; Jacquel, Dominique

2017-07-01

The extraction of heart rate from a video-based biosignal during motion using a novel wavelet-based ensemble averaging method is described. Running Wavelet Archetyping (RWA) allows for the enhanced extraction of pulse information from the time-frequency representation, from which a video-based heart rate (HRvid) can be derived. This compares favorably to a reference heart rate derived from a pulse oximeter.

Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics

PubMed Central

Khullar, Siddharth; Michael, Andrew; Correa, Nicolle; Adali, Tulay; Baum, Stefi A.; Calhoun, Vince D.

2010-01-01

We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D de-noising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional de-noising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the de-noised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of de-noised wavelet coefficients for each voxel. Given the decorrelated nature of these de-noised wavelet coefficients; it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules. First, the analysis module where we combine a new 3-D wavelet denoising approach with better signal separation properties of ICA in the wavelet domain, to yield an activation component that corresponds closely to the true underlying signal and is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing + spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic (ROC) curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positives voxels. PMID:21034833

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

NASA Astrophysics Data System (ADS)

Zborovský, I.

2018-04-01

Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

A fractal growth model: Exploring the connection pattern of hubs in complex networks

NASA Astrophysics Data System (ADS)

Li, Dongyan; Wang, Xingyuan; Huang, Penghe

2017-04-01

Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.

A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes

NASA Technical Reports Server (NTRS)

Hsui, Albert T.; Rust, Kelly A.; Klein, George D.

1993-01-01

Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.

Energy-Based Wavelet De-Noising of Hydrologic Time Series

PubMed Central

Sang, Yan-Fang; Liu, Changming; Wang, Zhonggen; Wen, Jun; Shang, Lunyu

2014-01-01

De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed. PMID:25360533

Aqueous synthesis of LiFePO4 with Fractal Granularity.

PubMed

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P; Gómez-Romero, Pedro

2016-06-03

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

Aqueous synthesis of LiFePO4 with Fractal Granularity

PubMed Central

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

2016-01-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes. PMID:27256504

Aqueous synthesis of LiFePO4 with Fractal Granularity

NASA Astrophysics Data System (ADS)

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

2016-06-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

Fractal markets: Liquidity and investors on different time horizons

NASA Astrophysics Data System (ADS)

Li, Da-Ye; Nishimura, Yusaku; Men, Ming

2014-08-01

In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

Evaluation of the temporal structure of postural sway fluctuations based on a comprehensive set of analysis tools

NASA Astrophysics Data System (ADS)

Kirchner, M.; Schubert, P.; Schmidtbleicher, D.; Haas, C. T.

2012-10-01

The analysis of postural control has a long history. Traditionally, the amount of body sway is solely used as an index of postural stability. Although this leads to some extent to an effective evaluation of balance performance, the control mechanisms involved have not yet been fully understood. The concept of nonlinear dynamics suggests that variability in the motor output is not randomness but structure, providing the stimulus to reveal the functionality of postural sway. The present work evaluates sway dynamics by means of COP excursions in a quiet standing task versus a dual-task condition in three different test times (30, 60, 300 s). Besides the application of traditional methods-which estimate the overall size of sway-the temporal pattern of body sway was quantified via wavelet transform, multiscale entropy and fractal analysis. We found higher sensitivity of the structural parameters to modulations of postural control strategies and partly an improved evaluation of sway dynamics in longer recordings. It could be shown that postural control modifications take place on different timescales corresponding to the interplay of the sensory systems. A continued application of nonlinear analysis can help to better understand postural control mechanisms.

Use of the Morlet mother wavelet in the frequency-scale domain decomposition technique for the modal identification of ambient vibration responses

NASA Astrophysics Data System (ADS)

Le, Thien-Phu

2017-10-01

The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Quality of reconstruction of compressed off-axis digital holograms by frequency filtering and wavelets.

PubMed

Cheremkhin, Pavel A; Kurbatova, Ekaterina A

2018-01-01

Compression of digital holograms can significantly help with the storage of objects and data in 2D and 3D form, its transmission, and its reconstruction. Compression of standard images by methods based on wavelets allows high compression ratios (up to 20-50 times) with minimum losses of quality. In the case of digital holograms, application of wavelets directly does not allow high values of compression to be obtained. However, additional preprocessing and postprocessing can afford significant compression of holograms and the acceptable quality of reconstructed images. In this paper application of wavelet transforms for compression of off-axis digital holograms are considered. The combined technique based on zero- and twin-order elimination, wavelet compression of the amplitude and phase components of the obtained Fourier spectrum, and further additional compression of wavelet coefficients by thresholding and quantization is considered. Numerical experiments on reconstruction of images from the compressed holograms are performed. The comparative analysis of applicability of various wavelets and methods of additional compression of wavelet coefficients is performed. Optimum parameters of compression of holograms by the methods can be estimated. Sizes of holographic information were decreased up to 190 times.

Crack image segmentation based on improved DBC method

NASA Astrophysics Data System (ADS)

Cao, Ting; Yang, Nan; Wang, Fengping; Gao, Ting; Wang, Weixing

2017-11-01

With the development of computer vision technology, crack detection based on digital image segmentation method arouses global attentions among researchers and transportation ministries. Since the crack always exhibits the random shape and complex texture, it is still a challenge to accomplish reliable crack detection results. Therefore, a novel crack image segmentation method based on fractal DBC (differential box counting) is introduced in this paper. The proposed method can estimate every pixel fractal feature based on neighborhood information which can consider the contribution from all possible direction in the related block. The block moves just one pixel every time so that it could cover all the pixels in the crack image. Unlike the classic DBC method which only describes fractal feature for the related region, this novel method can effectively achieve crack image segmentation according to the fractal feature of every pixel. The experiment proves the proposed method can achieve satisfactory results in crack detection.

Wavelet entropy characterization of elevated intracranial pressure.

PubMed

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

Effect of Fractal Dimension on the Strain Behavior of Particulate Media

NASA Astrophysics Data System (ADS)

Altun, Selim; Sezer, Alper; Goktepe, A. Burak

2016-12-01

In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress-strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

Time-frequency analysis of phonocardiogram signals using wavelet transform: a comparative study.

PubMed

Ergen, Burhan; Tatar, Yetkin; Gulcur, Halil Ozcan

2012-01-01

Analysis of phonocardiogram (PCG) signals provides a non-invasive means to determine the abnormalities caused by cardiovascular system pathology. In general, time-frequency representation (TFR) methods are used to study the PCG signal because it is one of the non-stationary bio-signals. The continuous wavelet transform (CWT) is especially suitable for the analysis of non-stationary signals and to obtain the TFR, due to its high resolution, both in time and in frequency and has recently become a favourite tool. It decomposes a signal in terms of elementary contributions called wavelets, which are shifted and dilated copies of a fixed mother wavelet function, and yields a joint TFR. Although the basic characteristics of the wavelets are similar, each type of the wavelets produces a different TFR. In this study, eight real types of the most known wavelets are examined on typical PCG signals indicating heart abnormalities in order to determine the best wavelet to obtain a reliable TFR. For this purpose, the wavelet energy and frequency spectrum estimations based on the CWT and the spectra of the chosen wavelets were compared with the energy distribution and the autoregressive frequency spectra in order to determine the most suitable wavelet. The results show that Morlet wavelet is the most reliable wavelet for the time-frequency analysis of PCG signals.

Multi-resolution analysis for ear recognition using wavelet features

NASA Astrophysics Data System (ADS)

Shoaib, M.; Basit, A.; Faye, I.

2016-11-01

Security is very important and in order to avoid any physical contact, identification of human when they are moving is necessary. Ear biometric is one of the methods by which a person can be identified using surveillance cameras. Various techniques have been proposed to increase the ear based recognition systems. In this work, a feature extraction method for human ear recognition based on wavelet transforms is proposed. The proposed features are approximation coefficients and specific details of level two after applying various types of wavelet transforms. Different wavelet transforms are applied to find the suitable wavelet. Minimum Euclidean distance is used as a matching criterion. Results achieved by the proposed method are promising and can be used in real time ear recognition system.

A Hybrid Wavelet-Based Method for the Peak Detection of Photoplethysmography Signals.

PubMed

Li, Suyi; Jiang, Shanqing; Jiang, Shan; Wu, Jiang; Xiong, Wenji; Diao, Shu

2017-01-01

The noninvasive peripheral oxygen saturation (SpO 2 ) and the pulse rate can be extracted from photoplethysmography (PPG) signals. However, the accuracy of the extraction is directly affected by the quality of the signal obtained and the peak of the signal identified; therefore, a hybrid wavelet-based method is proposed in this study. Firstly, we suppressed the partial motion artifacts and corrected the baseline drift by using a wavelet method based on the principle of wavelet multiresolution. And then, we designed a quadratic spline wavelet modulus maximum algorithm to identify the PPG peaks automatically. To evaluate this hybrid method, a reflective pulse oximeter was used to acquire ten subjects' PPG signals under sitting, raising hand, and gently walking postures, and the peak recognition results on the raw signal and on the corrected signal were compared, respectively. The results showed that the hybrid method not only corrected the morphologies of the signal well but also optimized the peaks identification quality, subsequently elevating the measurement accuracy of SpO 2 and the pulse rate. As a result, our hybrid wavelet-based method profoundly optimized the evaluation of respiratory function and heart rate variability analysis.

A Hybrid Wavelet-Based Method for the Peak Detection of Photoplethysmography Signals

PubMed Central

Jiang, Shanqing; Jiang, Shan; Wu, Jiang; Xiong, Wenji

2017-01-01

The noninvasive peripheral oxygen saturation (SpO2) and the pulse rate can be extracted from photoplethysmography (PPG) signals. However, the accuracy of the extraction is directly affected by the quality of the signal obtained and the peak of the signal identified; therefore, a hybrid wavelet-based method is proposed in this study. Firstly, we suppressed the partial motion artifacts and corrected the baseline drift by using a wavelet method based on the principle of wavelet multiresolution. And then, we designed a quadratic spline wavelet modulus maximum algorithm to identify the PPG peaks automatically. To evaluate this hybrid method, a reflective pulse oximeter was used to acquire ten subjects' PPG signals under sitting, raising hand, and gently walking postures, and the peak recognition results on the raw signal and on the corrected signal were compared, respectively. The results showed that the hybrid method not only corrected the morphologies of the signal well but also optimized the peaks identification quality, subsequently elevating the measurement accuracy of SpO2 and the pulse rate. As a result, our hybrid wavelet-based method profoundly optimized the evaluation of respiratory function and heart rate variability analysis. PMID:29250135

Content Based Image Retrieval based on Wavelet Transform coefficients distribution

PubMed Central

Lamard, Mathieu; Cazuguel, Guy; Quellec, Gwénolé; Bekri, Lynda; Roux, Christian; Cochener, Béatrice

2007-01-01

In this paper we propose a content based image retrieval method for diagnosis aid in medical fields. We characterize images without extracting significant features by using distribution of coefficients obtained by building signatures from the distribution of wavelet transform. The research is carried out by computing signature distances between the query and database images. Several signatures are proposed; they use a model of wavelet coefficient distribution. To enhance results, a weighted distance between signatures is used and an adapted wavelet base is proposed. Retrieval efficiency is given for different databases including a diabetic retinopathy, a mammography and a face database. Results are promising: the retrieval efficiency is higher than 95% for some cases using an optimization process. PMID:18003013

Application of quantum-behaved particle swarm optimization to motor imagery EEG classification.

PubMed

Hsu, Wei-Yen

2013-12-01

In this study, we propose a recognition system for single-trial analysis of motor imagery (MI) electroencephalogram (EEG) data. Applying event-related brain potential (ERP) data acquired from the sensorimotor cortices, the system chiefly consists of automatic artifact elimination, feature extraction, feature selection and classification. In addition to the use of independent component analysis, a similarity measure is proposed to further remove the electrooculographic (EOG) artifacts automatically. Several potential features, such as wavelet-fractal features, are then extracted for subsequent classification. Next, quantum-behaved particle swarm optimization (QPSO) is used to select features from the feature combination. Finally, selected sub-features are classified by support vector machine (SVM). Compared with without artifact elimination, feature selection using a genetic algorithm (GA) and feature classification with Fisher's linear discriminant (FLD) on MI data from two data sets for eight subjects, the results indicate that the proposed method is promising in brain-computer interface (BCI) applications.

Design of almost symmetric orthogonal wavelet filter bank via direct optimization.

PubMed

Murugesan, Selvaraaju; Tay, David B H

2012-05-01

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Wavelets and molecular structure

NASA Astrophysics Data System (ADS)

Carson, Mike

1996-08-01

The wavelet method offers possibilities for display, editing, and topological comparison of proteins at a user-specified level of detail. Wavelets are a mathematical tool that first found application in signal processing. The multiresolution analysis of a signal via wavelets provides a hierarchical series of `best' lower-resolution approximations. B-spline ribbons model the protein fold, with one control point per residue. Wavelet analysis sets limits on the information required to define the winding of the backbone through space, suggesting a recognizable fold is generated from a number of points equal to 1/4 or less the number of residues. Wavelets applied to surfaces and volumes show promise in structure-based drug design.

Terahertz response of fractal meta-atoms based on concentric rectangular square resonators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou

We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS whilemore » blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.« less

The design and implementation of signal decomposition system of CL multi-wavelet transform based on DSP builder

NASA Astrophysics Data System (ADS)

Huang, Yan; Wang, Zhihui

2015-12-01

With the development of FPGA, DSP Builder is widely applied to design system-level algorithms. The algorithm of CL multi-wavelet is more advanced and effective than scalar wavelets in processing signal decomposition. Thus, a system of CL multi-wavelet based on DSP Builder is designed for the first time in this paper. The system mainly contains three parts: a pre-filtering subsystem, a one-level decomposition subsystem and a two-level decomposition subsystem. It can be converted into hardware language VHDL by the Signal Complier block that can be used in Quartus II. After analyzing the energy indicator, it shows that this system outperforms Daubenchies wavelet in signal decomposition. Furthermore, it has proved to be suitable for the implementation of signal fusion based on SoPC hardware, and it will become a solid foundation in this new field.

Digital transceiver implementation for wavelet packet modulation

NASA Astrophysics Data System (ADS)

Lindsey, Alan R.; Dill, Jeffrey C.

1998-03-01

Current transceiver designs for wavelet-based communication systems are typically reliant on analog waveform synthesis, however, digital processing is an important part of the eventual success of these techniques. In this paper, a transceiver implementation is introduced for the recently introduced wavelet packet modulation scheme which moves the analog processing as far as possible toward the antenna. The transceiver is based on the discrete wavelet packet transform which incorporates level and node parameters for generalized computation of wavelet packets. In this transform no particular structure is imposed on the filter bank save dyadic branching, and a maximum level which is specified a priori and dependent mainly on speed and/or cost considerations. The transmitter/receiver structure takes a binary sequence as input and, based on the desired time- frequency partitioning, processes the signal through demultiplexing, synthesis, analysis, multiplexing and data determination completely in the digital domain - with exception of conversion in and out of the analog domain for transmission.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Wavelet based detection of manatee vocalizations

NASA Astrophysics Data System (ADS)

Gur, Berke M.; Niezrecki, Christopher

2005-04-01

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.

Estimation of Handgrip Force from SEMG Based on Wavelet Scale Selection.

PubMed

Wang, Kai; Zhang, Xianmin; Ota, Jun; Huang, Yanjiang

2018-02-24

This paper proposes a nonlinear correlation-based wavelet scale selection technology to select the effective wavelet scales for the estimation of handgrip force from surface electromyograms (SEMG). The SEMG signal corresponding to gripping force was collected from extensor and flexor forearm muscles during the force-varying analysis task. We performed a computational sensitivity analysis on the initial nonlinear SEMG-handgrip force model. To explore the nonlinear correlation between ten wavelet scales and handgrip force, a large-scale iteration based on the Monte Carlo simulation was conducted. To choose a suitable combination of scales, we proposed a rule to combine wavelet scales based on the sensitivity of each scale and selected the appropriate combination of wavelet scales based on sequence combination analysis (SCA). The results of SCA indicated that the scale combination VI is suitable for estimating force from the extensors and the combination V is suitable for the flexors. The proposed method was compared to two former methods through prolonged static and force-varying contraction tasks. The experiment results showed that the root mean square errors derived by the proposed method for both static and force-varying contraction tasks were less than 20%. The accuracy and robustness of the handgrip force derived by the proposed method is better than that obtained by the former methods.

An efficient coding algorithm for the compression of ECG signals using the wavelet transform.

PubMed

Rajoub, Bashar A

2002-04-01

A wavelet-based electrocardiogram (ECG) data compression algorithm is proposed in this paper. The ECG signal is first preprocessed, the discrete wavelet transform (DWT) is then applied to the preprocessed signal. Preprocessing guarantees that the magnitudes of the wavelet coefficients be less than one, and reduces the reconstruction errors near both ends of the compressed signal. The DWT coefficients are divided into three groups, each group is thresholded using a threshold based on a desired energy packing efficiency. A binary significance map is then generated by scanning the wavelet decomposition coefficients and outputting a binary one if the scanned coefficient is significant, and a binary zero if it is insignificant. Compression is achieved by 1) using a variable length code based on run length encoding to compress the significance map and 2) using direct binary representation for representing the significant coefficients. The ability of the coding algorithm to compress ECG signals is investigated, the results were obtained by compressing and decompressing the test signals. The proposed algorithm is compared with direct-based and wavelet-based compression algorithms and showed superior performance. A compression ratio of 24:1 was achieved for MIT-BIH record 117 with a percent root mean square difference as low as 1.08%.

An innovative approach for characteristic analysis and state-of-health diagnosis for a Li-ion cell based on the discrete wavelet transform

NASA Astrophysics Data System (ADS)

Kim, Jonghoon; Cho, B. H.

2014-08-01

This paper introduces an innovative approach to analyze electrochemical characteristics and state-of-health (SOH) diagnosis of a Li-ion cell based on the discrete wavelet transform (DWT). In this approach, the DWT has been applied as a powerful tool in the analysis of the discharging/charging voltage signal (DCVS) with non-stationary and transient phenomena for a Li-ion cell. Specifically, DWT-based multi-resolution analysis (MRA) is used for extracting information on the electrochemical characteristics in both time and frequency domain simultaneously. Through using the MRA with implementation of the wavelet decomposition, the information on the electrochemical characteristics of a Li-ion cell can be extracted from the DCVS over a wide frequency range. Wavelet decomposition based on the selection of the order 3 Daubechies wavelet (dB3) and scale 5 as the best wavelet function and the optimal decomposition scale is implemented. In particular, this present approach develops these investigations one step further by showing low and high frequency components (approximation component An and detail component Dn, respectively) extracted from variable Li-ion cells with different electrochemical characteristics caused by aging effect. Experimental results show the clearness of the DWT-based approach for the reliable diagnosis of the SOH for a Li-ion cell.

An Automated Parallel Image Registration Technique Based on the Correlation of Wavelet Features

NASA Technical Reports Server (NTRS)

LeMoigne, Jacqueline; Campbell, William J.; Cromp, Robert F.; Zukor, Dorothy (Technical Monitor)

2001-01-01

With the increasing importance of multiple platform/multiple remote sensing missions, fast and automatic integration of digital data from disparate sources has become critical to the success of these endeavors. Our work utilizes maxima of wavelet coefficients to form the basic features of a correlation-based automatic registration algorithm. Our wavelet-based registration algorithm is tested successfully with data from the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) and the Landsat/Thematic Mapper(TM), which differ by translation and/or rotation. By the choice of high-frequency wavelet features, this method is similar to an edge-based correlation method, but by exploiting the multi-resolution nature of a wavelet decomposition, our method achieves higher computational speeds for comparable accuracies. This algorithm has been implemented on a Single Instruction Multiple Data (SIMD) massively parallel computer, the MasPar MP-2, as well as on the CrayT3D, the Cray T3E and a Beowulf cluster of Pentium workstations.

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

PubMed Central

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

Evidence of diffusive fractal aggregation of TiO2 nanoparticles by femtosecond laser ablation at ambient conditions

NASA Astrophysics Data System (ADS)

Celardo, G. L.; Archetti, D.; Ferrini, G.; Gavioli, L.; Pingue, P.; Cavaliere, E.

2017-01-01

The specific mechanisms which lead to the formation of fractal nanostructures by pulsed laser deposition remain elusive despite intense research efforts, motivated mainly by the technological interest in obtaining tailored nanostructures with simple and scalable production methods. Here we focus on fractal nanostructures of titanium dioxide, TiO2, a strategic material for many applications, obtained by femtosecond laser ablation at ambient conditions. We compare a theoretical model of fractal formation with experimental data. The comparison of theory and experiment confirms that fractal aggregates are formed after landing of the ablated material on the substrate surface by a simple diffusive mechanism. We model the fractal formation through extensive Monte Carlo simulations based on a set of minimal assumptions: TiO2 nanoparticles arrive already formed on the substrate, then they diffuse in a size/mass independent way and stick irreversibly upon touching, thus forming fractal clusters. Despite its simplicity, our model explains the main features of the fractal structures arising from the complex interaction of large TiO2 nanoparticles with different substrates. Indeed our model is able to reproduce both the fractal dimensions and the area distributions of the nanostructures for different densities of the ablated material. Finally we discuss the role of the thermal conductivity of the substrate and the laser fluence on the properties of the fractal nanostructures. Our results represent an advancement towards controlling the production of fractal nanostructures by pulsed laser deposition.

Multidimensional, mapping-based complex wavelet transforms.

PubMed

Fernandes, Felix C A; van Spaendonck, Rutger L C; Burrus, C Sidney

2005-01-01

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3M - 1)/(2M - 1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.

Phase synchronization based on a Dual-Tree Complex Wavelet Transform

NASA Astrophysics Data System (ADS)

Ferreira, Maria Teodora; Domingues, Margarete Oliveira; Macau, Elbert E. N.

2016-11-01

In this work, we show the applicability of our Discrete Complex Wavelet Approach (DCWA) to verify the phenomenon of phase synchronization transition in two coupled chaotic Lorenz systems. DCWA is based on the phase assignment from complex wavelet coefficients obtained by using a Dual-Tree Complex Wavelet Transform (DT-CWT). We analyzed two coupled chaotic Lorenz systems, aiming to detect the transition from non-phase synchronization to phase synchronization. In addition, we check how good is the method in detecting periods of 2π phase-slips. In all experiments, DCWA is compared with classical phase detection methods such as the ones based on arctangent and Hilbert transform showing a much better performance.

Fractal continuum model for tracer transport in a porous medium.

PubMed

Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

2013-12-01

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wang, Heming; Liu, Yu; Song, Yongchen; Zhao, Yuechao; Zhao, Jiafei; Wang, Dayong

2012-11-01

Pore structure is one of important factors affecting the properties of porous media, but it is difficult to describe the complexity of pore structure exactly. Fractal theory is an effective and available method for quantifying the complex and irregular pore structure. In this paper, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores. The microstructure or pore distribution in the porous material was obtained using the nuclear magnetic resonance imaging (MRI). Three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis. To avoid the influence of box sizes, a sequence of divisors of the image was proposed and compared with other two algorithms (geometric sequence and arithmetic sequence) with its performance of partitioning the image completely and bringing the least fitted error. Threshold value selected manually and automatically showed that it plays an important role during the image binary processing and the minimum-error method can be used to obtain an appropriate or reasonable one. Images obtained under different pixel matrices in MRI were used to analyze the influence of image resolution. Higher image resolution can detect more quantity of pore structure and increase its irregularity. With benefits of those influence factors, fractal analysis on four kinds of artificial cores showed the fractal dimension can be used to distinguish the different kinds of artificial cores and the relationship between fractal dimension and porosity or permeability can be expressed by the model of D = a - bln(x + c).

Denoising embolic Doppler ultrasound signals using Dual Tree Complex Discrete Wavelet Transform.

PubMed

Serbes, Gorkem; Aydin, Nizamettin

2010-01-01

Early and accurate detection of asymptomatic emboli is important for monitoring of preventive therapy in stroke-prone patients. One of the problems in detection of emboli is the identification of an embolic signal caused by very small emboli. The amplitude of the embolic signal may be so small that advanced processing methods are required to distinguish these signals from Doppler signals arising from red blood cells. In this study instead of conventional discrete wavelet transform, the Dual Tree Complex Discrete Wavelet Transform was used for denoising embolic signals. Performances of both approaches were compared. Unlike the conventional discrete wavelet transform discrete complex wavelet transform is a shift invariant transform with limited redundancy. Results demonstrate that the Dual Tree Complex Discrete Wavelet Transform based denoising outperforms conventional discrete wavelet denoising. Approximately 8 dB improvement is obtained by using the Dual Tree Complex Discrete Wavelet Transform compared to the improvement provided by the conventional Discrete Wavelet Transform (less than 5 dB).

Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

Thanks to some recent research works, dynamic Bayesian wavelet transform as new methodology for extraction of repetitive transients is proposed in this short communication to reveal fault signatures hidden in rotating machine. The main idea of the dynamic Bayesian wavelet transform is to iteratively estimate posterior parameters of wavelet transform via artificial observations and dynamic Bayesian inference. First, a prior wavelet parameter distribution can be established by one of many fast detection algorithms, such as the fast kurtogram, the improved kurtogram, the enhanced kurtogram, the sparsogram, the infogram, continuous wavelet transform, discrete wavelet transform, wavelet packets, multiwavelets, empirical wavelet transform, empirical mode decomposition, local mean decomposition, etc.. Second, artificial observations can be constructed based on one of many metrics, such as kurtosis, the sparsity measurement, entropy, approximate entropy, the smoothness index, a synthesized criterion, etc., which are able to quantify repetitive transients. Finally, given artificial observations, the prior wavelet parameter distribution can be posteriorly updated over iterations by using dynamic Bayesian inference. More importantly, the proposed new methodology can be extended to establish the optimal parameters required by many other signal processing methods for extraction of repetitive transients.

The application of super wavelet finite element on temperature-pressure coupled field simulation of LPG tank under jet fire

NASA Astrophysics Data System (ADS)

Zhao, Bin

2015-02-01

Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.

Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

NASA Astrophysics Data System (ADS)

Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu

2017-06-01

Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing data and it is helpful to analyze the observation scale from different aspects. This research will ultimately benefit for remote sensing data selection and application.

Fractal dimension based damage identification incorporating multi-task sparse Bayesian learning

NASA Astrophysics Data System (ADS)

Huang, Yong; Li, Hui; Wu, Stephen; Yang, Yongchao

2018-07-01

Sensitivity to damage and robustness to noise are critical requirements for the effectiveness of structural damage detection. In this study, a two-stage damage identification method based on the fractal dimension analysis and multi-task Bayesian learning is presented. The Higuchi’s fractal dimension (HFD) based damage index is first proposed, directly examining the time-frequency characteristic of local free vibration data of structures based on the irregularity sensitivity and noise robustness analysis of HFD. Katz’s fractal dimension is then presented to analyze the abrupt irregularity change of the spatial curve of the displacement mode shape along the structure. At the second stage, the multi-task sparse Bayesian learning technique is employed to infer the final damage localization vector, which borrow the dependent strength of the two fractal dimension based damage indication information and also incorporate the prior knowledge that structural damage occurs at a limited number of locations in a structure in the absence of its collapse. To validate the capability of the proposed method, a steel beam and a bridge, named Yonghe Bridge, are analyzed as illustrative examples. The damage identification results demonstrate that the proposed method is capable of localizing single and multiple damages regardless of its severity, and show superior robustness under heavy noise as well.

Intelligent Gearbox Diagnosis Methods Based on SVM, Wavelet Lifting and RBR

PubMed Central

Gao, Lixin; Ren, Zhiqiang; Tang, Wenliang; Wang, Huaqing; Chen, Peng

2010-01-01

Given the problems in intelligent gearbox diagnosis methods, it is difficult to obtain the desired information and a large enough sample size to study; therefore, we propose the application of various methods for gearbox fault diagnosis, including wavelet lifting, a support vector machine (SVM) and rule-based reasoning (RBR). In a complex field environment, it is less likely for machines to have the same fault; moreover, the fault features can also vary. Therefore, a SVM could be used for the initial diagnosis. First, gearbox vibration signals were processed with wavelet packet decomposition, and the signal energy coefficients of each frequency band were extracted and used as input feature vectors in SVM for normal and faulty pattern recognition. Second, precision analysis using wavelet lifting could successfully filter out the noisy signals while maintaining the impulse characteristics of the fault; thus effectively extracting the fault frequency of the machine. Lastly, the knowledge base was built based on the field rules summarized by experts to identify the detailed fault type. Results have shown that SVM is a powerful tool to accomplish gearbox fault pattern recognition when the sample size is small, whereas the wavelet lifting scheme can effectively extract fault features, and rule-based reasoning can be used to identify the detailed fault type. Therefore, a method that combines SVM, wavelet lifting and rule-based reasoning ensures effective gearbox fault diagnosis. PMID:22399894

Intelligent gearbox diagnosis methods based on SVM, wavelet lifting and RBR.

PubMed

Gao, Lixin; Ren, Zhiqiang; Tang, Wenliang; Wang, Huaqing; Chen, Peng

2010-01-01

Given the problems in intelligent gearbox diagnosis methods, it is difficult to obtain the desired information and a large enough sample size to study; therefore, we propose the application of various methods for gearbox fault diagnosis, including wavelet lifting, a support vector machine (SVM) and rule-based reasoning (RBR). In a complex field environment, it is less likely for machines to have the same fault; moreover, the fault features can also vary. Therefore, a SVM could be used for the initial diagnosis. First, gearbox vibration signals were processed with wavelet packet decomposition, and the signal energy coefficients of each frequency band were extracted and used as input feature vectors in SVM for normal and faulty pattern recognition. Second, precision analysis using wavelet lifting could successfully filter out the noisy signals while maintaining the impulse characteristics of the fault; thus effectively extracting the fault frequency of the machine. Lastly, the knowledge base was built based on the field rules summarized by experts to identify the detailed fault type. Results have shown that SVM is a powerful tool to accomplish gearbox fault pattern recognition when the sample size is small, whereas the wavelet lifting scheme can effectively extract fault features, and rule-based reasoning can be used to identify the detailed fault type. Therefore, a method that combines SVM, wavelet lifting and rule-based reasoning ensures effective gearbox fault diagnosis.

Texture, microstructure, and fractal features of the low-cycle fatigue failure of the metal in pipeline welded joints

NASA Astrophysics Data System (ADS)

Usov, V. V.; Gopkalo, E. E.; Shkatulyak, N. M.; Gopkalo, A. P.; Cherneva, T. S.

2015-09-01

Crystallographic texture and fracture features are studied after low-cycle fatigue tests of laboratory specimens cut from the base metal and the characteristic zones of a welded joint in a pipeline after its longterm operation. The fractal dimensions of fracture surfaces are determined. The fractal dimension is shown to increase during the transition from ductile to quasi-brittle fracture, and a relation between the fractal dimension of a fracture surface and the fatigue life of the specimen is found.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling.

PubMed

Dinov, Ivo D; Boscardin, John W; Mega, Michael S; Sowell, Elizabeth L; Toga, Arthur W

2005-01-01

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

Research on artificial neural network intrusion detection photochemistry based on the improved wavelet analysis and transformation

NASA Astrophysics Data System (ADS)

Li, Hong; Ding, Xue

2017-03-01

This paper combines wavelet analysis and wavelet transform theory with artificial neural network, through the pretreatment on point feature attributes before in intrusion detection, to make them suitable for improvement of wavelet neural network. The whole intrusion classification model gets the better adaptability, self-learning ability, greatly enhances the wavelet neural network for solving the problem of field detection invasion, reduces storage space, contributes to improve the performance of the constructed neural network, and reduces the training time. Finally the results of the KDDCup99 data set simulation experiment shows that, this method reduces the complexity of constructing wavelet neural network, but also ensures the accuracy of the intrusion classification.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

PubMed

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

An Intelligent Pattern Recognition System Based on Neural Network and Wavelet Decomposition for Interpretation of Heart Sounds

DTIC Science & Technology

2001-10-25

wavelet decomposition of signals and classification using neural network. Inputs to the system are the heart sound signals acquired by a stethoscope in a...Proceedings. pp. 415–418, 1990. [3] G. Ergun, “An intelligent diagnostic system for interpretation of arterpartum fetal heart rate tracings based on ANNs and...AN INTELLIGENT PATTERN RECOGNITION SYSTEM BASED ON NEURAL NETWORK AND WAVELET DECOMPOSITION FOR INTERPRETATION OF HEART SOUNDS I. TURKOGLU1, A

A spectrum fractal feature classification algorithm for agriculture crops with hyper spectrum image

NASA Astrophysics Data System (ADS)

Su, Junying

2011-11-01

A fractal dimension feature analysis method in spectrum domain for hyper spectrum image is proposed for agriculture crops classification. Firstly, a fractal dimension calculation algorithm in spectrum domain is presented together with the fast fractal dimension value calculation algorithm using the step measurement method. Secondly, the hyper spectrum image classification algorithm and flowchart is presented based on fractal dimension feature analysis in spectrum domain. Finally, the experiment result of the agricultural crops classification with FCL1 hyper spectrum image set with the proposed method and SAM (spectral angle mapper). The experiment results show it can obtain better classification result than the traditional SAM feature analysis which can fulfill use the spectrum information of hyper spectrum image to realize precision agricultural crops classification.

Self-organized network of fractal-shaped components coupled through statistical interaction.

PubMed

Ugajin, R

2001-09-01

A dissipative dynamics is introduced to generate self-organized networks of interacting objects, which we call coupled-fractal networks. The growth model is constructed based on a growth hypothesis in which the growth rate of each object is a product of the probability of receiving source materials from faraway and the probability of receiving adhesives from other grown objects, where each object grows to be a random fractal if isolated, but connects with others if glued. The network is governed by the statistical interaction between fractal-shaped components, which can only be identified in a statistical manner over ensembles. This interaction is investigated using the degree of correlation between fractal-shaped components, enabling us to determine whether it is attractive or repulsive.

Distributed Compressive Sensing

DTIC Science & Technology

2009-01-01

example, smooth signals are sparse in the Fourier basis, and piecewise smooth signals are sparse in a wavelet basis [8]; the commercial coding standards MP3...including wavelets [8], Gabor bases [8], curvelets [35], etc., are widely used for representation and compression of natural signals, images, and...spikes and the sine waves of a Fourier basis, or the Fourier basis and wavelets . Signals that are sparsely represented in frames or unions of bases can

Wavelet-Based Signal and Image Processing for Target Recognition

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.

2002-11-01

The PI visited NSWC Dahlgren, VA, for six weeks in May-June 2002 and collaborated with scientists in the G33 TEAMS facility, and with Marilyn Rudzinsky of T44 Technology and Photonic Systems Branch. During this visit the PI also presented six educational seminars to NSWC scientists on various aspects of signal processing. Several items from the grant proposal were completed, including (1) wavelet-based algorithms for interpolation of 1-d signals and 2-d images; (2) Discrete Wavelet Transform domain based algorithms for filtering of image data; (3) wavelet-based smoothing of image sequence data originally obtained for the CRITTIR (Clutter Rejection Involving Temporal Techniques in the Infra-Red) project. The PI visited the University of Stellenbosch, South Africa to collaborate with colleagues Prof. B.M. Herbst and Prof. J. du Preez on the use of wavelet image processing in conjunction with pattern recognition techniques. The University of Stellenbosch has offered the PI partial funding to support a sabbatical visit in Fall 2003, the primary purpose of which is to enable the PI to develop and enhance his expertise in Pattern Recognition. During the first year, the grant supported publication of 3 referred papers, presentation of 9 seminars and an intensive two-day course on wavelet theory. The grant supported the work of two students who functioned as research assistants.

Short-term data forecasting based on wavelet transformation and chaos theory

NASA Astrophysics Data System (ADS)

Wang, Yi; Li, Cunbin; Zhang, Liang

2017-09-01

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Wavelet analysis for wind fields estimation.

PubMed

Leite, Gladeston C; Ushizima, Daniela M; Medeiros, Fátima N S; de Lima, Gilson G

2010-01-01

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B(3) spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms(-1). Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms.

Wavelet Transform Based Filter to Remove the Notches from Signal Under Harmonic Polluted Environment

NASA Astrophysics Data System (ADS)

Das, Sukanta; Ranjan, Vikash

2017-12-01

The work proposes to annihilate the notches present in the synchronizing signal required for converter operation appearing due to switching of semiconductor devices connected to the system in the harmonic polluted environment. The disturbances in the signal are suppressed by wavelet based novel filtering technique. In the proposed technique, the notches in the signal are determined and eliminated by the wavelet based multi-rate filter using `Daubechies4' (db4) as mother wavelet. The computational complexity of the adapted technique is very less as compared to any other conventional notch filtering techniques. The proposed technique is developed in MATLAB/Simulink and finally validated with dSPACE-1103 interface. The recovered signal, thus obtained, is almost free of the notches.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

The Generalization of Rook Number r2 for the Fractal Chessboard

NASA Astrophysics Data System (ADS)

Sangeetha, R.; Jayalalitha, G.

2018-04-01

In this paper we develop a generalized formula of r 2, the number of ways of placing two non-attacking Rooks for the Fractal Chessboard which is defined as a board that grows progressively in a consistent manner using a 2 × 2 chessboard to its sides and corners. The board is disintegrated into small sub boards based on their position in the whole Fractal Chessboard (FC). The board is disintegrated into sub boards based on their position in the whole board FC. By finding the value of r 2 for each of these sub boards and adding them, the r 2 value of the whole board FC is obtained. Finally the r 2 value is generalized the Fractal Chessboard at any iteration I ≥ 4 .

ICER-3D: A Progressive Wavelet-Based Compressor for Hyperspectral Images

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.; Xie, H.; Aranki, N.

2005-01-01

ICER-3D is a progressive, wavelet-based compressor for hyperspectral images. ICER-3D is derived from the ICER image compressor. ICER-3D can provide lossless and lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The three-dimensional wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of hyperspectral data sets, while facilitating elimination of spectral ringing artifacts. Correlation is further exploited by a context modeler that effectively exploits spectral dependencies in the wavelet-transformed hyperspectral data. Performance results illustrating the benefits of these features are presented.

Objective research of auscultation signals in Traditional Chinese Medicine based on wavelet packet energy and support vector machine.

PubMed

Yan, Jianjun; Shen, Xiaojing; Wang, Yiqin; Li, Fufeng; Xia, Chunming; Guo, Rui; Chen, Chunfeng; Shen, Qingwei

2010-01-01

This study aims at utilising Wavelet Packet Transform (WPT) and Support Vector Machine (SVM) algorithm to make objective analysis and quantitative research for the auscultation in Traditional Chinese Medicine (TCM) diagnosis. First, Wavelet Packet Decomposition (WPD) at level 6 was employed to split more elaborate frequency bands of the auscultation signals. Then statistic analysis was made based on the extracted Wavelet Packet Energy (WPE) features from WPD coefficients. Furthermore, the pattern recognition was used to distinguish mixed subjects' statistical feature values of sample groups through SVM. Finally, the experimental results showed that the classification accuracies were at a high level.

Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

NASA Astrophysics Data System (ADS)

Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander

2010-01-01

A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/rD∝r-D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A `box-counting' procedure could also be applied giving the `capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term `fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis. The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are:—Simple way to quantify scale-invariant distributions of complex objects or phenomena by a small number of parameters.—It is becoming evident that the applicability of fractal distributions to geological problems could have a more fundamental basis. Chaotic behaviour could underlay the geotectonic processes and the applicable statistics could often be fractal. The application of fractal distribution analysis has, however, some specific aspects. It is usually difficult to present an adequate interpretation of the obtained values of fractal coefficients for earthquake epicenter or hypocenter distributions. That is why in this paper we aimed at other goals—to verify how a fractal coefficient depends on different spatial distributions. We simulated earthquake spatial data by generating randomly points first in a 3D space - cube, then in a parallelepiped, diminishing one of its sides. We then continued this procedure in 2D and 1D space. For each simulated data set we calculated the points' fractal coefficient (correlation fractal dimension of epicentres) and then checked for correlation between the coefficients values and the type of spatial distribution. In that way one can obtain a set of standard fractal coefficients' values for varying spatial distributions. These then can be used when real earthquake data is analyzed by comparing the real data coefficients values to the standard fractal coefficients. Such an approach can help in interpreting the fractal analysis results through different types of spatial distributions.

Alcoholism detection in magnetic resonance imaging by Haar wavelet transform and back propagation neural network

NASA Astrophysics Data System (ADS)

Yu, Yali; Wang, Mengxia; Lima, Dimas

2018-04-01

In order to develop a novel alcoholism detection method, we proposed a magnetic resonance imaging (MRI)-based computer vision approach. We first use contrast equalization to increase the contrast of brain slices. Then, we perform Haar wavelet transform and principal component analysis. Finally, we use back propagation neural network (BPNN) as the classification tool. Our method yields a sensitivity of 81.71±4.51%, a specificity of 81.43±4.52%, and an accuracy of 81.57±2.18%. The Haar wavelet gives better performance than db4 wavelet and sym3 wavelet.

Wavelet-based polarimetry analysis

NASA Astrophysics Data System (ADS)

Ezekiel, Soundararajan; Harrity, Kyle; Farag, Waleed; Alford, Mark; Ferris, David; Blasch, Erik

2014-06-01

Wavelet transformation has become a cutting edge and promising approach in the field of image and signal processing. A wavelet is a waveform of effectively limited duration that has an average value of zero. Wavelet analysis is done by breaking up the signal into shifted and scaled versions of the original signal. The key advantage of a wavelet is that it is capable of revealing smaller changes, trends, and breakdown points that are not revealed by other techniques such as Fourier analysis. The phenomenon of polarization has been studied for quite some time and is a very useful tool for target detection and tracking. Long Wave Infrared (LWIR) polarization is beneficial for detecting camouflaged objects and is a useful approach when identifying and distinguishing manmade objects from natural clutter. In addition, the Stokes Polarization Parameters, which are calculated from 0°, 45°, 90°, 135° right circular, and left circular intensity measurements, provide spatial orientations of target features and suppress natural features. In this paper, we propose a wavelet-based polarimetry analysis (WPA) method to analyze Long Wave Infrared Polarimetry Imagery to discriminate targets such as dismounts and vehicles from background clutter. These parameters can be used for image thresholding and segmentation. Experimental results show the wavelet-based polarimetry analysis is efficient and can be used in a wide range of applications such as change detection, shape extraction, target recognition, and feature-aided tracking.

Quantitative assessment of early diabetic retinopathy using fractal analysis.

PubMed

Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

2009-01-01

Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

Acoustic emission detection for mass fractions of materials based on wavelet packet technology.

PubMed

Wang, Xianghong; Xiang, Jianjun; Hu, Hongwei; Xie, Wei; Li, Xiongbing

2015-07-01

Materials are often damaged during the process of detecting mass fractions by traditional methods. Acoustic emission (AE) technology combined with wavelet packet analysis is used to evaluate the mass fractions of microcrystalline graphite/polyvinyl alcohol (PVA) composites in this study. Attenuation characteristics of AE signals across the composites with different mass fractions are investigated. The AE signals are decomposed by wavelet packet technology to obtain the relationships between the energy and amplitude attenuation coefficients of feature wavelet packets and mass fractions as well. Furthermore, the relationship is validated by a sample. The larger proportion of microcrystalline graphite will correspond to the higher attenuation of energy and amplitude. The attenuation characteristics of feature wavelet packets with the frequency range from 125 kHz to 171.85 kHz are more suitable for the detection of mass fractions than those of the original AE signals. The error of the mass fraction of microcrystalline graphite calculated by the feature wavelet packet (1.8%) is lower than that of the original signal (3.9%). Therefore, AE detection base on wavelet packet analysis is an ideal NDT method for evaluate mass fractions of composite materials. Copyright © 2015 Elsevier B.V. All rights reserved.

Wavelet SVM in Reproducing Kernel Hilbert Space for hyperspectral remote sensing image classification

NASA Astrophysics Data System (ADS)

Du, Peijun; Tan, Kun; Xing, Xiaoshi

2010-12-01

Combining Support Vector Machine (SVM) with wavelet analysis, we constructed wavelet SVM (WSVM) classifier based on wavelet kernel functions in Reproducing Kernel Hilbert Space (RKHS). In conventional kernel theory, SVM is faced with the bottleneck of kernel parameter selection which further results in time-consuming and low classification accuracy. The wavelet kernel in RKHS is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. Implications on semiparametric estimation are proposed in this paper. Airborne Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing image with 64 bands and Reflective Optics System Imaging Spectrometer (ROSIS) data with 115 bands were used to experiment the performance and accuracy of the proposed WSVM classifier. The experimental results indicate that the WSVM classifier can obtain the highest accuracy when using the Coiflet Kernel function in wavelet transform. In contrast with some traditional classifiers, including Spectral Angle Mapping (SAM) and Minimum Distance Classification (MDC), and SVM classifier using Radial Basis Function kernel, the proposed wavelet SVM classifier using the wavelet kernel function in Reproducing Kernel Hilbert Space is capable of improving classification accuracy obviously.

Onboard image compression schemes for modular airborne imaging spectrometer (MAIS) based on wavelet transform

NASA Astrophysics Data System (ADS)

Zhu, Zhenyu; Wang, Jianyu

1996-11-01

In this paper, two compression schemes are presented to meet the urgent needs of compressing the huge volume and high data rate of imaging spectrometer images. According to the multidimensional feature of the images and the high fidelity requirement of the reconstruction, both schemes were devised to exploit the high redundancy in both spatial and spectral dimension based on the mature wavelet transform technology. Wavelet transform was applied here in two ways: First, with the spatial wavelet transform and the spectral DPCM decorrelation, a ratio up to 84.3 with PSNR > 48db's near-lossless result was attained. This is based ont he fact that the edge structure among all the spectral bands are similar while WT has higher resolution in high frequency components. Secondly, with the wavelet's high efficiency in processing the 'wideband transient' signals, it was used to transform the raw nonstationary signals in the spectral dimension. A good result was also attained.

Block-based scalable wavelet image codec

NASA Astrophysics Data System (ADS)

Bao, Yiliang; Kuo, C.-C. Jay

1999-10-01

This paper presents a high performance block-based wavelet image coder which is designed to be of very low implementational complexity yet with rich features. In this image coder, the Dual-Sliding Wavelet Transform (DSWT) is first applied to image data to generate wavelet coefficients in fixed-size blocks. Here, a block only consists of wavelet coefficients from a single subband. The coefficient blocks are directly coded with the Low Complexity Binary Description (LCBiD) coefficient coding algorithm. Each block is encoded using binary context-based bitplane coding. No parent-child correlation is exploited in the coding process. There is also no intermediate buffering needed in between DSWT and LCBiD. The compressed bit stream generated by the proposed coder is both SNR and resolution scalable, as well as highly resilient to transmission errors. Both DSWT and LCBiD process the data in blocks whose size is independent of the size of the original image. This gives more flexibility in the implementation. The codec has a very good coding performance even the block size is (16,16).

Analysis of embolic signals with directional dual tree rational dilation wavelet transform.

PubMed

Serbes, Gorkem; Aydin, Nizamettin

2016-08-01

The dyadic discrete wavelet transform (dyadic-DWT), which is based on fixed integer sampling factor, has been used before for processing piecewise smooth biomedical signals. However, the dyadic-DWT has poor frequency resolution due to the low-oscillatory nature of its wavelet bases and therefore, it is less effective in processing embolic signals (ESs). To process ESs more effectively, a wavelet transform having better frequency resolution than the dyadic-DWT is needed. Therefore, in this study two ESs, containing micro-emboli and artifact waveforms, are analyzed with the Directional Dual Tree Rational-Dilation Wavelet Transform (DDT-RADWT). The DDT-RADWT, which can be directly applied to quadrature signals, is based on rational dilation factors and has adjustable frequency resolution. The analyses are done for both low and high Q-factors. It is proved that, when high Q-factor filters are employed in the DDT-RADWT, clearer representations of ESs can be attained in decomposed sub-bands and artifacts can be successfully separated.

Simultaneous compression and encryption for secure real-time secure transmission of sensitive video transmission

NASA Astrophysics Data System (ADS)

Al-Hayani, Nazar; Al-Jawad, Naseer; Jassim, Sabah A.

2014-05-01

Video compression and encryption became very essential in a secured real time video transmission. Applying both techniques simultaneously is one of the challenges where the size and the quality are important in multimedia transmission. In this paper we proposed a new technique for video compression and encryption. Both encryption and compression are based on edges extracted from the high frequency sub-bands of wavelet decomposition. The compression algorithm based on hybrid of: discrete wavelet transforms, discrete cosine transform, vector quantization, wavelet based edge detection, and phase sensing. The compression encoding algorithm treats the video reference and non-reference frames in two different ways. The encryption algorithm utilized A5 cipher combined with chaotic logistic map to encrypt the significant parameters and wavelet coefficients. Both algorithms can be applied simultaneously after applying the discrete wavelet transform on each individual frame. Experimental results show that the proposed algorithms have the following features: high compression, acceptable quality, and resistance to the statistical and bruteforce attack with low computational processing.

Spectral information enhancement using wavelet-based iterative filtering for in vivo gamma spectrometry.

PubMed

Paul, Sabyasachi; Sarkar, P K

2013-04-01

Use of wavelet transformation in stationary signal processing has been demonstrated for denoising the measured spectra and characterisation of radionuclides in the in vivo monitoring analysis, where difficulties arise due to very low activity level to be estimated in biological systems. The large statistical fluctuations often make the identification of characteristic gammas from radionuclides highly uncertain, particularly when interferences from progenies are also present. A new wavelet-based noise filtering methodology has been developed for better detection of gamma peaks in noisy data. This sequential, iterative filtering method uses the wavelet multi-resolution approach for noise rejection and an inverse transform after soft 'thresholding' over the generated coefficients. Analyses of in vivo monitoring data of (235)U and (238)U were carried out using this method without disturbing the peak position and amplitude while achieving a 3-fold improvement in the signal-to-noise ratio, compared with the original measured spectrum. When compared with other data-filtering techniques, the wavelet-based method shows the best results.

Gait recognition based on Gabor wavelets and modified gait energy image for human identification

NASA Astrophysics Data System (ADS)

Huang, Deng-Yuan; Lin, Ta-Wei; Hu, Wu-Chih; Cheng, Chih-Hsiang

2013-10-01

This paper proposes a method for recognizing human identity using gait features based on Gabor wavelets and modified gait energy images (GEIs). Identity recognition by gait generally involves gait representation, extraction, and classification. In this work, a modified GEI convolved with an ensemble of Gabor wavelets is proposed as a gait feature. Principal component analysis is then used to project the Gabor-wavelet-based gait features into a lower-dimension feature space for subsequent classification. Finally, support vector machine classifiers based on a radial basis function kernel are trained and utilized to recognize human identity. The major contributions of this paper are as follows: (1) the consideration of the shadow effect to yield a more complete segmentation of gait silhouettes; (2) the utilization of motion estimation to track people when walkers overlap; and (3) the derivation of modified GEIs to extract more useful gait information. Extensive performance evaluation shows a great improvement of recognition accuracy due to the use of shadow removal, motion estimation, and gait representation using the modified GEIs and Gabor wavelets.

Fractal-based wideband invisibility cloak

NASA Astrophysics Data System (ADS)

Cohen, Nathan; Okoro, Obinna; Earle, Dan; Salkind, Phil; Unger, Barry; Yen, Sean; McHugh, Daniel; Polterzycki, Stefan; Shelman-Cohen, A. J.

2015-03-01

A wideband invisibility cloak (IC) at microwave frequencies is described. Using fractal resonators in closely spaced (sub wavelength) arrays as a minimal number of cylindrical layers (rings), the IC demonstrates that it is physically possible to attain a `see through' cloaking device with: (a) wideband coverage; (b) simple and attainable fabrication; (c) high fidelity emulation of the free path; (d) minimal side scattering; (d) a near absence of shadowing in the scattering. Although not a practical device, this fractal-enabled technology demonstrator opens up new opportunities for diverted-image (DI) technology and use of fractals in wideband optical, infrared, and microwave applications.

Noise adaptive wavelet thresholding for speckle noise removal in optical coherence tomography.

PubMed

Zaki, Farzana; Wang, Yahui; Su, Hao; Yuan, Xin; Liu, Xuan

2017-05-01

Optical coherence tomography (OCT) is based on coherence detection of interferometric signals and hence inevitably suffers from speckle noise. To remove speckle noise in OCT images, wavelet domain thresholding has demonstrated significant advantages in suppressing noise magnitude while preserving image sharpness. However, speckle noise in OCT images has different characteristics in different spatial scales, which has not been considered in previous applications of wavelet domain thresholding. In this study, we demonstrate a noise adaptive wavelet thresholding (NAWT) algorithm that exploits the difference of noise characteristics in different wavelet sub-bands. The algorithm is simple, fast, effective and is closely related to the physical origin of speckle noise in OCT image. Our results demonstrate that NAWT outperforms conventional wavelet thresholding.

A simple method for estimating the size of nuclei on fractal surfaces

NASA Astrophysics Data System (ADS)

Zeng, Qiang

2017-10-01

Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

Analysis on Behaviour of Wavelet Coefficient during Fault Occurrence in Transformer

NASA Astrophysics Data System (ADS)

Sreewirote, Bancha; Ngaopitakkul, Atthapol

2018-03-01

The protection system for transformer has play significant role in avoiding severe damage to equipment when disturbance occur and ensure overall system reliability. One of the methodology that widely used in protection scheme and algorithm is discrete wavelet transform. However, characteristic of coefficient under fault condition must be analyzed to ensure its effectiveness. So, this paper proposed study and analysis on wavelet coefficient characteristic when fault occur in transformer in both high- and low-frequency component from discrete wavelet transform. The effect of internal and external fault on wavelet coefficient of both fault and normal phase has been taken into consideration. The fault signal has been simulate using transmission connected to transformer experimental setup on laboratory level that modelled after actual system. The result in term of wavelet coefficient shown a clearly differentiate between wavelet characteristic in both high and low frequency component that can be used to further design and improve detection and classification algorithm that based on discrete wavelet transform methodology in the future.

Fast, large-scale hologram calculation in wavelet domain

NASA Astrophysics Data System (ADS)

Shimobaba, Tomoyoshi; Matsushima, Kyoji; Takahashi, Takayuki; Nagahama, Yuki; Hasegawa, Satoki; Sano, Marie; Hirayama, Ryuji; Kakue, Takashi; Ito, Tomoyoshi

2018-04-01

We propose a large-scale hologram calculation using WAvelet ShrinkAge-Based superpositIon (WASABI), a wavelet transform-based algorithm. An image-type hologram calculated using the WASABI method is printed on a glass substrate with the resolution of 65 , 536 × 65 , 536 pixels and a pixel pitch of 1 μm. The hologram calculation time amounts to approximately 354 s on a commercial CPU, which is approximately 30 times faster than conventional methods.

Fractals and Transformations.

ERIC Educational Resources Information Center

Bannon, Thomas J.

1991-01-01

Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

Automatic Image Registration of Multimodal Remotely Sensed Data with Global Shearlet Features

NASA Technical Reports Server (NTRS)

Murphy, James M.; Le Moigne, Jacqueline; Harding, David J.

2015-01-01

Automatic image registration is the process of aligning two or more images of approximately the same scene with minimal human assistance. Wavelet-based automatic registration methods are standard, but sometimes are not robust to the choice of initial conditions. That is, if the images to be registered are too far apart relative to the initial guess of the algorithm, the registration algorithm does not converge or has poor accuracy, and is thus not robust. These problems occur because wavelet techniques primarily identify isotropic textural features and are less effective at identifying linear and curvilinear edge features. We integrate the recently developed mathematical construction of shearlets, which is more effective at identifying sparse anisotropic edges, with an existing automatic wavelet-based registration algorithm. Our shearlet features algorithm produces more distinct features than wavelet features algorithms; the separation of edges from textures is even stronger than with wavelets. Our algorithm computes shearlet and wavelet features for the images to be registered, then performs least squares minimization on these features to compute a registration transformation. Our algorithm is two-staged and multiresolution in nature. First, a cascade of shearlet features is used to provide a robust, though approximate, registration. This is then refined by registering with a cascade of wavelet features. Experiments across a variety of image classes show an improved robustness to initial conditions, when compared to wavelet features alone.

Automatic Image Registration of Multi-Modal Remotely Sensed Data with Global Shearlet Features

PubMed Central

Murphy, James M.; Le Moigne, Jacqueline; Harding, David J.

2017-01-01

Automatic image registration is the process of aligning two or more images of approximately the same scene with minimal human assistance. Wavelet-based automatic registration methods are standard, but sometimes are not robust to the choice of initial conditions. That is, if the images to be registered are too far apart relative to the initial guess of the algorithm, the registration algorithm does not converge or has poor accuracy, and is thus not robust. These problems occur because wavelet techniques primarily identify isotropic textural features and are less effective at identifying linear and curvilinear edge features. We integrate the recently developed mathematical construction of shearlets, which is more effective at identifying sparse anisotropic edges, with an existing automatic wavelet-based registration algorithm. Our shearlet features algorithm produces more distinct features than wavelet features algorithms; the separation of edges from textures is even stronger than with wavelets. Our algorithm computes shearlet and wavelet features for the images to be registered, then performs least squares minimization on these features to compute a registration transformation. Our algorithm is two-staged and multiresolution in nature. First, a cascade of shearlet features is used to provide a robust, though approximate, registration. This is then refined by registering with a cascade of wavelet features. Experiments across a variety of image classes show an improved robustness to initial conditions, when compared to wavelet features alone. PMID:29123329

Improved medical image fusion based on cascaded PCA and shift invariant wavelet transforms.

PubMed

Reena Benjamin, J; Jayasree, T

2018-02-01

In the medical field, radiologists need more informative and high-quality medical images to diagnose diseases. Image fusion plays a vital role in the field of biomedical image analysis. It aims to integrate the complementary information from multimodal images, producing a new composite image which is expected to be more informative for visual perception than any of the individual input images. The main objective of this paper is to improve the information, to preserve the edges and to enhance the quality of the fused image using cascaded principal component analysis (PCA) and shift invariant wavelet transforms. A novel image fusion technique based on cascaded PCA and shift invariant wavelet transforms is proposed in this paper. PCA in spatial domain extracts relevant information from the large dataset based on eigenvalue decomposition, and the wavelet transform operating in the complex domain with shift invariant properties brings out more directional and phase details of the image. The significance of maximum fusion rule applied in dual-tree complex wavelet transform domain enhances the average information and morphological details. The input images of the human brain of two different modalities (MRI and CT) are collected from whole brain atlas data distributed by Harvard University. Both MRI and CT images are fused using cascaded PCA and shift invariant wavelet transform method. The proposed method is evaluated based on three main key factors, namely structure preservation, edge preservation, contrast preservation. The experimental results and comparison with other existing fusion methods show the superior performance of the proposed image fusion framework in terms of visual and quantitative evaluations. In this paper, a complex wavelet-based image fusion has been discussed. The experimental results demonstrate that the proposed method enhances the directional features as well as fine edge details. Also, it reduces the redundant details, artifacts, distortions.

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

NASA Technical Reports Server (NTRS)

Baxes, Gregory A. (Inventor); Linger, Timothy C. (Inventor)

2011-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

NASA Technical Reports Server (NTRS)

Baxes, Gregory A. (Inventor)

2010-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

A fractal model of effective stress of porous media and the analysis of influence factors

NASA Astrophysics Data System (ADS)

Li, Wei; Zhao, Huan; Li, Siqi; Sun, Wenfeng; Wang, Lei; Li, Bing

2018-03-01

The basic concept of effective stress describes the characteristics of fluid and solid interaction in porous media. In this paper, based on the theory of fractal geometry, a fractal model was built to analyze the relationship between the microstructure and the effective stress of porous media. From the microscopic point of view, the influence of effective stress on pore structure of porous media was demonstrated. Theoretical analysis and experimental results show that: (i) the fractal model of effective stress can be used to describe the relationship between effective stress and the microstructure of porous media; (ii) a linear increase in the effective stress leads to exponential increases in fractal dimension, porosity and pore number of the porous media, and causes a decreasing trend in the average pore radius.

Fractal based curves in musical creativity: A critical annotation

NASA Astrophysics Data System (ADS)

Georgaki, Anastasia; Tsolakis, Christos

In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

The fractal architecture of cytoplasmic organization: scaling, kinetics and emergence in metabolic networks.

PubMed

Aon, Miguel Antonio; O'Rourke, Brian; Cortassa, Sonia

2004-01-01

In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.

Application of wavelet transformation and adaptive neighborhood based modified backpropagation (ANMBP) for classification of brain cancer

NASA Astrophysics Data System (ADS)

Werdiningsih, Indah; Zaman, Badrus; Nuqoba, Barry

2017-08-01

This paper presents classification of brain cancer using wavelet transformation and Adaptive Neighborhood Based Modified Backpropagation (ANMBP). Three stages of the processes, namely features extraction, features reduction, and classification process. Wavelet transformation is used for feature extraction and ANMBP is used for classification process. The result of features extraction is feature vectors. Features reduction used 100 energy values per feature and 10 energy values per feature. Classifications of brain cancer are normal, alzheimer, glioma, and carcinoma. Based on simulation results, 10 energy values per feature can be used to classify brain cancer correctly. The correct classification rate of proposed system is 95 %. This research demonstrated that wavelet transformation can be used for features extraction and ANMBP can be used for classification of brain cancer.

Wavelet Analysis for Wind Fields Estimation

PubMed Central

Leite, Gladeston C.; Ushizima, Daniela M.; Medeiros, Fátima N. S.; de Lima, Gilson G.

2010-01-01

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B3 spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms−1. Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms. PMID:22219699

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

PubMed Central

Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J.; Pastor, María A.

2013-01-01

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies. PMID:23831414

Dynamic fractals in spatial evolutionary games

NASA Astrophysics Data System (ADS)

Kolotev, Sergei; Malyutin, Aleksandr; Burovski, Evgeni; Krashakov, Sergei; Shchur, Lev

2018-06-01

We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

Modular continuous wavelet processing of biosignals: extracting heart rate and oxygen saturation from a video signal

PubMed Central

2016-01-01

A novel method of extracting heart rate and oxygen saturation from a video-based biosignal is described. The method comprises a novel modular continuous wavelet transform approach which includes: performing the transform, undertaking running wavelet archetyping to enhance the pulse information, extraction of the pulse ridge time–frequency information [and thus a heart rate (HRvid) signal], creation of a wavelet ratio surface, projection of the pulse ridge onto the ratio surface to determine the ratio of ratios from which a saturation trending signal is derived, and calibrating this signal to provide an absolute saturation signal (SvidO2). The method is illustrated through its application to a video photoplethysmogram acquired during a porcine model of acute desaturation. The modular continuous wavelet transform-based approach is advocated by the author as a powerful methodology to deal with noisy, non-stationary biosignals in general. PMID:27382479

An improved wavelet-Galerkin method for dynamic response reconstruction and parameter identification of shear-type frames

NASA Astrophysics Data System (ADS)

Bu, Haifeng; Wang, Dansheng; Zhou, Pin; Zhu, Hongping

2018-04-01

An improved wavelet-Galerkin (IWG) method based on the Daubechies wavelet is proposed for reconstructing the dynamic responses of shear structures. The proposed method flexibly manages wavelet resolution level according to excitation, thereby avoiding the weakness of the wavelet-Galerkin multiresolution analysis (WGMA) method in terms of resolution and the requirement of external excitation. IWG is implemented by this work in certain case studies, involving single- and n-degree-of-freedom frame structures subjected to a determined discrete excitation. Results demonstrate that IWG performs better than WGMA in terms of accuracy and computation efficiency. Furthermore, a new method for parameter identification based on IWG and an optimization algorithm are also developed for shear frame structures, and a simultaneous identification of structural parameters and excitation is implemented. Numerical results demonstrate that the proposed identification method is effective for shear frame structures.

Denoising time-domain induced polarisation data using wavelet techniques

NASA Astrophysics Data System (ADS)

Deo, Ravin N.; Cull, James P.

2016-05-01

Time-domain induced polarisation (TDIP) methods are routinely used for near-surface evaluations in quasi-urban environments harbouring networks of buried civil infrastructure. A conventional technique for improving signal to noise ratio in such environments is by using analogue or digital low-pass filtering followed by stacking and rectification. However, this induces large distortions in the processed data. In this study, we have conducted the first application of wavelet based denoising techniques for processing raw TDIP data. Our investigation included laboratory and field measurements to better understand the advantages and limitations of this technique. It was found that distortions arising from conventional filtering can be significantly avoided with the use of wavelet based denoising techniques. With recent advances in full-waveform acquisition and analysis, incorporation of wavelet denoising techniques can further enhance surveying capabilities. In this work, we present the rationale for utilising wavelet denoising methods and discuss some important implications, which can positively influence TDIP methods.

Application of improved wavelet total variation denoising for rolling bearing incipient fault diagnosis

NASA Astrophysics Data System (ADS)

Zhang, W.; Jia, M. P.

2018-06-01

When incipient fault appear in the rolling bearing, the fault feature is too small and easily submerged in the strong background noise. In this paper, wavelet total variation denoising based on kurtosis (Kurt-WATV) is studied, which can extract the incipient fault feature of the rolling bearing more effectively. The proposed algorithm contains main steps: a) establish a sparse diagnosis model, b) represent periodic impulses based on the redundant wavelet dictionary, c) solve the joint optimization problem by alternating direction method of multipliers (ADMM), d) obtain the reconstructed signal using kurtosis value as criterion and then select optimal wavelet subbands. This paper uses overcomplete rational-dilation wavelet transform (ORDWT) as a dictionary, and adjusts the control parameters to achieve the concentration in the time-frequency plane. Incipient fault of rolling bearing is used as an example, and the result shows that the effectiveness and superiority of the proposed Kurt- WATV bearing fault diagnosis algorithm.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

Comprehensive Fractal Description of Porosity of Coal of Different Ranks

PubMed Central

Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

2014-01-01

We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China.

PubMed

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-12-03

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.

Effects of Anisotropy on Scalar Field Ghost Dark Energy and the Non-Equilibrium Thermodynamics in Fractal Cosmology

NASA Astrophysics Data System (ADS)

Najafi, A.; Hossienkhani, H.

2017-10-01

Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, ρ, the deceleration parameter, q, the equations of state parameter, {ω }{{}D}, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the GSLT of thermodynamics in a fractal cosmology.

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

PubMed Central

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-01-01

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458

Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.

PubMed

Boon, Mei Ying; Henry, Bruce Ian; Chu, Byoung Sun; Basahi, Nour; Suttle, Catherine May; Luu, Chi; Leung, Harry; Hing, Stephen

2016-01-01

The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Continuous time wavelet entropy of auditory evoked potentials.

PubMed

Cek, M Emre; Ozgoren, Murat; Savaci, F Acar

2010-01-01

In this paper, the continuous time wavelet entropy (CTWE) of auditory evoked potentials (AEP) has been characterized by evaluating the relative wavelet energies (RWE) in specified EEG frequency bands. Thus, the rapid variations of CTWE due to the auditory stimulation could be detected in post-stimulus time interval. This approach removes the probability of missing the information hidden in short time intervals. The discrete time and continuous time wavelet based wavelet entropy variations were compared on non-target and target AEP data. It was observed that CTWE can also be an alternative method to analyze entropy as a function of time. 2009 Elsevier Ltd. All rights reserved.

Cell edge detection in JPEG2000 wavelet domain - analysis on sigmoid function edge model.

PubMed

Punys, Vytenis; Maknickas, Ramunas

2011-01-01

Big virtual microscopy images (80K x 60K pixels and larger) are usually stored using the JPEG2000 image compression scheme. Diagnostic quantification, based on image analysis, might be faster if performed on compressed data (approx. 20 times less the original amount), representing the coefficients of the wavelet transform. The analysis of possible edge detection without reverse wavelet transform is presented in the paper. Two edge detection methods, suitable for JPEG2000 bi-orthogonal wavelets, are proposed. The methods are adjusted according calculated parameters of sigmoid edge model. The results of model analysis indicate more suitable method for given bi-orthogonal wavelet.

A wavelet analysis of co-movements in Asian gold markets

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Kannadhasan, M.; Al-Yahyaee, Khamis Hamed; Yoon, Seong-Min

2018-02-01

This study assesses the cross-country co-movements of gold spot returns among the major gold consuming countries in Asia using wavelet-based analysis for a dataset spanning over 26 years. Wavelet-based analysis is used since it allows measuring co-movements in a time-frequency space. The results suggest intense and positive co-movements in Asia after the Asian financial crisis of 1997 at all frequencies. In addition, the Asian gold spot markets depict a state of impending perfect market integration. Finally, Thailand emerges as the potential market leader in all wavelet scales except one, which is led by India. The study has important implications for international diversification of a single-asset (gold) portfolio.

Numerical solution of the Black-Scholes equation using cubic spline wavelets

NASA Astrophysics Data System (ADS)

Černá, Dana

2016-12-01

The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.

Detection method of flexion relaxation phenomenon based on wavelets for patients with low back pain

NASA Astrophysics Data System (ADS)

Nougarou, François; Massicotte, Daniel; Descarreaux, Martin

2012-12-01

The flexion relaxation phenomenon (FRP) can be defined as a reduction or silence of myoelectric activity of the lumbar erector spinae muscle during full trunk flexion. It is typically absent in patients with chronic low back pain (LBP). Before any broad clinical utilization of this neuromuscular response can be made, effective, standardized, and accurate methods of identifying FRP limits are needed. However, this phenomenon is clearly more difficult to detect for LBP patients than for healthy patients. The main goal of this study is to develop an automated method based on wavelet transformation that would improve time point limits detection of surface electromyography signals of the FRP in case of LBP patients. Conventional visual identification and proposed automated methods of time point limits detection of relaxation phase were compared on experimental data using criteria of accuracy and repeatability based on physiological properties. The evaluation demonstrates that the use of wavelet transform (WT) yields better results than methods without wavelet decomposition. Furthermore, methods based on wavelet per packet transform are more effective than algorithms employing discrete WT. Compared to visual detection, in addition to demonstrating an obvious saving of time, the use of wavelet per packet transform improves the accuracy and repeatability in the detection of the FRP limits. These results clearly highlight the value of the proposed technique in identifying onset and offset of the flexion relaxation response in LBP subjects.

Wavelet based de-noising of breath air absorption spectra profiles for improved classification by principal component analysis

NASA Astrophysics Data System (ADS)

Kistenev, Yu. V.; Shapovalov, A. V.; Borisov, A. V.; Vrazhnov, D. A.; Nikolaev, V. V.; Nikiforova, O. Yu.

2015-11-01

The comparison results of different mother wavelets used for de-noising of model and experimental data which were presented by profiles of absorption spectra of exhaled air are presented. The impact of wavelets de-noising on classification quality made by principal component analysis are also discussed.

Multiadaptive Bionic Wavelet Transform: Application to ECG Denoising and Baseline Wandering Reduction

NASA Astrophysics Data System (ADS)

Sayadi, Omid; Shamsollahi, Mohammad B.

2007-12-01

We present a new modified wavelet transform, called the multiadaptive bionic wavelet transform (MABWT), that can be applied to ECG signals in order to remove noise from them under a wide range of variations for noise. By using the definition of bionic wavelet transform and adaptively determining both the center frequency of each scale together with the[InlineEquation not available: see fulltext.]-function, the problem of desired signal decomposition is solved. Applying a new proposed thresholding rule works successfully in denoising the ECG. Moreover by using the multiadaptation scheme, lowpass noisy interference effects on the baseline of ECG will be removed as a direct task. The method was extensively clinically tested with real and simulated ECG signals which showed high performance of noise reduction, comparable to those of wavelet transform (WT). Quantitative evaluation of the proposed algorithm shows that the average SNR improvement of MABWT is 1.82 dB more than the WT-based results, for the best case. Also the procedure has largely proved advantageous over wavelet-based methods for baseline wandering cancellation, including both DC components and baseline drifts.

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Research on the fault diagnosis of bearing based on wavelet and demodulation

NASA Astrophysics Data System (ADS)

Li, Jiapeng; Yuan, Yu

2017-05-01

As a most commonly-used machine part, antifriction bearing is extensively used in mechanical equipment. Vibration signal analysis is one of the methods to monitor and diagnose the running status of antifriction bearings. Therefore, using wavelet analysis for demising is of great importance in the engineering practice. This paper firstly presented the basic theory of wavelet analysis to study the transformation, decomposition and reconstruction of wavelet. In addition, edition software LabVIEW was adopted to conduct wavelet and demodulation upon the vibration signal of antifriction bearing collected. With the combination of Hilbert envelop demodulation analysis, the fault character frequencies of the demised signal were extracted to conduct fault diagnosis analysis, which serves as a reference for the wavelet and demodulation of the vibration signal in engineering practice.

Design of a wide-band metamaterial absorber based on fractal frequency selective surface and resistive films

NASA Astrophysics Data System (ADS)

Cheng, Yong-Zhi; Nie, Yan; Gong, Rong-Zhou

2013-10-01

We present the design of a wide-band metamaterial absorber, based on fractal frequency selective surface and resistive films. The total thickness is only 0.8 mm and shows a polarization-insensitive and wide-angle strong absorption. Due to the multiband resonance properties of the Minkowski fractal loop structure and Ohmic loss properties of resistive films, a strongly absorptive bandwidth of about 19 GHz is demonstrated numerically in the range 6.51-25.42 GHz. This design provides an effective and feasible way to construct a broad-band absorber in stealth technology.

Perceptual compression of magnitude-detected synthetic aperture radar imagery

NASA Technical Reports Server (NTRS)

Gorman, John D.; Werness, Susan A.

1994-01-01

A perceptually-based approach for compressing synthetic aperture radar (SAR) imagery is presented. Key components of the approach are a multiresolution wavelet transform, a bit allocation mask based on an empirical human visual system (HVS) model, and hybrid scalar/vector quantization. Specifically, wavelet shrinkage techniques are used to segregate wavelet transform coefficients into three components: local means, edges, and texture. Each of these three components is then quantized separately according to a perceptually-based bit allocation scheme. Wavelet coefficients associated with local means and edges are quantized using high-rate scalar quantization while texture information is quantized using low-rate vector quantization. The impact of the perceptually-based multiresolution compression algorithm on visual image quality, impulse response, and texture properties is assessed for fine-resolution magnitude-detected SAR imagery; excellent image quality is found at bit rates at or above 1 bpp along with graceful performance degradation at rates below 1 bpp.

H-fractal seismic metamaterial with broadband low-frequency bandgaps

NASA Astrophysics Data System (ADS)

Du, Qiujiao; Zeng, Yi; Xu, Yang; Yang, Hongwu; Zeng, Zuoxun

2018-03-01

The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer's disease.

PubMed

Warsi, Mohammed A; Molloy, William; Noseworthy, Michael D

2012-10-01

To correlate temporal fractal structure of resting state blood oxygen level dependent (rsBOLD) functional magnetic resonance imaging (fMRI) with in vivo proton magnetic resonance spectroscopy ((1)H-MRS), in Alzheimer's disease (AD) and healthy age-matched normal controls (NC). High temporal resolution (4 Hz) rsBOLD signal and single voxel (left putamen) magnetic resonance spectroscopy data was acquired in 33 AD patients and 13 NC. The rsBOLD data was analyzed using two types of fractal dimension (FD) analysis based on relative dispersion and frequency power spectrum. Comparisons in FD were performed between AD and NC, and FD measures were correlated with (1)H-MRS findings. Temporal fractal analysis of rsBOLD, was able to differentiate AD from NC subjects (P = 0.03). Low FD correlated with markers of AD severity including decreased concentrations of N-acetyl aspartate (R = 0.44, P = 0.015) and increased myoinositol (mI) (R = -0.45, P = 0.012). Based on these results we suggest fractal analysis of rsBOLD could provide an early marker of AD.

[Modeling continuous scaling of NDVI based on fractal theory].

PubMed

Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng

2013-07-01

Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.

Wavelet-based segmentation of renal compartments in DCE-MRI of human kidney: initial results in patients and healthy volunteers.

PubMed

Li, Sheng; Zöllner, Frank G; Merrem, Andreas D; Peng, Yinghong; Roervik, Jarle; Lundervold, Arvid; Schad, Lothar R

2012-03-01

Renal diseases can lead to kidney failure that requires life-long dialysis or renal transplantation. Early detection and treatment can prevent progression towards end stage renal disease. MRI has evolved into a standard examination for the assessment of the renal morphology and function. We propose a wavelet-based clustering to group the voxel time courses and thereby, to segment the renal compartments. This approach comprises (1) a nonparametric, discrete wavelet transform of the voxel time course, (2) thresholding of the wavelet coefficients using Stein's Unbiased Risk estimator, and (3) k-means clustering of the wavelet coefficients to segment the kidneys. Our method was applied to 3D dynamic contrast enhanced (DCE-) MRI data sets of human kidney in four healthy volunteers and three patients. On average, the renal cortex in the healthy volunteers could be segmented at 88%, the medulla at 91%, and the pelvis at 98% accuracy. In the patient data, with aberrant voxel time courses, the segmentation was also feasible with good results for the kidney compartments. In conclusion wavelet based clustering of DCE-MRI of kidney is feasible and a valuable tool towards automated perfusion and glomerular filtration rate quantification. Copyright © 2011 Elsevier Ltd. All rights reserved.

A de-noising method using the improved wavelet threshold function based on noise variance estimation

NASA Astrophysics Data System (ADS)

Liu, Hui; Wang, Weida; Xiang, Changle; Han, Lijin; Nie, Haizhao

2018-01-01

The precise and efficient noise variance estimation is very important for the processing of all kinds of signals while using the wavelet transform to analyze signals and extract signal features. In view of the problem that the accuracy of traditional noise variance estimation is greatly affected by the fluctuation of noise values, this study puts forward the strategy of using the two-state Gaussian mixture model to classify the high-frequency wavelet coefficients in the minimum scale, which takes both the efficiency and accuracy into account. According to the noise variance estimation, a novel improved wavelet threshold function is proposed by combining the advantages of hard and soft threshold functions, and on the basis of the noise variance estimation algorithm and the improved wavelet threshold function, the research puts forth a novel wavelet threshold de-noising method. The method is tested and validated using random signals and bench test data of an electro-mechanical transmission system. The test results indicate that the wavelet threshold de-noising method based on the noise variance estimation shows preferable performance in processing the testing signals of the electro-mechanical transmission system: it can effectively eliminate the interference of transient signals including voltage, current, and oil pressure and maintain the dynamic characteristics of the signals favorably.

A high-performance seizure detection algorithm based on Discrete Wavelet Transform (DWT) and EEG

PubMed Central

Chen, Duo; Wan, Suiren; Xiang, Jing; Bao, Forrest Sheng

2017-01-01

In the past decade, Discrete Wavelet Transform (DWT), a powerful time-frequency tool, has been widely used in computer-aided signal analysis of epileptic electroencephalography (EEG), such as the detection of seizures. One of the important hurdles in the applications of DWT is the settings of DWT, which are chosen empirically or arbitrarily in previous works. The objective of this study aimed to develop a framework for automatically searching the optimal DWT settings to improve accuracy and to reduce computational cost of seizure detection. To address this, we developed a method to decompose EEG data into 7 commonly used wavelet families, to the maximum theoretical level of each mother wavelet. Wavelets and decomposition levels providing the highest accuracy in each wavelet family were then searched in an exhaustive selection of frequency bands, which showed optimal accuracy and low computational cost. The selection of frequency bands and features removed approximately 40% of redundancies. The developed algorithm achieved promising performance on two well-tested EEG datasets (accuracy >90% for both datasets). The experimental results of the developed method have demonstrated that the settings of DWT affect its performance on seizure detection substantially. Compared with existing seizure detection methods based on wavelet, the new approach is more accurate and transferable among datasets. PMID:28278203

Classification of daily solar irradiation by fractional analysis of 10-min-means of solar irradiance

NASA Astrophysics Data System (ADS)

Harrouni, S.; Guessoum, A.; Maafi, A.

2005-02-01

This paper deals with fractal analysis of daily solar irradiances measured with a time step of 10 minutes at Golden and Boulder located in Colorado. The aim is to estimate the fractal dimensions in order to perform classification of daily solar irradiances. The estimated fractal dimension hat{D} and the clearness index KT are used as classification criteria. The results show that these criteria lead to three classes: clear sky, partially covered sky and overcast sky. The results also show that the evaluation of the fractal dimension of the irradiance signal based on a data set with 10 minutes time step is possible.

Surface fractal dimension, water adsorption efficiency, and cloud nucleation activity of insoluble aerosol.

PubMed

Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping

2016-05-03

Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.

Surface fractal dimension, water adsorption efficiency, and cloud nucleation activity of insoluble aerosol

NASA Astrophysics Data System (ADS)

Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping

2016-05-01

Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.

Identification of large geomorphological anomalies based on 2D discrete wavelet transform

NASA Astrophysics Data System (ADS)

Doglioni, A.; Simeone, V.

2012-04-01

The identification and analysis based on quantitative evidences of large geomorphological anomalies is an important stage for the study of large landslides. Numerical geomorphic analyses represent an interesting approach to this kind of studies, allowing for a detailed and pretty accurate identification of hidden topographic anomalies that may be related to large landslides. Here a geomorphic numerical analyses of the Digital Terrain Model (DTM) is presented. The introduced approach is based on 2D discrete wavelet transform (Antoine et al., 2003; Bruun and Nilsen, 2003, Booth et al., 2009). The 2D wavelet decomposition of the DTM, and in particular the analysis of the detail coefficients of the wavelet transform can provide evidences of anomalies or singularities, i.e. discontinuities of the land surface. These discontinuities are not very evident from the DTM as it is, while 2D wavelet transform allows for grid-based analysis of DTM and for mapping the decomposition. In fact, the grid-based DTM can be assumed as a matrix, where a discrete wavelet transform (Daubechies, 1992) is performed columnwise and linewise, which basically represent horizontal and vertical directions. The outcomes of this analysis are low-frequency approximation coefficients and high-frequency detail coefficients. Detail coefficients are analyzed, since their variations are associated to discontinuities of the DTM. Detailed coefficients are estimated assuming to perform 2D wavelet transform both for the horizontal direction (east-west) and for the vertical direction (north-south). Detail coefficients are then mapped for both the cases, thus allowing to visualize and quantify potential anomalies of the land surface. Moreover, wavelet decomposition can be pushed to further levels, assuming a higher scale number of the transform. This may potentially return further interesting results, in terms of identification of the anomalies of land surface. In this kind of approach, the choice of a proper mother wavelet function is a tricky point, since it conditions the analysis and then their outcomes. Therefore multiple levels as well as multiple wavelet analyses are guessed. Here the introduced approach is applied to some interesting cases study of south Italy, in particular for the identification of large anomalies associated to large landslides at the transition between Apennine chain domain and the foredeep domain. In particular low Biferno valley and Fortore valley are here analyzed. Finally, the wavelet transforms are performed on multiple levels, thus trying to address the problem of which is the level extent for an accurate analysis fit to a specific problem. Antoine J.P., Carrette P., Murenzi R., and Piette B., (2003), Image analysis with two-dimensional continuous wavelet transform, Signal Processing, 31(3), pp. 241-272, doi:10.1016/0165-1684(93)90085-O. Booth A.M., Roering J.J., and Taylor Perron J., (2009), Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon, Geomorphology, 109(3-4), pp. 132-147, doi:10.1016/j.geomorph.2009.02.027. Bruun B.T., and Nilsen S., (2003), Wavelet representation of large digital terrain models, Computers and Geoscience, 29(6), pp. 695-703, doi:10.1016/S0098-3004(03)00015-3. Daubechies, I. (1992), Ten lectures on wavelets, SIAM.

Multi-source feature extraction and target recognition in wireless sensor networks based on adaptive distributed wavelet compression algorithms

NASA Astrophysics Data System (ADS)

Hortos, William S.

2008-04-01

Proposed distributed wavelet-based algorithms are a means to compress sensor data received at the nodes forming a wireless sensor network (WSN) by exchanging information between neighboring sensor nodes. Local collaboration among nodes compacts the measurements, yielding a reduced fused set with equivalent information at far fewer nodes. Nodes may be equipped with multiple sensor types, each capable of sensing distinct phenomena: thermal, humidity, chemical, voltage, or image signals with low or no frequency content as well as audio, seismic or video signals within defined frequency ranges. Compression of the multi-source data through wavelet-based methods, distributed at active nodes, reduces downstream processing and storage requirements along the paths to sink nodes; it also enables noise suppression and more energy-efficient query routing within the WSN. Targets are first detected by the multiple sensors; then wavelet compression and data fusion are applied to the target returns, followed by feature extraction from the reduced data; feature data are input to target recognition/classification routines; targets are tracked during their sojourns through the area monitored by the WSN. Algorithms to perform these tasks are implemented in a distributed manner, based on a partition of the WSN into clusters of nodes. In this work, a scheme of collaborative processing is applied for hierarchical data aggregation and decorrelation, based on the sensor data itself and any redundant information, enabled by a distributed, in-cluster wavelet transform with lifting that allows multiple levels of resolution. The wavelet-based compression algorithm significantly decreases RF bandwidth and other resource use in target processing tasks. Following wavelet compression, features are extracted. The objective of feature extraction is to maximize the probabilities of correct target classification based on multi-source sensor measurements, while minimizing the resource expenditures at participating nodes. Therefore, the feature-extraction method based on the Haar DWT is presented that employs a maximum-entropy measure to determine significant wavelet coefficients. Features are formed by calculating the energy of coefficients grouped around the competing clusters. A DWT-based feature extraction algorithm used for vehicle classification in WSNs can be enhanced by an added rule for selecting the optimal number of resolution levels to improve the correct classification rate and reduce energy consumption expended in local algorithm computations. Published field trial data for vehicular ground targets, measured with multiple sensor types, are used to evaluate the wavelet-assisted algorithms. Extracted features are used in established target recognition routines, e.g., the Bayesian minimum-error-rate classifier, to compare the effects on the classification performance of the wavelet compression. Simulations of feature sets and recognition routines at different resolution levels in target scenarios indicate the impact on classification rates, while formulas are provided to estimate reduction in resource use due to distributed compression.

Displaying radiologic images on personal computers: image storage and compression--Part 2.

PubMed

Gillespy, T; Rowberg, A H

1994-02-01

This is part 2 of our article on image storage and compression, the third article of our series for radiologists and imaging scientists on displaying, manipulating, and analyzing radiologic images on personal computers. Image compression is classified as lossless (nondestructive) or lossy (destructive). Common lossless compression algorithms include variable-length bit codes (Huffman codes and variants), dictionary-based compression (Lempel-Ziv variants), and arithmetic coding. Huffman codes and the Lempel-Ziv-Welch (LZW) algorithm are commonly used for image compression. All of these compression methods are enhanced if the image has been transformed into a differential image based on a differential pulse-code modulation (DPCM) algorithm. The LZW compression after the DPCM image transformation performed the best on our example images, and performed almost as well as the best of the three commercial compression programs tested. Lossy compression techniques are capable of much higher data compression, but reduced image quality and compression artifacts may be noticeable. Lossy compression is comprised of three steps: transformation, quantization, and coding. Two commonly used transformation methods are the discrete cosine transformation and discrete wavelet transformation. In both methods, most of the image information is contained in a relatively few of the transformation coefficients. The quantization step reduces many of the lower order coefficients to 0, which greatly improves the efficiency of the coding (compression) step. In fractal-based image compression, image patterns are stored as equations that can be reconstructed at different levels of resolution.

Influence of condition of growth of bacterial colonies on fractal dimension of bacterial speckle patterns

NASA Astrophysics Data System (ADS)

Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.

2010-10-01

New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.

Influence of condition of growth of bacterial colonies on fractal dimension of bacterial speckle patterns

NASA Astrophysics Data System (ADS)

Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.

2011-03-01

New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.

Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge

USGS Publications Warehouse

Zhang, You‐Kuan; Schilling, Keith

2004-01-01

Spectral analyses were conducted for hourly hydraulic head (h) data observed over a 4‐year period at seven monitoring wells in the Walnut Creek watershed, Iowa. The log power spectral density of the hydraulic head fluctuations versus log frequency (f) at all seven wells is shown to have a distinct slope or fractal dimension (D), indicating temporal scaling in the time series of water level fluctuations. The fractal dimension of the time series varies from well to well, and the spectrum for the average h over all seven wells has a fractal dimension of 1.46 and Hurst coefficient of 0.54. The log power spectral density of estimated base flow in the Walnut Creek and four other watersheds versus log f is shown to have two distinct slopes with a break in scaling at about 30 days. It is shown that the groundwater recharge process in a basin can be estimated from a head spectrum based on existing theoretical results. Hydraulic head in an aquifer may fluctuate as a fractal in time in response to either a white noise or fractal recharge process, depending on physical parameters (i.e., transmissivity and specific yield) of the aquifer. The recharge process at the Walnut Creek watershed is shown to have a white noise spectrum based on the observed head spectrum.

Determination of Irreducible Water Saturation from nuclear magnetic resonance based on fractal theory — a case study of sandstone with complex pore structure

NASA Astrophysics Data System (ADS)

Peng, L.; Pan, H.; Ma, H.; Zhao, P.; Qin, R.; Deng, C.

2017-12-01

The irreducible water saturation (Swir) is a vital parameter for permeability prediction and original oil and gas estimation. However, the complex pore structure of the rocks makes the parameter difficult to be calculated from both laboratory and conventional well logging methods. In this study, an effective statistical method to predict Swir is derived directly from nuclear magnetic resonance (NMR) data based on fractal theory. The spectrum of transversal relaxation time (T2) is normally considered as an indicator of pore size distribution, and the micro- and meso-pore's fractal dimension in two specific range of T2 spectrum distribution are calculated. Based on the analysis of the fractal characteristics of 22 core samples, which were drilled from four boreholes of tight lithologic oil reservoirs of Ordos Basin in China, the positive correlation between Swir and porosity is derived. Afterwards a predicting model for Swir based on linear regressions of fractal dimensions is proposed. It reveals that the Swir is controlled by the pore size and the roughness of the pore. The reliability of this model is tested and an ideal consistency between predicted results and experimental data is found. This model is a reliable supplementary to predict the irreducible water saturation in the case that T2 cutoff value cannot be accurately determined.

Detection of small bowel tumors in capsule endoscopy frames using texture analysis based on the discrete wavelet transform.

PubMed

Barbosa, Daniel J C; Ramos, Jaime; Lima, Carlos S

2008-01-01

Capsule endoscopy is an important tool to diagnose tumor lesions in the small bowel. The capsule endoscopic images possess vital information expressed by color and texture. This paper presents an approach based in the textural analysis of the different color channels, using the wavelet transform to select the bands with the most significant texture information. A new image is then synthesized from the selected wavelet bands, trough the inverse wavelet transform. The features of each image are based on second-order textural information, and they are used in a classification scheme using a multilayer perceptron neural network. The proposed methodology has been applied in real data taken from capsule endoscopic exams and reached 98.7% sensibility and 96.6% specificity. These results support the feasibility of the proposed algorithm.

Fractals in the neurosciences, Part II: clinical applications and future perspectives.

PubMed

Di Ieva, Antonio; Esteban, Francisco J; Grizzi, Fabio; Klonowski, Wlodzimierz; Martín-Landrove, Miguel

2015-02-01

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain. © The Author(s) 2013.

A robust algorithm for optimisation and customisation of fractal dimensions of time series modified by nonlinearly scaling their time derivatives: mathematical theory and practical applications.

PubMed

Fuss, Franz Konstantin

2013-01-01

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

PubMed Central

2013-01-01

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals. PMID:24151522

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

PubMed

Lilly, Jonathan M

2017-04-01

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized 'events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event's 'region of influence' within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis , is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.

3D High Resolution Mesh Deformation Based on Multi Library Wavelet Neural Network Architecture

NASA Astrophysics Data System (ADS)

Dhibi, Naziha; Elkefi, Akram; Bellil, Wajdi; Amar, Chokri Ben

2016-12-01

This paper deals with the features of a novel technique for large Laplacian boundary deformations using estimated rotations. The proposed method is based on a Multi Library Wavelet Neural Network structure founded on several mother wavelet families (MLWNN). The objective is to align features of mesh and minimize distortion with a fixed feature that minimizes the sum of the distances between all corresponding vertices. New mesh deformation method worked in the domain of Region of Interest (ROI). Our approach computes deformed ROI, updates and optimizes it to align features of mesh based on MLWNN and spherical parameterization configuration. This structure has the advantage of constructing the network by several mother wavelets to solve high dimensions problem using the best wavelet mother that models the signal better. The simulation test achieved the robustness and speed considerations when developing deformation methodologies. The Mean-Square Error and the ratio of deformation are low compared to other works from the state of the art. Our approach minimizes distortions with fixed features to have a well reconstructed object.

Interactions between a fractal tree-like object and hydrodynamic turbulence: flow structure and characteristic mixing length

NASA Astrophysics Data System (ADS)

Meneveau, C. V.; Bai, K.; Katz, J.

2011-12-01

The vegetation canopy has a significant impact on various physical and biological processes such as forest microclimate, rainfall evaporation distribution and climate change. Most scaled laboratory experimental studies have used canopy element models that consist of rigid vertical strips or cylindrical rods that can be typically represented through only one or a few characteristic length scales, for example the diameter and height for cylindrical rods. However, most natural canopies and vegetation are highly multi-scale with branches and sub-branches, covering a wide range of length scales. Fractals provide a convenient idealization of multi-scale objects, since their multi-scale properties can be described in simple ways (Mandelbrot 1982). While fractal aspects of turbulence have been studied in several works in the past decades, research on turbulence generated by fractal objects started more recently. We present an experimental study of boundary layer flow over fractal tree-like objects. Detailed Particle-Image-Velocimetry (PIV) measurements are carried out in the near-wake of a fractal-like tree. The tree is a pre-fractal with five generations, with three branches and a scale reduction factor 1/2 at each generation. Its similarity fractal dimension (Mandelbrot 1982) is D ~ 1.58. Detailed mean velocity and turbulence stress profiles are documented, as well as their downstream development. We then turn attention to the turbulence mixing properties of the flow, specifically to the question whether a mixing length-scale can be identified in this flow, and if so, how it relates to the geometric length-scales in the pre-fractal object. Scatter plots of mean velocity gradient (shear) and Reynolds shear stress exhibit good linear relation at all locations in the flow. Therefore, in the transverse direction of the wake evolution, the Boussinesq eddy viscosity concept is appropriate to describe the mixing. We find that the measured mixing length increases with increasing streamwise locations. Conversely, the measured eddy viscosity and mixing length decrease with increasing elevation, which differs from eddy viscosity and mixing length behaviors of traditional boundary layers or canopies studied before. In order to find an appropriate length for the flow, several models based on the notion of superposition of scales are proposed and examined. One approach is based on spectral distributions. Another more practical approach is based on length-scale distributions evaluated using fractal geometry tools. These proposed models agree well with the measured mixing length. The results indicate that information about multi-scale clustering of branches as it occurs in fractals has to be incorporated into models of the mixing length for flows through canopies with multiple scales. The research is supported by National Science Foundation grant ATM-0621396 and AGS-1047550.

Wavelet Transforms in Parallel Image Processing

DTIC Science & Technology

1994-01-27

NUMBER OF PAGES Object Segmentation, Texture Segmentation, Image Compression, Image 137 Halftoning , Neural Network, Parallel Algorithms, 2D and 3D...Vector Quantization of Wavelet Transform Coefficients ........ ............................. 57 B.1.f Adaptive Image Halftoning based on Wavelet...application has been directed to the adaptive image halftoning . The gray information at a pixel, including its gray value and gradient, is represented by

Numerical Simulation of Monitoring Corrosion in Reinforced Concrete Based on Ultrasonic Guided Waves

PubMed Central

Zheng, Zhupeng; Lei, Ying; Xue, Xin

2014-01-01

Numerical simulation based on finite element method is conducted to predict the location of pitting corrosion in reinforced concrete. Simulation results show that it is feasible to predict corrosion monitoring based on ultrasonic guided wave in reinforced concrete, and wavelet analysis can be used for the extremely weak signal of guided waves due to energy leaking into concrete. The characteristic of time-frequency localization of wavelet transform is adopted in the corrosion monitoring of reinforced concrete. Guided waves can be successfully used to identify corrosion defects in reinforced concrete with the analysis of suitable wavelet-based function and its scale. PMID:25013865

Site effect classification based on microtremor data analysis using a concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2015-01-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Site effect classification based on microtremor data analysis using concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2014-07-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

The generalized Morse wavelet method to determine refractive index dispersion of dielectric films

NASA Astrophysics Data System (ADS)

Kocahan, Özlem; Özcan, Seçkin; Coşkun, Emre; Özder, Serhat

2017-04-01

The continuous wavelet transform (CWT) method is a useful tool for the determination of refractive index dispersion of dielectric films. Mother wavelet selection is an important factor for the accuracy of the results when using CWT. In this study, generalized Morse wavelet (GMW) was proposed as the mother wavelet because of having two degrees of freedom. The simulation studies, based on error calculations and Cauchy Coefficient comparisons, were presented and also the noisy signal was tested by CWT method with GMW. The experimental validity of this method was checked by D263 T schott glass having 100 μm thickness and the results were compared to those from the catalog value.

Photoacoustic signals denoising of the glucose aqueous solutions using an improved wavelet threshold method

NASA Astrophysics Data System (ADS)

Ren, Zhong; Liu, Guodong; Xiong, Zhihua

2016-10-01

The photoacoustic signals denoising of glucose is one of most important steps in the quality identification of the fruit because the real-time photoacoustic singals of glucose are easily interfered by all kinds of noises. To remove the noises and some useless information, an improved wavelet threshld function were proposed. Compared with the traditional wavelet hard and soft threshold functions, the improved wavelet threshold function can overcome the pseudo-oscillation effect of the denoised photoacoustic signals due to the continuity of the improved wavelet threshold function, and the error between the denoised signals and the original signals can be decreased. To validate the feasibility of the improved wavelet threshold function denoising, the denoising simulation experiments based on MATLAB programmimg were performed. In the simulation experiments, the standard test signal was used, and three different denoising methods were used and compared with the improved wavelet threshold function. The signal-to-noise ratio (SNR) and the root-mean-square error (RMSE) values were used to evaluate the performance of the improved wavelet threshold function denoising. The experimental results demonstrate that the SNR value of the improved wavelet threshold function is largest and the RMSE value is lest, which fully verifies that the improved wavelet threshold function denoising is feasible. Finally, the improved wavelet threshold function denoising was used to remove the noises of the photoacoustic signals of the glucose solutions. The denoising effect is also very good. Therefore, the improved wavelet threshold function denoising proposed by this paper, has a potential value in the field of denoising for the photoacoustic singals.

Experimental study on Statistical Damage Detection of RC Structures based on Wavelet Packet Analysis

NASA Astrophysics Data System (ADS)

Zhu, X. Q.; Law, S. S.; Jayawardhan, M.

2011-07-01

A novel damage indicator based on wavelet packet transform is developed in this study for structural health monitoring. The response signal of a structure under an impact load is normalized and then decomposed into wavelet packet components. Energies of these wavelet packet components are then calculated to obtain the energy distribution. A statistical indicator is developed to describe the damage extent of the structure. This approach is applied to the test results from simply supported reinforced concrete beams in the laboratory. Cases with single damage are created from static loading, and accelerations of the structure from under impact loads are analyzed. Results show that the method can be used for the damage monitoring and assessment of the structure.

Application of based on improved wavelet algorithm in fiber temperature sensor

NASA Astrophysics Data System (ADS)

Qi, Hui; Tang, Wenjuan

2018-03-01

It is crucial point that accurate temperature in distributed optical fiber temperature sensor. In order to solve the problem of temperature measurement error due to weak Raman scattering signal and strong noise in system, a new based on improved wavelet algorithm is presented. On the basis of the traditional modulus maxima wavelet algorithm, signal correlation is considered to improve the ability to capture signals and noise, meanwhile, combined with wavelet decomposition scale adaptive method to eliminate signal loss or noise not filtered due to mismatch scale. Superiority of algorithm filtering is compared with others by Matlab. At last, the 3km distributed optical fiber temperature sensing system is used for verification. Experimental results show that accuracy of temperature generally increased by 0.5233.

Detection of spontaneous vesicle release at individual synapses using multiple wavelets in a CWT-based algorithm.

PubMed

Sokoll, Stefan; Tönnies, Klaus; Heine, Martin

2012-01-01

In this paper we present an algorithm for the detection of spontaneous activity at individual synapses in microscopy images. By employing the optical marker pHluorin, we are able to visualize synaptic vesicle release with a spatial resolution in the nm range in a non-invasive manner. We compute individual synaptic signals from automatically segmented regions of interest and detect peaks that represent synaptic activity using a continuous wavelet transform based algorithm. As opposed to standard peak detection algorithms, we employ multiple wavelets to match all relevant features of the peak. We evaluate our multiple wavelet algorithm (MWA) on real data and assess the performance on synthetic data over a wide range of signal-to-noise ratios.

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

NASA Technical Reports Server (NTRS)

Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

1999-01-01

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis

PubMed Central

Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

2015-01-01

AIM To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. METHODS This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. RESULTS It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). CONCLUSION The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals. PMID:26309878

Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis.

PubMed

Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

2015-01-01

To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals.

EEG Artifact Removal Using a Wavelet Neural Network

NASA Technical Reports Server (NTRS)

Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom

2011-01-01

!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

NASA Astrophysics Data System (ADS)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

A Brief Historical Introduction to Fractals and Fractal Geometry

ERIC Educational Resources Information Center

Debnath, Lokenath

2006-01-01

This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

Frequency-Specific Fractal Analysis of Postural Control Accounts for Control Strategies

PubMed Central

Gilfriche, Pierre; Deschodt-Arsac, Véronique; Blons, Estelle; Arsac, Laurent M.

2018-01-01

Diverse indicators of postural control in Humans have been explored for decades, mostly based on the trajectory of the center-of-pressure. Classical approaches focus on variability, based on the notion that if a posture is too variable, the subject is not stable. Going deeper, an improved understanding of underlying physiology has been gained from studying variability in different frequency ranges, pointing to specific short-loops (proprioception), and long-loops (visuo-vestibular) in neural control. More recently, fractal analyses have proliferated and become useful additional metrics of postural control. They allowed identifying two scaling phenomena, respectively in short and long timescales. Here, we show that one of the most widely used methods for fractal analysis, Detrended Fluctuation Analysis, could be enhanced to account for scalings on specific frequency ranges. By computing and filtering a bank of synthetic fractal signals, we established how scaling analysis can be focused on specific frequency components. We called the obtained method Frequency-specific Fractal Analysis (FsFA) and used it to associate the two scaling phenomena of postural control to proprioceptive-based control loop and visuo-vestibular based control loop. After that, convincing arguments of method validity came from an application on the study of unaltered vs. altered postural control in athletes. Overall, the analysis suggests that at least two timescales contribute to postural control: a velocity-based control in short timescales relying on proprioceptive sensors, and a position-based control in longer timescales with visuo-vestibular sensors, which is a brand-new vision of postural control. Frequency-specific scaling exponents are promising markers of control strategies in Humans. PMID:29643816

Real-time modeling of primitive environments through wavelet sensors and Hebbian learning

NASA Astrophysics Data System (ADS)

Vaccaro, James M.; Yaworsky, Paul S.

1999-06-01

Modeling the world through sensory input necessarily provides a unique perspective for the observer. Given a limited perspective, objects and events cannot always be encoded precisely but must involve crude, quick approximations to deal with sensory information in a real- time manner. As an example, when avoiding an oncoming car, a pedestrian needs to identify the fact that a car is approaching before ascertaining the model or color of the vehicle. In our methodology, we use wavelet-based sensors with self-organized learning to encode basic sensory information in real-time. The wavelet-based sensors provide necessary transformations while a rank-based Hebbian learning scheme encodes a self-organized environment through translation, scale and orientation invariant sensors. Such a self-organized environment is made possible by combining wavelet sets which are orthonormal, log-scale with linear orientation and have automatically generated membership functions. In earlier work we used Gabor wavelet filters, rank-based Hebbian learning and an exponential modulation function to encode textural information from images. Many different types of modulation are possible, but based on biological findings the exponential modulation function provided a good approximation of first spike coding of `integrate and fire' neurons. These types of Hebbian encoding schemes (e.g., exponential modulation, etc.) are useful for quick response and learning, provide several advantages over contemporary neural network learning approaches, and have been found to quantize data nonlinearly. By combining wavelets with Hebbian learning we can provide a real-time front-end for modeling an intelligent process, such as the autonomous control of agents in a simulated environment.

Wavelet method for CT colonography computer-aided polyp detection.

PubMed

Li, Jiang; Van Uitert, Robert; Yao, Jianhua; Petrick, Nicholas; Franaszek, Marek; Huang, Adam; Summers, Ronald M

2008-08-01

Computed tomographic colonography (CTC) computer aided detection (CAD) is a new method to detect colon polyps. Colonic polyps are abnormal growths that may become cancerous. Detection and removal of colonic polyps, particularly larger ones, has been shown to reduce the incidence of colorectal cancer. While high sensitivities and low false positive rates are consistently achieved for the detection of polyps sized 1 cm or larger, lower sensitivities and higher false positive rates occur when the goal of CAD is to identify "medium"-sized polyps, 6-9 mm in diameter. Such medium-sized polyps may be important for clinical patient management. We have developed a wavelet-based postprocessor to reduce false positives for this polyp size range. We applied the wavelet-based postprocessor to CTC CAD findings from 44 patients in whom 45 polyps with sizes of 6-9 mm were found at segmentally unblinded optical colonoscopy and visible on retrospective review of the CT colonography images. Prior to the application of the wavelet-based postprocessor, the CTC CAD system detected 33 of the polyps (sensitivity 73.33%) with 12.4 false positives per patient, a sensitivity comparable to that of expert radiologists. Fourfold cross validation with 5000 bootstraps showed that the wavelet-based postprocessor could reduce the false positives by 56.61% (p <0.001), to 5.38 per patient (95% confidence interval [4.41, 6.34]), without significant sensitivity degradation (32/45, 71.11%, 95% confidence interval [66.39%, 75.74%], p=0.1713). We conclude that this wavelet-based postprocessor can substantially reduce the false positive rate of our CTC CAD for this important polyp size range.

Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.

PubMed

Arjunan, Sridhar P; Kumar, Dinesh K

2007-01-01

The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.

Fractal Analysis of Permeability of Unsaturated Fractured Rocks

PubMed Central

Jiang, Guoping; Shi, Wei; Huang, Lili

2013-01-01

A physical conceptual model for water retention in fractured rocks is derived while taking into account the effect of pore size distribution and tortuosity of capillaries. The formula of calculating relative hydraulic conductivity of fractured rock is given based on fractal theory. It is an issue to choose an appropriate capillary pressure-saturation curve in the research of unsaturated fractured mass. The geometric pattern of the fracture bulk is described based on the fractal distribution of tortuosity. The resulting water content expression is then used to estimate the unsaturated hydraulic conductivity of the fractured medium based on the well-known model of Burdine. It is found that for large enough ranges of fracture apertures the new constitutive model converges to the empirical Brooks-Corey model. PMID:23690746

Fractal analysis of permeability of unsaturated fractured rocks.

PubMed

Jiang, Guoping; Shi, Wei; Huang, Lili

2013-01-01

A physical conceptual model for water retention in fractured rocks is derived while taking into account the effect of pore size distribution and tortuosity of capillaries. The formula of calculating relative hydraulic conductivity of fractured rock is given based on fractal theory. It is an issue to choose an appropriate capillary pressure-saturation curve in the research of unsaturated fractured mass. The geometric pattern of the fracture bulk is described based on the fractal distribution of tortuosity. The resulting water content expression is then used to estimate the unsaturated hydraulic conductivity of the fractured medium based on the well-known model of Burdine. It is found that for large enough ranges of fracture apertures the new constitutive model converges to the empirical Brooks-Corey model.

Adaptive zero-tree structure for curved wavelet image coding

NASA Astrophysics Data System (ADS)

Zhang, Liang; Wang, Demin; Vincent, André

2006-02-01

We investigate the issue of efficient data organization and representation of the curved wavelet coefficients [curved wavelet transform (WT)]. We present an adaptive zero-tree structure that exploits the cross-subband similarity of the curved wavelet transform. In the embedded zero-tree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT), the parent-child relationship is defined in such a way that a parent has four children, restricted to a square of 2×2 pixels, the parent-child relationship in the adaptive zero-tree structure varies according to the curves along which the curved WT is performed. Five child patterns were determined based on different combinations of curve orientation. A new image coder was then developed based on this adaptive zero-tree structure and the set-partitioning technique. Experimental results using synthetic and natural images showed the effectiveness of the proposed adaptive zero-tree structure for encoding of the curved wavelet coefficients. The coding gain of the proposed coder can be up to 1.2 dB in terms of peak SNR (PSNR) compared to the SPIHT coder. Subjective evaluation shows that the proposed coder preserves lines and edges better than the SPIHT coder.

Wavelet-based analysis of circadian behavioral rhythms.

PubMed

Leise, Tanya L

2015-01-01

The challenging problems presented by noisy biological oscillators have led to the development of a great variety of methods for accurately estimating rhythmic parameters such as period and amplitude. This chapter focuses on wavelet-based methods, which can be quite effective for assessing how rhythms change over time, particularly if time series are at least a week in length. These methods can offer alternative views to complement more traditional methods of evaluating behavioral records. The analytic wavelet transform can estimate the instantaneous period and amplitude, as well as the phase of the rhythm at each time point, while the discrete wavelet transform can extract the circadian component of activity and measure the relative strength of that circadian component compared to those in other frequency bands. Wavelet transforms do not require the removal of noise or trend, and can, in fact, be effective at removing noise and trend from oscillatory time series. The Fourier periodogram and spectrogram are reviewed, followed by descriptions of the analytic and discrete wavelet transforms. Examples illustrate application of each method and their prior use in chronobiology is surveyed. Issues such as edge effects, frequency leakage, and implications of the uncertainty principle are also addressed. © 2015 Elsevier Inc. All rights reserved.

Local wavelet transform: a cost-efficient custom processor for space image compression

NASA Astrophysics Data System (ADS)

Masschelein, Bart; Bormans, Jan G.; Lafruit, Gauthier

2002-11-01

Thanks to its intrinsic scalability features, the wavelet transform has become increasingly popular as decorrelator in image compression applications. Throuhgput, memory requirements and complexity are important parameters when developing hardware image compression modules. An implementation of the classical, global wavelet transform requires large memory sizes and implies a large latency between the availability of the input image and the production of minimal data entities for entropy coding. Image tiling methods, as proposed by JPEG2000, reduce the memory sizes and the latency, but inevitably introduce image artefacts. The Local Wavelet Transform (LWT), presented in this paper, is a low-complexity wavelet transform architecture using a block-based processing that results in the same transformed images as those obtained by the global wavelet transform. The architecture minimizes the processing latency with a limited amount of memory. Moreover, as the LWT is an instruction-based custom processor, it can be programmed for specific tasks, such as push-broom processing of infinite-length satelite images. The features of the LWT makes it appropriate for use in space image compression, where high throughput, low memory sizes, low complexity, low power and push-broom processing are important requirements.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

An improved method based on wavelet coefficient correlation to filter noise in Doppler ultrasound blood flow signals

NASA Astrophysics Data System (ADS)

Wan, Renzhi; Zu, Yunxiao; Shao, Lin

2018-04-01

The blood echo signal maintained through Medical ultrasound Doppler devices would always include vascular wall pulsation signal .The traditional method to de-noise wall signal is using high-pass filter, which will also remove the lowfrequency part of the blood flow signal. Some scholars put forward a method based on region selective reduction, which at first estimates of the wall pulsation signals and then removes the wall signal from the mixed signal. Apparently, this method uses the correlation between wavelet coefficients to distinguish blood signal from wall signal, but in fact it is a kind of wavelet threshold de-noising method, whose effect is not so much ideal. In order to maintain a better effect, this paper proposes an improved method based on wavelet coefficient correlation to separate blood signal and wall signal, and simulates the algorithm by computer to verify its validity.

Noise Reduction in Breath Sound Files Using Wavelet Transform Based Filter

NASA Astrophysics Data System (ADS)

Syahputra, M. F.; Situmeang, S. I. G.; Rahmat, R. F.; Budiarto, R.

2017-04-01

The development of science and technology in the field of healthcare increasingly provides convenience in diagnosing respiratory system problem. Recording the breath sounds is one example of these developments. Breath sounds are recorded using a digital stethoscope, and then stored in a file with sound format. This breath sounds will be analyzed by health practitioners to diagnose the symptoms of disease or illness. However, the breath sounds is not free from interference signals. Therefore, noise filter or signal interference reduction system is required so that breath sounds component which contains information signal can be clarified. In this study, we designed a filter called a wavelet transform based filter. The filter that is designed in this study is using Daubechies wavelet with four wavelet transform coefficients. Based on the testing of the ten types of breath sounds data, the data is obtained in the largest SNRdB bronchial for 74.3685 decibels.

Wavelet energy-guided level set-based active contour: a segmentation method to segment highly similar regions.

PubMed

Achuthan, Anusha; Rajeswari, Mandava; Ramachandram, Dhanesh; Aziz, Mohd Ezane; Shuaib, Ibrahim Lutfi

2010-07-01

This paper introduces an approach to perform segmentation of regions in computed tomography (CT) images that exhibit intra-region intensity variations and at the same time have similar intensity distributions with surrounding/adjacent regions. In this work, we adapt a feature computed from wavelet transform called wavelet energy to represent the region information. The wavelet energy is embedded into a level set model to formulate the segmentation model called wavelet energy-guided level set-based active contour (WELSAC). The WELSAC model is evaluated using several synthetic and CT images focusing on tumour cases, which contain regions demonstrating the characteristics of intra-region intensity variations and having high similarity in intensity distributions with the adjacent regions. The obtained results show that the proposed WELSAC model is able to segment regions of interest in close correspondence with the manual delineation provided by the medical experts and to provide a solution for tumour detection. Copyright 2010 Elsevier Ltd. All rights reserved.

Improving liquid chromatography-tandem mass spectrometry determinations by modifying noise frequency spectrum between two consecutive wavelet-based low-pass filtering procedures.

PubMed

Chen, Hsiao-Ping; Liao, Hui-Ju; Huang, Chih-Min; Wang, Shau-Chun; Yu, Sung-Nien

2010-04-23

This paper employs one chemometric technique to modify the noise spectrum of liquid chromatography-tandem mass spectrometry (LC-MS/MS) chromatogram between two consecutive wavelet-based low-pass filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. Although similar techniques of using other sets of low-pass procedures such as matched filters have been published, the procedures developed in this work are able to avoid peak broadening disadvantages inherent in matched filters. In addition, unlike Fourier transform-based low-pass filters, wavelet-based filters efficiently reject noises in the chromatograms directly in the time domain without distorting the original signals. In this work, the low-pass filtering procedures sequentially convolve the original chromatograms against each set of low pass filters to result in approximation coefficients, representing the low-frequency wavelets, of the first five resolution levels. The tedious trials of setting threshold values to properly shrink each wavelet are therefore no longer required. This noise modification technique is to multiply one wavelet-based low-pass filtered LC-MS/MS chromatogram with another artificial chromatogram added with thermal noises prior to the other wavelet-based low-pass filter. Because low-pass filter cannot eliminate frequency components below its cut-off frequency, more efficient peak S/N ratio improvement cannot be accomplished using consecutive low-pass filter procedures to process LC-MS/MS chromatograms. In contrast, when the low-pass filtered LC-MS/MS chromatogram is conditioned with the multiplication alteration prior to the other low-pass filter, much better ratio improvement is achieved. The noise frequency spectrum of low-pass filtered chromatogram, which originally contains frequency components below the filter cut-off frequency, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the high frequency regimes, the other low-pass filter is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC-MS/MS chromatograms, of which typically less than 6-fold peak S/N ratio improvement achieved with two consecutive wavelet-based low-pass filters remains the same S/N ratio improvement using one-step wavelet-based low-pass filter, are improved to accomplish much better ratio enhancement 25-folds to 40-folds typically when the noise frequency spectrum is modified between two low-pass filters. The linear standard curves using the filtered LC-MS/MS signals are validated. The filtered LC-MS/MS signals are also reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 7-9) are obtained using the filtered signals than the determinations using the original signals. Copyright 2010 Elsevier B.V. All rights reserved.

TEC variations over North-western Balkan Peninsula before and during the seismic activity of 24th May 2009

NASA Astrophysics Data System (ADS)

Contadakis, M. E.; Arabelos, D. N.; Vergos, G.

2012-04-01

In this paper the Total Electron Content (TEC) data of 8 Global Positioning System (GPS) stations of the EUREF network, 4 close and 4 remote to EQ epicentre stations, which are being provided by IONOLAB (Turkey), were analysed using wavelet analysis and Discrete Fourier Analysis in order to investigate the TEC variations over North-western Balkan Peninsula before and during the seismic activity of 24th of May, 2009. The main conclusions of this analysis are the following. (a) TEC oscillations in a broad range of frequencies occur randomly over a broad area of several hundred km from the earthquake and (b) high frequency oscillations (f ≥ 0.0003Hz, periods T ≤ 60m) seems to point to the location of the earthquake with a questionable accuracy but the fractal characteristics of the frequencies distribution, points to the locus of the earthquake with a rather higher accuracy. We conclude that the LAIC mechanism through acoustic or gravity wave could explain this phenomenology.

EUS elastography (strain ratio) and fractal-based quantitative analysis for the diagnosis of solid pancreatic lesions.

PubMed

Carrara, Silvia; Di Leo, Milena; Grizzi, Fabio; Correale, Loredana; Rahal, Daoud; Anderloni, Andrea; Auriemma, Francesco; Fugazza, Alessandro; Preatoni, Paoletta; Maselli, Roberta; Hassan, Cesare; Finati, Elena; Mangiavillano, Benedetto; Repici, Alessandro

2018-06-01

EUS elastography is useful in characterizing solid pancreatic lesions (SPLs), and fractal analysis-based technology has been used to evaluate geometric complexity in oncology. The aim of this study was to evaluate EUS elastography (strain ratio) and fractal analysis for the characterization of SPLs. Consecutive patients with SPLs were prospectively enrolled between December 2015 and February 2017. Elastographic evaluation included parenchymal strain ratio (pSR) and wall strain ratio (wSR) and was performed with a new compact US processor. Elastographic images were analyzed using a computer program to determine the 3-dimensional histogram fractal dimension. A composite cytology/histology/clinical reference standard was used to assess sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve. Overall, 102 SPLs from 100 patients were studied. At final diagnosis, 69 (68%) were malignant and 33 benign. At elastography, both pSR and wSR appeared to be significantly higher in malignant as compared with benign SPLs (pSR, 24.5 vs 6.4 [P < .001]; wSR, 56.6 vs 15.3 [P < .001]). When the best cut-off levels of pSR and wSR at 9.10 and 16.2, respectively, were used, sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve were 88.4%, 78.8%, 89.7%, 76.9%, and 86.7% and 91.3%, 69.7%, 86.5%, 80%, and 85.7%, respectively. Fractal analysis showed a significant statistical difference (P = .0087) between the mean surface fractal dimension of malignant lesions (D = 2.66 ± .01) versus neuroendocrine tumor (D = 2.73 ± .03) and a statistical difference for all 3 channels red, green, and blue (P < .0001). EUS elastography with pSR and fractal-based analysis are useful in characterizing SPLs. (Clinical trial registration number: NCT02855151.). Copyright © 2018 American Society for Gastrointestinal Endoscopy. Published by Elsevier Inc. All rights reserved.

Fractal planetary rings: Energy inequalities and random field model

NASA Astrophysics Data System (ADS)

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2017-12-01

This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F2 of the radial cross-section F of the rings, where F is a fat fractal.

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.

PubMed

da Silva, Núbia Rosa; Florindo, João Batista; Gómez, María Cecilia; Rossatto, Davi Rodrigo; Kolb, Rosana Marta; Bruno, Odemir Martinez

2015-01-01

The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

A Wavelet-Based Methodology for Grinding Wheel Condition Monitoring

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, T. W.; Ting, C.F.; Qu, Jun

2007-01-01

Grinding wheel surface condition changes as more material is removed. This paper presents a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals. Grinding experiments in creep feed mode were conducted to grind alumina specimens with a resinoid-bonded diamond wheel using two different conditions. During the experiments, AE signals were collected when the wheel was 'sharp' and when the wheel was 'dull'. Discriminant features were then extracted from each raw AE signal segment using the discrete wavelet decomposition procedure. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish differentmore » states of grinding wheel condition. The test results indicate that the proposed methodology can achieve 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for the combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected.« less

Design and application of discrete wavelet packet transform based multiresolution controller for liquid level system.

PubMed

Paul, Rimi; Sengupta, Anindita

2017-11-01

A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

I. W. Ginsberg

Multiresolutional decompositions known as spectral fingerprints are often used to extract spectral features from multispectral/hyperspectral data. In this study, the authors investigate the use of wavelet-based algorithms for generating spectral fingerprints. The wavelet-based algorithms are compared to the currently used method, traditional convolution with first-derivative Gaussian filters. The comparison analyses consists of two parts: (a) the computational expense of the new method is compared with the computational costs of the current method and (b) the outputs of the wavelet-based methods are compared with those of the current method to determine any practical differences in the resulting spectral fingerprints. The resultsmore » show that the wavelet-based algorithms can greatly reduce the computational expense of generating spectral fingerprints, while practically no differences exist in the resulting fingerprints. The analysis is conducted on a database of hyperspectral signatures, namely, Hyperspectral Digital Image Collection Experiment (HYDICE) signatures. The reduction in computational expense is by a factor of about 30, and the average Euclidean distance between resulting fingerprints is on the order of 0.02.« less

Wavelets and the squeezed states of quantum optics

NASA Technical Reports Server (NTRS)

Defacio, B.

1992-01-01

Wavelets are new mathematical objects which act as 'designer trigonometric functions.' To obtain a wavelet, the original function space of finite energy signals is generalized to a phase-space, and the translation operator in the original space has a scale change in the new variable adjoined to the translation. Localization properties in the phase-space can be improved and unconditional bases are obtained for a broad class of function and distribution spaces. Operators in phase space are 'almost diagonal' instead of the traditional condition of being diagonal in the original function space. These wavelets are applied to the squeezed states of quantum optics. The scale change required for a quantum wavelet is shown to be a Yuen squeeze operator acting on an arbitrary density operator.

Fractal based observables to probe jet substructure of quarks and gluons

NASA Astrophysics Data System (ADS)

Davighi, Joe; Harris, Philip

2018-04-01

New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.

Multi-level basis selection of wavelet packet decomposition tree for heart sound classification.

PubMed

Safara, Fatemeh; Doraisamy, Shyamala; Azman, Azreen; Jantan, Azrul; Abdullah Ramaiah, Asri Ranga

2013-10-01

Wavelet packet transform decomposes a signal into a set of orthonormal bases (nodes) and provides opportunities to select an appropriate set of these bases for feature extraction. In this paper, multi-level basis selection (MLBS) is proposed to preserve the most informative bases of a wavelet packet decomposition tree through removing less informative bases by applying three exclusion criteria: frequency range, noise frequency, and energy threshold. MLBS achieved an accuracy of 97.56% for classifying normal heart sound, aortic stenosis, mitral regurgitation, and aortic regurgitation. MLBS is a promising basis selection to be suggested for signals with a small range of frequencies. Copyright © 2013 The Authors. Published by Elsevier Ltd.. All rights reserved.

A comparative study on book shelf structure based on different domain modal analysis

NASA Astrophysics Data System (ADS)

Sabamehr, Ardalan; Roy, Timir Baran; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) based on the vibration of structures has been very attractive topic for researchers in different fields such as: civil, aeronautical and mechanical engineering. The aim of this paper is to compare three most common modal identification techniques such as Frequency Domain Decomposition (FDD), Stochastic Subspace Identification (SSI) and Continuous Wavelet Transform (CWT) to find modal properties (such as natural frequency, mode shape and damping ratio) of three story book shelf steel structure which was built in Concordia University Lab. The modified Complex Morlet wavelet have been selected for wavelet in order to use asymptotic signal rather than real one with variable bandwidth and wavelet central frequency. So, CWT is able to detect instantaneous modulus and phase by use of local maxima ridge detection.

Analysis of photonic Doppler velocimetry data based on the continuous wavelet transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Shouxian; Wang Detian; Li Tao

2011-02-15

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated bymore » a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.« less

Radiomics-based differentiation of lung disease models generated by polluted air based on X-ray computed tomography data.

PubMed

Szigeti, Krisztián; Szabó, Tibor; Korom, Csaba; Czibak, Ilona; Horváth, Ildikó; Veres, Dániel S; Gyöngyi, Zoltán; Karlinger, Kinga; Bergmann, Ralf; Pócsik, Márta; Budán, Ferenc; Máthé, Domokos

2016-02-11

Lung diseases (resulting from air pollution) require a widely accessible method for risk estimation and early diagnosis to ensure proper and responsive treatment. Radiomics-based fractal dimension analysis of X-ray computed tomography attenuation patterns in chest voxels of mice exposed to different air polluting agents was performed to model early stages of disease and establish differential diagnosis. To model different types of air pollution, BALBc/ByJ mouse groups were exposed to cigarette smoke combined with ozone, sulphur dioxide gas and a control group was established. Two weeks after exposure, the frequency distributions of image voxel attenuation data were evaluated. Specific cut-off ranges were defined to group voxels by attenuation. Cut-off ranges were binarized and their spatial pattern was associated with calculated fractal dimension, then abstracted by the fractal dimension -- cut-off range mathematical function. Nonparametric Kruskal-Wallis (KW) and Mann-Whitney post hoc (MWph) tests were used. Each cut-off range versus fractal dimension function plot was found to contain two distinctive Gaussian curves. The ratios of the Gaussian curve parameters are considerably significant and are statistically distinguishable within the three exposure groups. A new radiomics evaluation method was established based on analysis of the fractal dimension of chest X-ray computed tomography data segments. The specific attenuation patterns calculated utilizing our method may diagnose and monitor certain lung diseases, such as chronic obstructive pulmonary disease (COPD), asthma, tuberculosis or lung carcinomas.

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

PubMed

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

Analysis of the tennis racket vibrations during forehand drives: Selection of the mother wavelet.

PubMed

Blache, Y; Hautier, C; Lefebvre, F; Djordjevic, A; Creveaux, T; Rogowski, I

2017-08-16

The time-frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time-frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25±17%, 2±5%, 5±7% and 27±27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fingerprint recognition of wavelet-based compressed images by neuro-fuzzy clustering

NASA Astrophysics Data System (ADS)

Liu, Ti C.; Mitra, Sunanda

1996-06-01

Image compression plays a crucial role in many important and diverse applications requiring efficient storage and transmission. This work mainly focuses on a wavelet transform (WT) based compression of fingerprint images and the subsequent classification of the reconstructed images. The algorithm developed involves multiresolution wavelet decomposition, uniform scalar quantization, entropy and run- length encoder/decoder and K-means clustering of the invariant moments as fingerprint features. The performance of the WT-based compression algorithm has been compared with JPEG current image compression standard. Simulation results show that WT outperforms JPEG in high compression ratio region and the reconstructed fingerprint image yields proper classification.

Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

NASA Astrophysics Data System (ADS)

Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

2014-05-01

Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.

Texture Analysis of Recurrence Plots Based on Wavelets and PSO for Laryngeal Pathologies Detection.

PubMed

Souza, Taciana A; Vieira, Vinícius J D; Correia, Suzete E N; Costa, Silvana L N C; de A Costa, Washington C; Souza, Micael A

2015-01-01

This paper deals with the discrimination between healthy and pathological speech signals using recurrence plots and wavelet transform with texture features. Approximation and detail coefficients are obtained from the recurrence plots using Haar wavelet transform, considering one decomposition level. The considered laryngeal pathologies are: paralysis, Reinke's edema and nodules. Accuracy rates above 86% were obtained by means of the employed method.

Mouse EEG spike detection based on the adapted continuous wavelet transform

NASA Astrophysics Data System (ADS)

Tieng, Quang M.; Kharatishvili, Irina; Chen, Min; Reutens, David C.

2016-04-01

Objective. Electroencephalography (EEG) is an important tool in the diagnosis of epilepsy. Interictal spikes on EEG are used to monitor the development of epilepsy and the effects of drug therapy. EEG recordings are generally long and the data voluminous. Thus developing a sensitive and reliable automated algorithm for analyzing EEG data is necessary. Approach. A new algorithm for detecting and classifying interictal spikes in mouse EEG recordings is proposed, based on the adapted continuous wavelet transform (CWT). The construction of the adapted mother wavelet is founded on a template obtained from a sample comprising the first few minutes of an EEG data set. Main Result. The algorithm was tested with EEG data from a mouse model of epilepsy and experimental results showed that the algorithm could distinguish EEG spikes from other transient waveforms with a high degree of sensitivity and specificity. Significance. Differing from existing approaches, the proposed approach combines wavelet denoising, to isolate transient signals, with adapted CWT-based template matching, to detect true interictal spikes. Using the adapted wavelet constructed from a predefined template, the adapted CWT is calculated on small EEG segments to fit dynamical changes in the EEG recording.

ECG compression using non-recursive wavelet transform with quality control

NASA Astrophysics Data System (ADS)

Liu, Je-Hung; Hung, King-Chu; Wu, Tsung-Ching

2016-09-01

While wavelet-based electrocardiogram (ECG) data compression using scalar quantisation (SQ) yields excellent compression performance, a wavelet's SQ scheme, however, must select a set of multilevel quantisers for each quantisation process. As a result of the properties of multiple-to-one mapping, however, this scheme is not conducive for reconstruction error control. In order to address this problem, this paper presents a single-variable control SQ scheme able to guarantee the reconstruction quality of wavelet-based ECG data compression. Based on the reversible round-off non-recursive discrete periodised wavelet transform (RRO-NRDPWT), the SQ scheme is derived with a three-stage design process that first uses genetic algorithm (GA) for high compression ratio (CR), followed by a quadratic curve fitting for linear distortion control, and the third uses a fuzzy decision-making for minimising data dependency effect and selecting the optimal SQ. The two databases, Physikalisch-Technische Bundesanstalt (PTB) and Massachusetts Institute of Technology (MIT) arrhythmia, are used to evaluate quality control performance. Experimental results show that the design method guarantees a high compression performance SQ scheme with statistically linear distortion. This property can be independent of training data and can facilitate rapid error control.

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series

PubMed Central

2017-01-01

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized ‘events’. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event’s ‘region of influence’ within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis, is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry. PMID:28484325

Application of wavelet-based multi-model Kalman filters to real-time flood forecasting

NASA Astrophysics Data System (ADS)

Chou, Chien-Ming; Wang, Ru-Yih

2004-04-01

This paper presents the application of a multimodel method using a wavelet-based Kalman filter (WKF) bank to simultaneously estimate decomposed state variables and unknown parameters for real-time flood forecasting. Applying the Haar wavelet transform alters the state vector and input vector of the state space. In this way, an overall detail plus approximation describes each new state vector and input vector, which allows the WKF to simultaneously estimate and decompose state variables. The wavelet-based multimodel Kalman filter (WMKF) is a multimodel Kalman filter (MKF), in which the Kalman filter has been substituted for a WKF. The WMKF then obtains M estimated state vectors. Next, the M state-estimates, each of which is weighted by its possibility that is also determined on-line, are combined to form an optimal estimate. Validations conducted for the Wu-Tu watershed, a small watershed in Taiwan, have demonstrated that the method is effective because of the decomposition of wavelet transform, the adaptation of the time-varying Kalman filter and the characteristics of the multimodel method. Validation results also reveal that the resulting method enhances the accuracy of the runoff prediction of the rainfall-runoff process in the Wu-Tu watershed.

Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

NASA Astrophysics Data System (ADS)

Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.

2014-08-01

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver hfodd that is based on the harmonic-oscillator basis expansion. Several examples are considered, including the self-consistent HFB problem for spin-polarized trapped cold fermions and the Skyrme-Hartree-Fock (+BCS) problem for triaxial deformed nuclei. Conclusions: The new madness-hfb framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion, and exotic pasta phases that appear in neutron star crust.

Wavelet-based study of valence-arousal model of emotions on EEG signals with LabVIEW.

PubMed

Guzel Aydin, Seda; Kaya, Turgay; Guler, Hasan

2016-06-01

This paper illustrates the wavelet-based feature extraction for emotion assessment using electroencephalogram (EEG) signal through graphical coding design. Two-dimensional (valence-arousal) emotion model was studied. Different emotions (happy, joy, melancholy, and disgust) were studied for assessment. These emotions were stimulated by video clips. EEG signals obtained from four subjects were decomposed into five frequency bands (gamma, beta, alpha, theta, and delta) using "db5" wavelet function. Relative features were calculated to obtain further information. Impact of the emotions according to valence value was observed to be optimal on power spectral density of gamma band. The main objective of this work is not only to investigate the influence of the emotions on different frequency bands but also to overcome the difficulties in the text-based program. This work offers an alternative approach for emotion evaluation through EEG processing. There are a number of methods for emotion recognition such as wavelet transform-based, Fourier transform-based, and Hilbert-Huang transform-based methods. However, the majority of these methods have been applied with the text-based programming languages. In this study, we proposed and implemented an experimental feature extraction with graphics-based language, which provides great convenience in bioelectrical signal processing.

Identification Method of Mud Shale Fractures Base on Wavelet Transform

NASA Astrophysics Data System (ADS)

Xia, Weixu; Lai, Fuqiang; Luo, Han

2018-01-01

In recent years, inspired by seismic analysis technology, a new method for analysing mud shale fractures oil and gas reservoirs by logging properties has emerged. By extracting the high frequency attribute of the wavelet transform in the logging attribute, the formation information hidden in the logging signal is extracted, identified the fractures that are not recognized by conventional logging and in the identified fracture segment to show the “cycle jump”, “high value”, “spike” and other response effect is more obvious. Finally formed a complete wavelet denoising method and wavelet high frequency identification fracture method.

Privacy Preserving Technique for Euclidean Distance Based Mining Algorithms Using a Wavelet Related Transform

NASA Astrophysics Data System (ADS)

Kadampur, Mohammad Ali; D. v. L. N., Somayajulu

Privacy preserving data mining is an art of knowledge discovery without revealing the sensitive data of the data set. In this paper a data transformation technique using wavelets is presented for privacy preserving data mining. Wavelets use well known energy compaction approach during data transformation and only the high energy coefficients are published to the public domain instead of the actual data proper. It is found that the transformed data preserves the Eucleadian distances and the method can be used in privacy preserving clustering. Wavelets offer the inherent improved time complexity.

Wavelet analysis and scaling properties of time series

NASA Astrophysics Data System (ADS)

Manimaran, P.; Panigrahi, Prasanta K.; Parikh, Jitendra C.

2005-10-01

We propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multifractal behavior.

Wavelet Applications for Flight Flutter Testing

NASA Technical Reports Server (NTRS)

Lind, Rick; Brenner, Marty; Freudinger, Lawrence C.

1999-01-01

Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.

Highly efficient codec based on significance-linked connected-component analysis of wavelet coefficients

NASA Astrophysics Data System (ADS)

Chai, Bing-Bing; Vass, Jozsef; Zhuang, Xinhua

1997-04-01

Recent success in wavelet coding is mainly attributed to the recognition of importance of data organization. There has been several very competitive wavelet codecs developed, namely, Shapiro's Embedded Zerotree Wavelets (EZW), Servetto et. al.'s Morphological Representation of Wavelet Data (MRWD), and Said and Pearlman's Set Partitioning in Hierarchical Trees (SPIHT). In this paper, we propose a new image compression algorithm called Significant-Linked Connected Component Analysis (SLCCA) of wavelet coefficients. SLCCA exploits both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. A so-called significant link between connected components is designed to reduce the positional overhead of MRWD. In addition, the significant coefficients' magnitude are encoded in bit plane order to match the probability model of the adaptive arithmetic coder. Experiments show that SLCCA outperforms both EZW and MRWD, and is tied with SPIHT. Furthermore, it is observed that SLCCA generally has the best performance on images with large portion of texture. When applied to fingerprint image compression, it outperforms FBI's wavelet scalar quantization by about 1 dB.

Characteristic Analysis of Air-gun Source Wavelet based on the Vertical Cable Data

NASA Astrophysics Data System (ADS)

Xing, L.

2016-12-01

Air guns are important sources for marine seismic exploration. Far-field wavelets of air gun arrays, as a necessary parameter for pre-stack processing and source models, plays an important role during marine seismic data processing and interpretation. When an air gun fires, it generates a series of air bubbles. Similar to onshore seismic exploration, the water forms a plastic fluid near the bubble; the farther the air gun is located from the measurement, the more steady and more accurately represented the wavelet will be. In practice, hydrophones should be placed more than 100 m from the air gun; however, traditional seismic cables cannot meet this requirement. On the other hand, vertical cables provide a viable solution to this problem. This study uses a vertical cable to receive wavelets from 38 air guns and data are collected offshore Southeast Qiong, where the water depth is over 1000 m. In this study, the wavelets measured using this technique coincide very well with the simulated wavelets and can therefore represent the real shape of the wavelets. This experiment fills a technology gap in China.

Regional-specific Stochastic Simulation of Spatially-distributed Ground-motion Time Histories using Wavelet Packet Analysis

NASA Astrophysics Data System (ADS)

Huang, D.; Wang, G.

2014-12-01

Stochastic simulation of spatially distributed ground-motion time histories is important for performance-based earthquake design of geographically distributed systems. In this study, we develop a novel technique to stochastically simulate regionalized ground-motion time histories using wavelet packet analysis. First, a transient acceleration time history is characterized by wavelet-packet parameters proposed by Yamamoto and Baker (2013). The wavelet-packet parameters fully characterize ground-motion time histories in terms of energy content, time- frequency-domain characteristics and time-frequency nonstationarity. This study further investigates the spatial cross-correlations of wavelet-packet parameters based on geostatistical analysis of 1500 regionalized ground motion data from eight well-recorded earthquakes in California, Mexico, Japan and Taiwan. The linear model of coregionalization (LMC) is used to develop a permissible spatial cross-correlation model for each parameter group. The geostatistical analysis of ground-motion data from different regions reveals significant dependence of the LMC structure on regional site conditions, which can be characterized by the correlation range of Vs30 in each region. In general, the spatial correlation and cross-correlation of wavelet-packet parameters are stronger if the site condition is more homogeneous. Using the regional-specific spatial cross-correlation model and cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground-motion time histories can be synthesized. Case studies and blind tests demonstrated that the simulated ground motions generally agree well with the actual recorded data, if the influence of regional-site conditions is considered. The developed method has great potential to be used in computational-based seismic analysis and loss estimation in a regional scale.

Identification of the subthalamic nucleus in deep brain stimulation surgery with a novel wavelet-derived measure of neural background activity.

PubMed

Snellings, André; Sagher, Oren; Anderson, David J; Aldridge, J Wayne

2009-10-01

The authors developed a wavelet-based measure for quantitative assessment of neural background activity during intraoperative neurophysiological recordings so that the boundaries of the subthalamic nucleus (STN) can be more easily localized for electrode implantation. Neural electrophysiological data were recorded in 14 patients (20 tracks and 275 individual recording sites) with dopamine-sensitive idiopathic Parkinson disease during the target localization portion of deep brain stimulator implantation surgery. During intraoperative recording, the STN was identified based on audio and visual monitoring of neural firing patterns, kinesthetic tests, and comparisons between neural behavior and the known characteristics of the target nucleus. The quantitative wavelet-based measure was applied offline using commercially available software to measure the magnitude of the neural background activity, and the results of this analysis were compared with the intraoperative conclusions. Wavelet-derived estimates were also compared with power spectral density measurements. The wavelet-derived background levels were significantly higher in regions encompassed by the clinically estimated boundaries of the STN than in the surrounding regions (STN, 225 +/- 61 microV; ventral to the STN, 112 +/- 32 microV; and dorsal to the STN, 136 +/- 66 microV). In every track, the absolute maximum magnitude was found within the clinically identified STN. The wavelet-derived background levels provided a more consistent index with less variability than measurements with power spectral density. Wavelet-derived background activity can be calculated quickly, does not require spike sorting, and can be used to identify the STN reliably with very little subjective interpretation required. This method may facilitate the rapid intraoperative identification of STN borders.

Identification of the subthalamic nucleus in deep brain stimulation surgery with a novel wavelet-derived measure of neural background activity

PubMed Central

Snellings, André; Sagher, Oren; Anderson, David J.; Aldridge, J. Wayne

2016-01-01

Object A wavelet-based measure was developed to quantitatively assess neural background activity taken during surgical neurophysiological recordings to localize the boundaries of the subthalamic nucleus during target localization for deep brain stimulator implant surgery. Methods Neural electrophysiological data was recorded from 14 patients (20 tracks, n = 275 individual recording sites) with dopamine-sensitive idiopathic Parkinson’s disease during the target localization portion of deep brain stimulator implant surgery. During intraoperative recording the STN was identified based upon audio and visual monitoring of neural firing patterns, kinesthetic tests, and comparisons between neural behavior and known characteristics of the target nucleus. The quantitative wavelet-based measure was applied off-line using MATLAB software to measure the magnitude of the neural background activity, and the results of this analysis were compared to the intraoperative conclusions. Wavelet-derived estimates were compared to power spectral density measures. Results The wavelet-derived background levels were significantly higher in regions encompassed by the clinically estimated boundaries of the STN than in surrounding regions (STN: 225 ± 61 μV vs. ventral to STN: 112 ± 32 μV, and dorsal to STN: 136 ± 66 μV). In every track, the absolute maximum magnitude was found within the clinically identified STN. The wavelet-derived background levels provided a more consistent index with less variability than power spectral density. Conclusions The wavelet-derived background activity assessor can be calculated quickly, requires no spike sorting, and can be reliably used to identify the STN with very little subjective interpretation required. This method may facilitate rapid intraoperative identification of subthalamic nucleus borders. PMID:19344225

Classification of arterial and venous cerebral vasculature based on wavelet postprocessing of CT perfusion data.

PubMed

Havla, Lukas; Schneider, Moritz J; Thierfelder, Kolja M; Beyer, Sebastian E; Ertl-Wagner, Birgit; Reiser, Maximilian F; Sommer, Wieland H; Dietrich, Olaf

2016-02-01

The purpose of this study was to propose and evaluate a new wavelet-based technique for classification of arterial and venous vessels using time-resolved cerebral CT perfusion data sets. Fourteen consecutive patients (mean age 73 yr, range 17-97) with suspected stroke but no pathology in follow-up MRI were included. A CT perfusion scan with 32 dynamic phases was performed during intravenous bolus contrast-agent application. After rigid-body motion correction, a Paul wavelet (order 1) was used to calculate voxelwise the wavelet power spectrum (WPS) of each attenuation-time course. The angiographic intensity A was defined as the maximum of the WPS, located at the coordinates T (time axis) and W (scale/width axis) within the WPS. Using these three parameters (A, T, W) separately as well as combined by (1) Fisher's linear discriminant analysis (FLDA), (2) logistic regression (LogR) analysis, or (3) support vector machine (SVM) analysis, their potential to classify 18 different arterial and venous vessel segments per subject was evaluated. The best vessel classification was obtained using all three parameters A and T and W [area under the curve (AUC): 0.953 with FLDA and 0.957 with LogR or SVM]. In direct comparison, the wavelet-derived parameters provided performance at least equal to conventional attenuation-time-course parameters. The maximum AUC obtained from the proposed wavelet parameters was slightly (although not statistically significantly) higher than the maximum AUC (0.945) obtained from the conventional parameters. A new method to classify arterial and venous cerebral vessels with high statistical accuracy was introduced based on the time-domain wavelet transform of dynamic CT perfusion data in combination with linear or nonlinear multidimensional classification techniques.

Directional dual-tree rational-dilation complex wavelet transform.

PubMed

Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin

2014-01-01

Dyadic discrete wavelet transform (DWT) has been used successfully in processing signals having non-oscillatory transient behaviour. However, due to the low Q-factor property of their wavelet atoms, the dyadic DWT is less effective in processing oscillatory signals such as embolic signals (ESs). ESs are extracted from quadrature Doppler signals, which are the output of Doppler ultrasound systems. In order to process ESs, firstly, a pre-processing operation known as phase filtering for obtaining directional signals from quadrature Doppler signals must be employed. Only then, wavelet based methods can be applied to these directional signals for further analysis. In this study, a directional dual-tree rational-dilation complex wavelet transform, which can be applied directly to quadrature signals and has the ability of extracting directional information during analysis, is introduced.

Sensor system for heart sound biomonitor

NASA Astrophysics Data System (ADS)

Maple, Jarrad L.; Hall, Leonard T.; Agzarian, John; Abbott, Derek

1999-09-01

Heart sounds can be utilized more efficiently by medical doctors when they are displayed visually, rather than through a conventional stethoscope. A system whereby a digital stethoscope interfaces directly to a PC will be directly along with signal processing algorithms, adopted. The sensor is based on a noise cancellation microphone, with a 450 Hz bandwidth and is sampled at 2250 samples/sec with 12-bit resolution. Further to this, we discuss for comparison a piezo-based sensor with a 1 kHz bandwidth. A major problem is that the recording of the heart sound into these devices is subject to unwanted background noise which can override the heart sound and results in a poor visual representation. This noise originates from various sources such as skin contact with the stethoscope diaphragm, lung sounds, and other surrounding sounds such as speech. Furthermore we demonstrate a solution using 'wavelet denoising'. The wavelet transform is used because of the similarity between the shape of wavelets and the time-domain shape of a heartbeat sound. Thus coding of the waveform into the wavelet domain is achieved with relatively few wavelet coefficients, in contrast to the many Fourier components that would result from conventional decomposition. We show that the background noise can be dramatically reduced by a thresholding operation in the wavelet domain. The principle is that the background noise codes into many small broadband wavelet coefficients that can be removed without significant degradation of the signal of interest.

Noncoding sequence classification based on wavelet transform analysis: part II

NASA Astrophysics Data System (ADS)

Paredes, O.; Strojnik, M.; Romo-Vázquez, R.; Vélez-Pérez, H.; Ranta, R.; Garcia-Torales, G.; Scholl, M. K.; Morales, J. A.

2017-09-01

DNA sequences in human genome can be divided into the coding and noncoding ones. We hypothesize that the characteristic periodicities of the noncoding sequences are related to their function. We describe the procedure to identify these characteristic periodicities using the wavelet analysis. Our results show that three groups of noncoding sequences, each one with different biological function, may be differentiated by their wavelet coefficients within specific frequency range.

Shearlet Features for Registration of Remotely Sensed Multitemporal Images

NASA Technical Reports Server (NTRS)

Murphy, James M.; Le Moigne, Jacqueline

2015-01-01

We investigate the role of anisotropic feature extraction methods for automatic image registration of remotely sensed multitemporal images. Building on the classical use of wavelets in image registration, we develop an algorithm based on shearlets, a mathematical generalization of wavelets that offers increased directional sensitivity. Initial experimental results on LANDSAT images are presented, which indicate superior performance of the shearlet algorithm when compared to classical wavelet algorithms.

A simple structure wavelet transform circuit employing function link neural networks and SI filters

NASA Astrophysics Data System (ADS)

Mu, Li; Yigang, He

2016-12-01

Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. Implementing wavelet transform (WT) using analog circuits is of great interest when low-power consumption becomes an important issue. In this article, a novel simple structure WT circuit in analog domain is presented by employing functional link neural network (FLNN) and switched-current (SI) filters. First, the wavelet base is approximated using FLNN algorithms for giving a filter transfer function that is suitable for simple structure WT circuit implementation. Next, the WT circuit is constructed with the wavelet filter bank, whose impulse response is the approximated wavelet and its dilations. The filter design that follows is based on a follow-the-leader feedback (FLF) structure with multiple output bilinear SI integrators and current mirrors as the main building blocks. SI filter is well suited for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by the clock frequency of the circuit with the same system architecture. Finally, to illustrate the design procedure, a seventh-order FLNN-approximated Gaussian wavelet is implemented as an example. Simulations have successfully verified that the designed simple structure WT circuit has low sensitivity, low-power consumption and litter effect to the imperfections.

Directional dual-tree complex wavelet packet transforms for processing quadrature signals.

PubMed

Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin

2016-03-01

Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.

Applications of wavelets in morphometric analysis of medical images

NASA Astrophysics Data System (ADS)

Davatzikos, Christos; Tao, Xiaodong; Shen, Dinggang

2003-11-01

Morphometric analysis of medical images is playing an increasingly important role in understanding brain structure and function, as well as in understanding the way in which these change during development, aging and pathology. This paper presents three wavelet-based methods with related applications in morphometric analysis of magnetic resonance (MR) brain images. The first method handles cases where very limited datasets are available for the training of statistical shape models in the deformable segmentation. The method is capable of capturing a larger range of shape variability than the standard active shape models (ASMs) can, by using the elegant spatial-frequency decomposition of the shape contours provided by wavelet transforms. The second method addresses the difficulty of finding correspondences in anatomical images, which is a key step in shape analysis and deformable registration. The detection of anatomical correspondences is completed by using wavelet-based attribute vectors as morphological signatures of voxels. The third method uses wavelets to characterize the morphological measurements obtained from all voxels in a brain image, and the entire set of wavelet coefficients is further used to build a brain classifier. Since the classification scheme operates in a very-high-dimensional space, it can determine subtle population differences with complex spatial patterns. Experimental results are provided to demonstrate the performance of the proposed methods.

Wavelet analysis of hemispheroid flow separation toward understanding human vocal fold pathologies

NASA Astrophysics Data System (ADS)

Plesniak, Daniel H.; Carr, Ian A.; Bulusu, Kartik V.; Plesniak, Michael W.

2014-11-01

Physiological flows observed in human vocal fold pathologies, such as polyps and nodules, can be modeled by flow over a wall-mounted protuberance. The experimental investigation of flow separation over a surface-mounted hemispheroid was performed using particle image velocimetry (PIV) and measurements of surface pressure in a low-speed wind tunnel. This study builds on the hypothesis that the signatures of vortical structures associated with flow separation are imprinted on the surface pressure distributions. Wavelet decomposition methods in one- and two-dimensions were utilized to elucidate the flow behavior. First, a complex Gaussian wavelet was used for the reconstruction of surface pressure time series from static pressure measurements acquired from ports upstream, downstream, and on the surface of the hemispheroid. This was followed by the application of a novel continuous wavelet transform algorithm (PIVlet 1.2) using a 2D-Ricker wavelet for coherent structure detection on instantaneous PIV-data. The goal of this study is to correlate phase shifts in surface pressure with Strouhal numbers associated with the vortex shedding. Ultimately, the wavelet-based analytical framework will be aimed at addressing pulsatile flows. This material is based in part upon work supported by the National Science Foundation under Grant Number CBET-1236351, and GW Center for Biomimetics and Bioinspired Engineering (COBRE).

Exploring an optimal wavelet-based filter for cryo-ET imaging.

PubMed

Huang, Xinrui; Li, Sha; Gao, Song

2018-02-07

Cryo-electron tomography (cryo-ET) is one of the most advanced technologies for the in situ visualization of molecular machines by producing three-dimensional (3D) biological structures. However, cryo-ET imaging has two serious disadvantages-low dose and low image contrast-which result in high-resolution information being obscured by noise and image quality being degraded, and this causes errors in biological interpretation. The purpose of this research is to explore an optimal wavelet denoising technique to reduce noise in cryo-ET images. We perform tests using simulation data and design a filter using the optimum selected wavelet parameters (three-level decomposition, level-1 zeroed out, subband-dependent threshold, a soft-thresholding and spline-based discrete dyadic wavelet transform (DDWT)), which we call a modified wavelet shrinkage filter; this filter is suitable for noisy cryo-ET data. When testing using real cryo-ET experiment data, higher quality images and more accurate measures of a biological structure can be obtained with the modified wavelet shrinkage filter processing compared with conventional processing. Because the proposed method provides an inherent advantage when dealing with cryo-ET images, it can therefore extend the current state-of-the-art technology in assisting all aspects of cryo-ET studies: visualization, reconstruction, structural analysis, and interpretation.

Artificial retina model for the retinally blind based on wavelet transform

NASA Astrophysics Data System (ADS)

Zeng, Yan-an; Song, Xin-qiang; Jiang, Fa-gang; Chang, Da-ding

2007-01-01

Artificial retina is aimed for the stimulation of remained retinal neurons in the patients with degenerated photoreceptors. Microelectrode arrays have been developed for this as a part of stimulator. Design such microelectrode arrays first requires a suitable mathematical method for human retinal information processing. In this paper, a flexible and adjustable human visual information extracting model is presented, which is based on the wavelet transform. With the flexible of wavelet transform to image information processing and the consistent to human visual information extracting, wavelet transform theory is applied to the artificial retina model for the retinally blind. The response of the model to synthetic image is shown. The simulated experiment demonstrates that the model behaves in a manner qualitatively similar to biological retinas and thus may serve as a basis for the development of an artificial retina.

Wavelet-based adaptive thresholding method for image segmentation

NASA Astrophysics Data System (ADS)

Chen, Zikuan; Tao, Yang; Chen, Xin; Griffis, Carl

2001-05-01

A nonuniform background distribution may cause a global thresholding method to fail to segment objects. One solution is using a local thresholding method that adapts to local surroundings. In this paper, we propose a novel local thresholding method for image segmentation, using multiscale threshold functions obtained by wavelet synthesis with weighted detail coefficients. In particular, the coarse-to- fine synthesis with attenuated detail coefficients produces a threshold function corresponding to a high-frequency- reduced signal. This wavelet-based local thresholding method adapts to both local size and local surroundings, and its implementation can take advantage of the fast wavelet algorithm. We applied this technique to physical contaminant detection for poultry meat inspection using x-ray imaging. Experiments showed that inclusion objects in deboned poultry could be extracted at multiple resolutions despite their irregular sizes and uneven backgrounds.

Implementation in an FPGA circuit of Edge detection algorithm based on the Discrete Wavelet Transforms

NASA Astrophysics Data System (ADS)

Bouganssa, Issam; Sbihi, Mohamed; Zaim, Mounia

2017-07-01

The 2D Discrete Wavelet Transform (DWT) is a computationally intensive task that is usually implemented on specific architectures in many imaging systems in real time. In this paper, a high throughput edge or contour detection algorithm is proposed based on the discrete wavelet transform. A technique for applying the filters on the three directions (Horizontal, Vertical and Diagonal) of the image is used to present the maximum of the existing contours. The proposed architectures were designed in VHDL and mapped to a Xilinx Sparten6 FPGA. The results of the synthesis show that the proposed architecture has a low area cost and can operate up to 100 MHz, which can perform 2D wavelet analysis for a sequence of images while maintaining the flexibility of the system to support an adaptive algorithm.

Wavelet Filter Banks for Super-Resolution SAR Imaging

NASA Technical Reports Server (NTRS)

Sheybani, Ehsan O.; Deshpande, Manohar; Memarsadeghi, Nargess

2011-01-01

This paper discusses Innovative wavelet-based filter banks designed to enhance the analysis of super resolution Synthetic Aperture Radar (SAR) images using parametric spectral methods and signal classification algorithms, SAR finds applications In many of NASA's earth science fields such as deformation, ecosystem structure, and dynamics of Ice, snow and cold land processes, and surface water and ocean topography. Traditionally, standard methods such as Fast-Fourier Transform (FFT) and Inverse Fast-Fourier Transform (IFFT) have been used to extract Images from SAR radar data, Due to non-parametric features of these methods and their resolution limitations and observation time dependence, use of spectral estimation and signal pre- and post-processing techniques based on wavelets to process SAR radar data has been proposed. Multi-resolution wavelet transforms and advanced spectral estimation techniques have proven to offer efficient solutions to this problem.

A novel neural-wavelet approach for process diagnostics and complex system modeling

NASA Astrophysics Data System (ADS)

Gao, Rong

Neural networks have been effective in several engineering applications because of their learning abilities and robustness. However certain shortcomings, such as slow convergence and local minima, are always associated with neural networks, especially neural networks applied to highly nonlinear and non-stationary problems. These problems can be effectively alleviated by integrating a new powerful tool, wavelets, into conventional neural networks. The multi-resolution analysis and feature localization capabilities of the wavelet transform offer neural networks new possibilities for learning. A neural wavelet network approach developed in this thesis enjoys fast convergence rate with little possibility to be caught at a local minimum. It combines the localization properties of wavelets with the learning abilities of neural networks. Two different testbeds are used for testing the efficiency of the new approach. The first is magnetic flowmeter-based process diagnostics: here we extend previous work, which has demonstrated that wavelet groups contain process information, to more general process diagnostics. A loop at Applied Intelligent Systems Lab (AISL) is used for collecting and analyzing data through the neural-wavelet approach. The research is important for thermal-hydraulic processes in nuclear and other engineering fields. The neural-wavelet approach developed is also tested with data from the electric power grid. More specifically, the neural-wavelet approach is used for performing short-term and mid-term prediction of power load demand. In addition, the feasibility of determining the type of load using the proposed neural wavelet approach is also examined. The notion of cross scale product has been developed as an expedient yet reliable discriminator of loads. Theoretical issues involved in the integration of wavelets and neural networks are discussed and future work outlined.

Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world

PubMed Central

Zueva, Marina V.

2015-01-01

The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232

Harmonic wavelet packet transform for on-line system health diagnosis

NASA Astrophysics Data System (ADS)

Yan, Ruqiang; Gao, Robert X.

2004-07-01

This paper presents a new approach to on-line health diagnosis of mechanical systems, based on the wavelet packet transform. Specifically, signals acquired from vibration sensors are decomposed into sub-bands by means of the discrete harmonic wavelet packet transform (DHWPT). Based on the Fisher linear discriminant criterion, features in the selected sub-bands are then used as inputs to three classifiers (Nearest Neighbor rule-based and two Neural Network-based), for system health condition assessment. Experimental results have confirmed that, comparing to the conventional approach where statistical parameters from raw signals are used, the presented approach enabled higher signal-to-noise ratio for more effective and intelligent use of the sensory information, thus leading to more accurate system health diagnosis.

Wavelet-based associative memory

NASA Astrophysics Data System (ADS)

Jones, Katharine J.

2004-04-01

Faces provide important characteristics of a person"s identification. In security checks, face recognition still remains the method in continuous use despite other approaches (i.e. fingerprints, voice recognition, pupil contraction, DNA scanners). With an associative memory, the output data is recalled directly using the input data. This can be achieved with a Nonlinear Holographic Associative Memory (NHAM). This approach can also distinguish between strongly correlated images and images that are partially or totally enclosed by others. Adaptive wavelet lifting has been used for Content-Based Image Retrieval. In this paper, adaptive wavelet lifting will be applied to face recognition to achieve an associative memory.

Compression of real time volumetric echocardiographic data using modified SPIHT based on the three-dimensional wavelet packet transform.

PubMed

Hang, X; Greenberg, N L; Shiota, T; Firstenberg, M S; Thomas, J D

2000-01-01

Real-time three-dimensional echocardiography has been introduced to provide improved quantification and description of cardiac function. Data compression is desired to allow efficient storage and improve data transmission. Previous work has suggested improved results utilizing wavelet transforms in the compression of medical data including 2D echocardiogram. Set partitioning in hierarchical trees (SPIHT) was extended to compress volumetric echocardiographic data by modifying the algorithm based on the three-dimensional wavelet packet transform. A compression ratio of at least 40:1 resulted in preserved image quality.

Numerical Algorithms Based on Biorthogonal Wavelets

NASA Technical Reports Server (NTRS)

Ponenti, Pj.; Liandrat, J.

1996-01-01

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Modified signed-digit trinary addition using synthetic wavelet filter

NASA Astrophysics Data System (ADS)

Iftekharuddin, K. M.; Razzaque, M. A.

2000-09-01

The modified signed-digit (MSD) number system has been a topic of interest as it allows for parallel carry-free addition of two numbers for digital optical computing. In this paper, harmonic wavelet joint transform (HWJT)-based correlation technique is introduced for optical implementation of MSD trinary adder implementation. The realization of the carry-propagation-free addition of MSD trinary numerals is demonstrated using synthetic HWJT correlator model. It is also shown that the proposed synthetic wavelet filter-based correlator shows high performance in logic processing. Simulation results are presented to validate the performance of the proposed technique.

Wavelet transform analysis of transient signals: the seismogram and the electrocardiogram

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anant, K.S.

1997-06-01

In this dissertation I quantitatively demonstrate how the wavelet transform can be an effective mathematical tool for the analysis of transient signals. The two key signal processing applications of the wavelet transform, namely feature identification and representation (i.e., compression), are shown by solving important problems involving the seismogram and the electrocardiogram. The seismic feature identification problem involved locating in time the P and S phase arrivals. Locating these arrivals accurately (particularly the S phase) has been a constant issue in seismic signal processing. In Chapter 3, I show that the wavelet transform can be used to locate both the Pmore » as well as the S phase using only information from single station three-component seismograms. This is accomplished by using the basis function (wave-let) of the wavelet transform as a matching filter and by processing information across scales of the wavelet domain decomposition. The `pick` time results are quite promising as compared to analyst picks. The representation application involved the compression of the electrocardiogram which is a recording of the electrical activity of the heart. Compression of the electrocardiogram is an important problem in biomedical signal processing due to transmission and storage limitations. In Chapter 4, I develop an electrocardiogram compression method that applies vector quantization to the wavelet transform coefficients. The best compression results were obtained by using orthogonal wavelets, due to their ability to represent a signal efficiently. Throughout this thesis the importance of choosing wavelets based on the problem at hand is stressed. In Chapter 5, I introduce a wavelet design method that uses linear prediction in order to design wavelets that are geared to the signal or feature being analyzed. The use of these designed wavelets in a test feature identification application led to positive results. The methods developed in this thesis; the feature identification methods of Chapter 3, the compression methods of Chapter 4, as well as the wavelet design methods of Chapter 5, are general enough to be easily applied to other transient signals.« less

A neural network detection model of spilled oil based on the texture analysis of SAR image

NASA Astrophysics Data System (ADS)

An, Jubai; Zhu, Lisong

2006-01-01

A Radial Basis Function Neural Network (RBFNN) Model is investigated for the detection of spilled oil based on the texture analysis of SAR imagery. In this paper, to take the advantage of the abundant texture information of SAR imagery, the texture features are extracted by both wavelet transform and the Gray Level Co-occurrence matrix. The RBFNN Model is fed with a vector of these texture features. The RBFNN Model is trained and tested by the sample data set of the feature vectors. Finally, a SAR image is classified by this model. The classification results of a spilled oil SAR image show that the classification accuracy for oil spill is 86.2 by the RBFNN Model using both wavelet texture and gray texture, while the classification accuracy for oil spill is 78.0 by same RBFNN Model using only wavelet texture as the input of this RBFNN model. The model using both wavelet transform and the Gray Level Co-occurrence matrix is more effective than that only using wavelet texture. Furthermore, it keeps the complicated proximity and has a good performance of classification.

Luminance sticker based facial expression recognition using discrete wavelet transform for physically disabled persons.

PubMed

Nagarajan, R; Hariharan, M; Satiyan, M

2012-08-01

Developing tools to assist physically disabled and immobilized people through facial expression is a challenging area of research and has attracted many researchers recently. In this paper, luminance stickers based facial expression recognition is proposed. Recognition of facial expression is carried out by employing Discrete Wavelet Transform (DWT) as a feature extraction method. Different wavelet families with their different orders (db1 to db20, Coif1 to Coif 5 and Sym2 to Sym8) are utilized to investigate their performance in recognizing facial expression and to evaluate their computational time. Standard deviation is computed for the coefficients of first level of wavelet decomposition for every order of wavelet family. This standard deviation is used to form a set of feature vectors for classification. In this study, conventional validation and cross validation are performed to evaluate the efficiency of the suggested feature vectors. Three different classifiers namely Artificial Neural Network (ANN), k-Nearest Neighborhood (kNN) and Linear Discriminant Analysis (LDA) are used to classify a set of eight facial expressions. The experimental results demonstrate that the proposed method gives very promising classification accuracies.

Reconstructing Past Admixture Processes from Local Genomic Ancestry Using Wavelet Transformation

PubMed Central

Sanderson, Jean; Sudoyo, Herawati; Karafet, Tatiana M.; Hammer, Michael F.; Cox, Murray P.

2015-01-01

Admixture between long-separated populations is a defining feature of the genomes of many species. The mosaic block structure of admixed genomes can provide information about past contact events, including the time and extent of admixture. Here, we describe an improved wavelet-based technique that better characterizes ancestry block structure from observed genomic patterns. principal components analysis is first applied to genomic data to identify the primary population structure, followed by wavelet decomposition to develop a new characterization of local ancestry information along the chromosomes. For testing purposes, this method is applied to human genome-wide genotype data from Indonesia, as well as virtual genetic data generated using genome-scale sequential coalescent simulations under a wide range of admixture scenarios. Time of admixture is inferred using an approximate Bayesian computation framework, providing robust estimates of both admixture times and their associated levels of uncertainty. Crucially, we demonstrate that this revised wavelet approach, which we have released as the R package adwave, provides improved statistical power over existing wavelet-based techniques and can be used to address a broad range of admixture questions. PMID:25852078

Correlative weighted stacking for seismic data in the wavelet domain

USGS Publications Warehouse

Zhang, S.; Xu, Y.; Xia, J.; ,

2004-01-01

Horizontal stacking plays a crucial role for modern seismic data processing, for it not only compresses random noise and multiple reflections, but also provides a foundational data for subsequent migration and inversion. However, a number of examples showed that random noise in adjacent traces exhibits correlation and coherence. The average stacking and weighted stacking based on the conventional correlative function all result in false events, which are caused by noise. Wavelet transform and high order statistics are very useful methods for modern signal processing. The multiresolution analysis in wavelet theory can decompose signal on difference scales, and high order correlative function can inhibit correlative noise, for which the conventional correlative function is of no use. Based on the theory of wavelet transform and high order statistics, high order correlative weighted stacking (HOCWS) technique is presented in this paper. Its essence is to stack common midpoint gathers after the normal moveout correction by weight that is calculated through high order correlative statistics in the wavelet domain. Synthetic examples demonstrate its advantages in improving the signal to noise (S/N) ration and compressing the correlative random noise.

WaveJava: Wavelet-based network computing

NASA Astrophysics Data System (ADS)

Ma, Kun; Jiao, Licheng; Shi, Zhuoer

1997-04-01

Wavelet is a powerful theory, but its successful application still needs suitable programming tools. Java is a simple, object-oriented, distributed, interpreted, robust, secure, architecture-neutral, portable, high-performance, multi- threaded, dynamic language. This paper addresses the design and development of a cross-platform software environment for experimenting and applying wavelet theory. WaveJava, a wavelet class library designed by the object-orient programming, is developed to take advantage of the wavelets features, such as multi-resolution analysis and parallel processing in the networking computing. A new application architecture is designed for the net-wide distributed client-server environment. The data are transmitted with multi-resolution packets. At the distributed sites around the net, these data packets are done the matching or recognition processing in parallel. The results are fed back to determine the next operation. So, the more robust results can be arrived quickly. The WaveJava is easy to use and expand for special application. This paper gives a solution for the distributed fingerprint information processing system. It also fits for some other net-base multimedia information processing, such as network library, remote teaching and filmless picture archiving and communications.

Parallel adaptive wavelet collocation method for PDEs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nejadmalayeri, Alireza, E-mail: Alireza.Nejadmalayeri@gmail.com; Vezolainen, Alexei, E-mail: Alexei.Vezolainen@Colorado.edu; Brown-Dymkoski, Eric, E-mail: Eric.Browndymkoski@Colorado.edu

2015-10-01

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allowsmore » fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.« less

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain

NASA Astrophysics Data System (ADS)

Ghadimi, Rasoul; Sugimoto, Takanori; Tohyama, Takami

2017-11-01

We theoretically study a Kitaev chain with a quasiperiodic potential, where the quasiperiodicity is introduced by a Fibonacci sequence. Based on an analysis of the Majorana zero-energy mode, we find the critical p-wave superconducting pairing potential separating a topological phase and a non-topological phase. The topological phase diagram with respect to Fibonacci potentials follow a self-similar fractal structure characterized by the box-counting dimension, which is an example of the interplay of fractal and topology like the Hofstadter's butterfly in quantum Hall insulators.

Method for non-referential defect characterization using fractal encoding and active contours

DOEpatents

Gleason, Shaun S [Knoxville, TN; Sari-Sarraf, Hamed [Lubbock, TX

2007-05-15

A method for identification of anomalous structures, such as defects, includes the steps of providing a digital image and applying fractal encoding to identify a location of at least one anomalous portion of the image. The method does not require a reference image to identify the location of the anomalous portion. The method can further include the step of initializing an active contour based on the location information obtained from the fractal encoding step and deforming an active contour to enhance the boundary delineation of the anomalous portion.

Wavelet-based tracking of bacteria in unreconstructed off-axis holograms.

PubMed

Marin, Zach; Wallace, J Kent; Nadeau, Jay; Khalil, Andre

2018-03-01

We propose an automated wavelet-based method of tracking particles in unreconstructed off-axis holograms to provide rough estimates of the presence of motion and particle trajectories in digital holographic microscopy (DHM) time series. The wavelet transform modulus maxima segmentation method is adapted and tailored to extract Airy-like diffraction disks, which represent bacteria, from DHM time series. In this exploratory analysis, the method shows potential for estimating bacterial tracks in low-particle-density time series, based on a preliminary analysis of both living and dead Serratia marcescens, and for rapidly providing a single-bit answer to whether a sample chamber contains living or dead microbes or is empty. Copyright © 2017 Elsevier Inc. All rights reserved.

Remote sensing of soil organic matter of farmland with hyperspectral image

NASA Astrophysics Data System (ADS)

Gu, Xiaohe; Wang, Lei; Yang, Guijun; Zhang, Liyan

2017-10-01

Monitoring soil organic matter (SOM) of cultivated land quantitively and mastering its spatial change are helpful for fertility adjustment and sustainable development of agriculture. The study aimed to analyze the response between SOM and reflectivity of hyperspectral image with different pixel size and develop the optimal model of estimating SOM with imaging spectral technology. The wavelet transform method was used to analyze the correlation between the hyperspectral reflectivity and SOM. Then the optimal pixel size and sensitive wavelet feature scale were screened to develop the inversion model of SOM. Result showed that wavelet transform of soil hyperspectrum was help to improve the correlation between the wavelet features and SOM. In the visible wavelength range, the susceptible wavelet features of SOM mainly concentrated 460 603 nm. As the wavelength increased, the wavelet scale corresponding correlation coefficient increased maximum and then gradually decreased. In the near infrared wavelength range, the susceptible wavelet features of SOM mainly concentrated 762 882 nm. As the wavelength increased, the wavelet scale gradually decreased. The study developed multivariate model of continuous wavelet transforms by the method of stepwise linear regression (SLR). The CWT-SLR models reached higher accuracies than those of univariate models. With the resampling scale increasing, the accuracies of CWT-SLR models gradually increased, while the determination coefficients (R2) fluctuated from 0.52 to 0.59. The R2 of 5*5 scale reached highest (0.5954), while the RMSE reached lowest (2.41 g/kg). It indicated that multivariate model based on continuous wavelet transform had better ability for estimating SOM than univariate model.

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

NASA Astrophysics Data System (ADS)

Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.

2008-12-01

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

The wavelet response as a multiscale characterization of scattering processes at granular interfaces.

PubMed

Le Gonidec, Yves; Gibert, Dominique

2006-11-01

We perform a multiscale analysis of the backscattering properties of a complex interface between water and a layer of randomly arranged glass beads with diameter D=1 mm. An acoustical experiment is done to record the wavelet response of the interface in a large frequency range from lambda/D=0.3 to lambda/D=15. The wavelet response is a physical analog of the mathematical wavelet transform which possesses nice properties to detect and characterize abrupt changes in signals. The experimental wavelet response allows to identify five frequency domains corresponding to different backscattering properties of the complex interface. This puts quantitative limits to the validity domains of the models used to represent the interface and which are flat elastic, flat visco-elastic, rough random half-space with multiple scattering, and rough elastic from long to short wavelengths respectively. A physical explanation based on Mie scattering theory is proposed to explain the origin of the five frequency domains identified in the wavelet response.

Evaluating the Efficacy of Wavelet Configurations on Turbulent-Flow Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Shaomeng; Gruchalla, Kenny; Potter, Kristin

2015-10-25

I/O is increasingly becoming a significant constraint for simulation codes and visualization tools on modern supercomputers. Data compression is an attractive workaround, and, in particular, wavelets provide a promising solution. However, wavelets can be applied in multiple configurations, and the variations in configuration impact accuracy, storage cost, and execution time. While the variation in these factors over wavelet configurations have been explored in image processing, they are not well understood for visualization and analysis of scientific data. To illuminate this issue, we evaluate multiple wavelet configurations on turbulent-flow data. Our approach is to repeat established analysis routines on uncompressed andmore » lossy-compressed versions of a data set, and then quantitatively compare their outcomes. Our findings show that accuracy varies greatly based on wavelet configuration, while storage cost and execution time vary less. Overall, our study provides new insights for simulation analysts and visualization experts, who need to make tradeoffs between accuracy, storage cost, and execution time.« less

Impulse Noise Cancellation of Medical Images Using Wavelet Networks and Median Filters

PubMed Central

Sadri, Amir Reza; Zekri, Maryam; Sadri, Saeid; Gheissari, Niloofar

2012-01-01

This paper presents a new two-stage approach to impulse noise removal for medical images based on wavelet network (WN). The first step is noise detection, in which the so-called gray-level difference and average background difference are considered as the inputs of a WN. Wavelet Network is used as a preprocessing for the second stage. The second step is removing impulse noise with a median filter. The wavelet network presented here is a fixed one without learning. Experimental results show that our method acts on impulse noise effectively, and at the same time preserves chromaticity and image details very well. PMID:23493998

Seismic instantaneous frequency extraction based on the SST-MAW

NASA Astrophysics Data System (ADS)

Liu, Naihao; Gao, Jinghuai; Jiang, Xiudi; Zhang, Zhuosheng; Wang, Ping

2018-06-01

The instantaneous frequency (IF) extraction of seismic data has been widely applied to seismic exploration for decades, such as detecting seismic absorption and characterizing depositional thicknesses. Based on the complex-trace analysis, the Hilbert transform (HT) can extract the IF directly, which is a traditional method and susceptible to noise. In this paper, a robust approach based on the synchrosqueezing transform (SST) is proposed to extract the IF from seismic data. In this process, a novel analytical wavelet is developed and chosen as the basic wavelet, which is called the modified analytical wavelet (MAW) and comes from the three parameter wavelet. After transforming the seismic signal into a sparse time-frequency domain via the SST taking the MAW (SST-MAW), an adaptive threshold is introduced to improve the noise immunity and accuracy of the IF extraction in a noisy environment. Note that the SST-MAW reconstructs a complex trace to extract seismic IF. To demonstrate the effectiveness of the proposed method, we apply the SST-MAW to synthetic data and field seismic data. Numerical experiments suggest that the proposed procedure yields the higher resolution and the better anti-noise performance compared to the conventional IF extraction methods based on the HT method and continuous wavelet transform. Moreover, geological features (such as the channels) are well characterized, which is insightful for further oil/gas reservoir identification.

A fast method for the detection of vascular structure in images, based on the continuous wavelet transform with the Morlet wavelet having a low central frequency

NASA Astrophysics Data System (ADS)

Postnikov, Eugene B.; Tsoy, Maria O.; Kurochkin, Maxim A.; Postnov, Dmitry E.

2017-04-01

A manual measurement of blood vessels diameter is a conventional component of routine visual assessment of microcirculation, say, during optical capillaroscopy. However, many modern optical methods for blood flow measurements demand the reliable procedure for a fully automated detection of vessels and estimation of their diameter that is a challenging task. Specifically, if one measure the velocity of red blood cells by means of laser speckle imaging, then visual measurements become impossible, while the velocity-based estimation has their own limitations. One of promising approaches is based on fast switching of illumination type, but it drastically reduces the observation time, and hence, the achievable quality of images. In the present work we address this problem proposing an alternative method for the processing of noisy images of vascular structure, which extracts the mask denoting locations of vessels, based on the application of the continuous wavelet transform with the Morlet wavelet having small central frequencies. Such a method combines a reasonable accuracy with the possibility of fast direct implementation to images. Discussing the latter, we describe in details a new MATLAB program code realization for the CWT with the Morlet wavelet, which does not use loops completely replaced with element-by-element operations that drastically reduces the computation time.

Definition of fractal topography to essential understanding of scale-invariance

NASA Astrophysics Data System (ADS)

Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

2017-04-01

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

Wavelet-based hierarchical surface approximation from height fields

Treesearch

Sang-Mook Lee; A. Lynn Abbott; Daniel L. Schmoldt

2004-01-01

This paper presents a novel hierarchical approach to triangular mesh generation from height fields. A wavelet-based multiresolution analysis technique is used to estimate local shape information at different levels of resolution. Using predefined templates at the coarsest level, the method constructs an initial triangulation in which underlying object shapes are well...

Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

NASA Astrophysics Data System (ADS)

Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

2017-10-01

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

Fractal and twin SVM-based handgrip recognition for healthy subjects and trans-radial amputees using myoelectric signal.

PubMed

Arjunan, Sridhar Poosapadi; Kumar, Dinesh Kant; Jayadeva J

2016-02-01

Identifying functional handgrip patterns using surface electromygram (sEMG) signal recorded from amputee residual muscle is required for controlling the myoelectric prosthetic hand. In this study, we have computed the signal fractal dimension (FD) and maximum fractal length (MFL) during different grip patterns performed by healthy and transradial amputee subjects. The FD and MFL of the sEMG, referred to as the fractal features, were classified using twin support vector machines (TSVM) to recognize the handgrips. TSVM requires fewer support vectors, is suitable for data sets with unbalanced distributions, and can simultaneously be trained for improving both sensitivity and specificity. When compared with other methods, this technique resulted in improved grip recognition accuracy, sensitivity, and specificity, and this improvement was significant (κ=0.91).

Music Tune Restoration Based on a Mother Wavelet Construction

NASA Astrophysics Data System (ADS)

Fadeev, A. S.; Konovalov, V. I.; Butakova, T. I.; Sobetsky, A. V.

2017-01-01

It is offered to use the mother wavelet function obtained from the local part of an analyzed music signal. Requirements for the constructed function are proposed and the implementation technique and its properties are described. The suggested approach allows construction of mother wavelet families with specified identifying properties. Consequently, this makes possible to identify the basic signal variations of complex music signals including local time-frequency characteristics of the basic one.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

a Predictive Model of Permeability for Fractal-Based Rough Rock Fractures during Shear

NASA Astrophysics Data System (ADS)

Huang, Na; Jiang, Yujing; Liu, Richeng; Li, Bo; Zhang, Zhenyu

This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent (H), in which H = 3 - Df, where Df is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between H and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

On the fractal characterization of Paretian Poisson processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

A Wavelet Neural Network Optimal Control Model for Traffic-Flow Prediction in Intelligent Transport Systems

NASA Astrophysics Data System (ADS)

Huang, Darong; Bai, Xing-Rong

Based on wavelet transform and neural network theory, a traffic-flow prediction model, which was used in optimal control of Intelligent Traffic system, is constructed. First of all, we have extracted the scale coefficient and wavelet coefficient from the online measured raw data of traffic flow via wavelet transform; Secondly, an Artificial Neural Network model of Traffic-flow Prediction was constructed and trained using the coefficient sequences as inputs and raw data as outputs; Simultaneous, we have designed the running principium of the optimal control system of traffic-flow Forecasting model, the network topological structure and the data transmitted model; Finally, a simulated example has shown that the technique is effectively and exactly. The theoretical results indicated that the wavelet neural network prediction model and algorithms have a broad prospect for practical application.

Wavelet-based energy features for glaucomatous image classification.

PubMed

Dua, Sumeet; Acharya, U Rajendra; Chowriappa, Pradeep; Sree, S Vinitha

2012-01-01

Texture features within images are actively pursued for accurate and efficient glaucoma classification. Energy distribution over wavelet subbands is applied to find these important texture features. In this paper, we investigate the discriminatory potential of wavelet features obtained from the daubechies (db3), symlets (sym3), and biorthogonal (bio3.3, bio3.5, and bio3.7) wavelet filters. We propose a novel technique to extract energy signatures obtained using 2-D discrete wavelet transform, and subject these signatures to different feature ranking and feature selection strategies. We have gauged the effectiveness of the resultant ranked and selected subsets of features using a support vector machine, sequential minimal optimization, random forest, and naïve Bayes classification strategies. We observed an accuracy of around 93% using tenfold cross validations to demonstrate the effectiveness of these methods.

Convex composite wavelet frame and total variation-based image deblurring using nonconvex penalty functions

NASA Astrophysics Data System (ADS)

Shen, Zhengwei; Cheng, Lishuang

2017-09-01

Total variation (TV)-based image deblurring method can bring on staircase artifacts in the homogenous region of the latent images recovered from the degraded images while a wavelet/frame-based image deblurring method will lead to spurious noise spikes and pseudo-Gibbs artifacts in the vicinity of discontinuities of the latent images. To suppress these artifacts efficiently, we propose a nonconvex composite wavelet/frame and TV-based image deblurring model. In this model, the wavelet/frame and the TV-based methods may complement each other, which are verified by theoretical analysis and experimental results. To further improve the quality of the latent images, nonconvex penalty function is used to be the regularization terms of the model, which may induce a stronger sparse solution and will more accurately estimate the relative large gradient or wavelet/frame coefficients of the latent images. In addition, by choosing a suitable parameter to the nonconvex penalty function, the subproblem that splits by the alternative direction method of multipliers algorithm from the proposed model can be guaranteed to be a convex optimization problem; hence, each subproblem can converge to a global optimum. The mean doubly augmented Lagrangian and the isotropic split Bregman algorithms are used to solve these convex subproblems where the designed proximal operator is used to reduce the computational complexity of the algorithms. Extensive numerical experiments indicate that the proposed model and algorithms are comparable to other state-of-the-art model and methods.

A new multiscale noise tuning stochastic resonance for enhanced fault diagnosis in wind turbine drivetrains

NASA Astrophysics Data System (ADS)

Hu, Bingbing; Li, Bing

2016-02-01

It is very difficult to detect weak fault signatures due to the large amount of noise in a wind turbine system. Multiscale noise tuning stochastic resonance (MSTSR) has proved to be an effective way to extract weak signals buried in strong noise. However, the MSTSR method originally based on discrete wavelet transform (DWT) has disadvantages such as shift variance and the aliasing effects in engineering application. In this paper, the dual-tree complex wavelet transform (DTCWT) is introduced into the MSTSR method, which makes it possible to further improve the system output signal-to-noise ratio and the accuracy of fault diagnosis by the merits of DTCWT (nearly shift invariant and reduced aliasing effects). Moreover, this method utilizes the relationship between the two dual-tree wavelet basis functions, instead of matching the single wavelet basis function to the signal being analyzed, which may speed up the signal processing and be employed in on-line engineering monitoring. The proposed method is applied to the analysis of bearing outer ring and shaft coupling vibration signals carrying fault information. The results confirm that the method performs better in extracting the fault features than the original DWT-based MSTSR, the wavelet transform with post spectral analysis, and EMD-based spectral analysis methods.

An improved method of continuous LOD based on fractal theory in terrain rendering

NASA Astrophysics Data System (ADS)

Lin, Lan; Li, Lijun

2007-11-01

With the improvement of computer graphic hardware capability, the algorithm of 3D terrain rendering is going into the hot topic of real-time visualization. In order to solve conflict between the rendering speed and reality of rendering, this paper gives an improved method of terrain rendering which improves the traditional continuous level of detail technique based on fractal theory. This method proposes that the program needn't to operate the memory repeatedly to obtain different resolution terrain model, instead, obtains the fractal characteristic parameters of different region according to the movement of the viewpoint. Experimental results show that the method guarantees the authenticity of landscape, and increases the real-time 3D terrain rendering speed.

On the spline-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing.

PubMed

Hou, Tingbo; Qin, Hong

2013-01-01

As signal processing tools, diffusion wavelets and biorthogonal diffusion wavelets have been propelled by recent research in mathematics. They employ diffusion as a smoothing and scaling process to empower multiscale analysis. However, their applications in graphics and visualization are overshadowed by nonadmissible wavelets and their expensive computation. In this paper, our motivation is to broaden the application scope to space-frequency processing of shape geometry and scalar fields. We propose the admissible diffusion wavelets (ADW) on meshed surfaces and point clouds. The ADW are constructed in a bottom-up manner that starts from a local operator in a high frequency, and dilates by its dyadic powers to low frequencies. By relieving the orthogonality and enforcing normalization, the wavelets are locally supported and admissible, hence facilitating data analysis and geometry processing. We define the novel rapid reconstruction, which recovers the signal from multiple bands of high frequencies and a low-frequency base in full resolution. It enables operations localized in both space and frequency by manipulating wavelet coefficients through space-frequency filters. This paper aims to build a common theoretic foundation for a host of applications, including saliency visualization, multiscale feature extraction, spectral geometry processing, etc.

Fractals: To Know, to Do, to Simulate.

ERIC Educational Resources Information Center

Talanquer, Vicente; Irazoque, Glinda

1993-01-01

Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

PubMed

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Wavelet filtered shifted phase-encoded joint transform correlation for face recognition

NASA Astrophysics Data System (ADS)

Moniruzzaman, Md.; Alam, Mohammad S.

2017-05-01

A new wavelet-filtered-based Shifted- phase-encoded Joint Transform Correlation (WPJTC) technique has been proposed for efficient face recognition. The proposed technique uses discrete wavelet decomposition for preprocessing and can effectively accommodate various 3D facial distortions, effects of noise, and illumination variations. After analyzing different forms of wavelet basis functions, an optimal method has been proposed by considering the discrimination capability and processing speed as performance trade-offs. The proposed technique yields better correlation discrimination compared to alternate pattern recognition techniques such as phase-shifted phase-encoded fringe-adjusted joint transform correlator. The performance of the proposed WPJTC has been tested using the Yale facial database and extended Yale facial database under different environments such as illumination variation, noise, and 3D changes in facial expressions. Test results show that the proposed WPJTC yields better performance compared to alternate JTC based face recognition techniques.

Heart Rate Variability and Wavelet-based Studies on ECG Signals from Smokers and Non-smokers

NASA Astrophysics Data System (ADS)

Pal, K.; Goel, R.; Champaty, B.; Samantray, S.; Tibarewala, D. N.

2013-12-01

The current study deals with the heart rate variability (HRV) and wavelet-based ECG signal analysis of smokers and non-smokers. The results of HRV indicated dominance towards the sympathetic nervous system activity in smokers. The heart rate was found to be higher in case of smokers as compared to non-smokers ( p < 0.05). The frequency domain analysis showed an increase in the LF and LF/HF components with a subsequent decrease in the HF component. The HRV features were analyzed for classification of the smokers from the non-smokers. The results indicated that when RMSSD, SD1 and RR-mean features were used concurrently a classification efficiency of > 90 % was achieved. The wavelet decomposition of the ECG signal was done using the Daubechies (db 6) wavelet family. No difference was observed between the smokers and non-smokers which apparently suggested that smoking does not affect the conduction pathway of heart.

Wavelet based approach for posture transition estimation using a waist worn accelerometer.

PubMed

Bidargaddi, Niranjan; Klingbeil, Lasse; Sarela, Antti; Boyle, Justin; Cheung, Vivian; Yelland, Catherine; Karunanithi, Mohanraj; Gray, Len

2007-01-01

The ability to rise from a chair is considered to be important to achieve functional independence and quality of life. This sit-to-stand task is also a good indicator to assess condition of patients with chronic diseases. We developed a wavelet based algorithm for detecting and calculating the durations of sit-to-stand and stand-to-sit transitions from the signal vector magnitude of the measured acceleration signal. The algorithm was tested on waist worn accelerometer data collected from young subjects as well as geriatric patients. The test demonstrates that both transitions can be detected by using wavelet transformation applied to signal magnitude vector. Wavelet analysis produces an estimate of the transition pattern that can be used to calculate the transition duration that further gives clinically significant information on the patients condition. The method can be applied in a real life ambulatory monitoring system for assessing the condition of a patient living at home.

The EM Method in a Probabilistic Wavelet-Based MRI Denoising

PubMed Central

2015-01-01

Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images. PMID:26089959

The EM Method in a Probabilistic Wavelet-Based MRI Denoising.

PubMed

Martin-Fernandez, Marcos; Villullas, Sergio

2015-01-01

Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images.

Deriving leaf mass per area (LMA) from foliar reflectance across a variety of plant species using continuous wavelet analysis

NASA Astrophysics Data System (ADS)

Cheng, Tao; Rivard, Benoit; Sánchez-Azofeifa, Arturo G.; Féret, Jean-Baptiste; Jacquemoud, Stéphane; Ustin, Susan L.

2014-01-01

Leaf mass per area (LMA), the ratio of leaf dry mass to leaf area, is a trait of central importance to the understanding of plant light capture and carbon gain. It can be estimated from leaf reflectance spectroscopy in the infrared region, by making use of information about the absorption features of dry matter. This study reports on the application of continuous wavelet analysis (CWA) to the estimation of LMA across a wide range of plant species. We compiled a large database of leaf reflectance spectra acquired within the framework of three independent measurement campaigns (ANGERS, LOPEX and PANAMA) and generated a simulated database using the PROSPECT leaf optical properties model. CWA was applied to the measured and simulated databases to extract wavelet features that correlate with LMA. These features were assessed in terms of predictive capability and robustness while transferring predictive models from the simulated database to the measured database. The assessment was also conducted with two existing spectral indices, namely the Normalized Dry Matter Index (NDMI) and the Normalized Difference index for LMA (NDLMA). Five common wavelet features were determined from the two databases, which showed significant correlations with LMA (R2: 0.51-0.82, p < 0.0001). The best robustness (R2 = 0.74, RMSE = 18.97 g/m2 and Bias = 0.12 g/m2) was obtained using a combination of two low-scale features (1639 nm, scale 4) and (2133 nm, scale 5), the first being predominantly important. The transferability of the wavelet-based predictive model to the whole measured database was either better than or comparable to those based on spectral indices. Additionally, only the wavelet-based model showed consistent predictive capabilities among the three measured data sets. In comparison, the models based on spectral indices were sensitive to site-specific data sets. Integrating the NDLMA spectral index and the two robust wavelet features improved the LMA prediction. One of the bands used by this spectral index, 1368 nm, was located in a strong atmospheric water absorption region and replacing it with the next available band (1340 nm) led to lower predictive accuracies. However, the two wavelet features were not affected by data quality in the atmospheric absorption regions and therefore showed potential for canopy-level investigations. The wavelet approach provides a different perspective into spectral responses to LMA variation than the traditional spectral indices and holds greater promise for implementation with airborne or spaceborne imaging spectroscopy data for mapping canopy foliar dry biomass.

Wavelet-based multiscale performance analysis: An approach to assess and improve hydrological models

NASA Astrophysics Data System (ADS)

Rathinasamy, Maheswaran; Khosa, Rakesh; Adamowski, Jan; ch, Sudheer; Partheepan, G.; Anand, Jatin; Narsimlu, Boini

2014-12-01

The temporal dynamics of hydrological processes are spread across different time scales and, as such, the performance of hydrological models cannot be estimated reliably from global performance measures that assign a single number to the fit of a simulated time series to an observed reference series. Accordingly, it is important to analyze model performance at different time scales. Wavelets have been used extensively in the area of hydrological modeling for multiscale analysis, and have been shown to be very reliable and useful in understanding dynamics across time scales and as these evolve in time. In this paper, a wavelet-based multiscale performance measure for hydrological models is proposed and tested (i.e., Multiscale Nash-Sutcliffe Criteria and Multiscale Normalized Root Mean Square Error). The main advantage of this method is that it provides a quantitative measure of model performance across different time scales. In the proposed approach, model and observed time series are decomposed using the Discrete Wavelet Transform (known as the à trous wavelet transform), and performance measures of the model are obtained at each time scale. The applicability of the proposed method was explored using various case studies-both real as well as synthetic. The synthetic case studies included various kinds of errors (e.g., timing error, under and over prediction of high and low flows) in outputs from a hydrologic model. The real time case studies investigated in this study included simulation results of both the process-based Soil Water Assessment Tool (SWAT) model, as well as statistical models, namely the Coupled Wavelet-Volterra (WVC), Artificial Neural Network (ANN), and Auto Regressive Moving Average (ARMA) methods. For the SWAT model, data from Wainganga and Sind Basin (India) were used, while for the Wavelet Volterra, ANN and ARMA models, data from the Cauvery River Basin (India) and Fraser River (Canada) were used. The study also explored the effect of the choice of the wavelets in multiscale model evaluation. It was found that the proposed wavelet-based performance measures, namely the MNSC (Multiscale Nash-Sutcliffe Criteria) and MNRMSE (Multiscale Normalized Root Mean Square Error), are a more reliable measure than traditional performance measures such as the Nash-Sutcliffe Criteria (NSC), Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). Further, the proposed methodology can be used to: i) compare different hydrological models (both physical and statistical models), and ii) help in model calibration.

The "Chaos Theory" and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease?

PubMed

Krstacic, Goran; Krstacic, Antonija; Smalcelj, Anton; Milicic, Davor; Jembrek-Gostovic, Mirjana

2007-04-01

Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise electrocardiograph (ECG) test. The subjects were included in the series after complete cardiovascular diagnostic data. Series of R-R and ST-T intervals were obtained from exercise ECG data after sampling digitally. The range rescaled analysis method determined the fractal dimension of the intervals. To quantify fractal long-range correlation's properties of heart rate variability, the detrended fluctuation analysis technique was used. Approximate entropy (ApEn) was applied to quantify the regularity and complexity of time series, as well as unpredictability of fluctuations in time series. It was found that the short-term fractal scaling exponent (alpha(1)) is significantly lower in patients with CHD (0.93 +/- 0.07 vs 1.09 +/- 0.04; P < 0.001). The patients with CHD had higher fractal dimension in each exercise test program separately, as well as in exercise program at all. ApEn was significant lower in CHD group in both RR and ST-T ECG intervals (P < 0.001). The nonlinear dynamic methods could have clinical and prognostic applicability also in short-time ECG series. Dynamic analysis based on chaos theory during the exercise ECG test point out the multifractal time series in CHD patients who loss normal fractal characteristics and regularity in HRV. Nonlinear analysis technique may complement traditional ECG analysis.

A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data

NASA Astrophysics Data System (ADS)

Freeman, P. E.; Kashyap, V.; Rosner, R.; Lamb, D. Q.

2002-01-01

Wavelets are scalable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero, and thus may be used to simultaneously characterize the shape, location, and strength of astronomical sources. But in addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly nonzero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources. Source pixels are identified by comparing each correlation coefficient with its probability sampling distribution, which is a function of the (estimated or a priori known) background amplitude. In this paper, we describe the mission-independent, wavelet-based source detection algorithm ``WAVDETECT,'' part of the freely available Chandra Interactive Analysis of Observations (CIAO) software package. Our algorithm uses the Marr, or ``Mexican Hat'' wavelet function, but may be adapted for use with other wavelet functions. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e., flat-fielded) background maps; (2) the correction for exposure variations within the field of view (due to, e.g., telescope support ribs or the edge of the field); (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the robustness of WAVDETECT by applying it to an image from an idealized detector with a spatially invariant Gaussian PSF and an exposure map similar to that of the Einstein IPC; to Pleiades Cluster data collected by the ROSAT PSPC; and to simulated Chandra ACIS-I image of the Lockman Hole region.

A Novel Modeling Method for Aircraft Engine Using Nonlinear Autoregressive Exogenous (NARX) Models Based on Wavelet Neural Networks

NASA Astrophysics Data System (ADS)

Yu, Bing; Shu, Wenjun; Cao, Can

2018-05-01

A novel modeling method for aircraft engine using nonlinear autoregressive exogenous (NARX) models based on wavelet neural networks is proposed. The identification principle and process based on wavelet neural networks are studied, and the modeling scheme based on NARX is proposed. Then, the time series data sets from three types of aircraft engines are utilized to build the corresponding NARX models, and these NARX models are validated by the simulation. The results show that all the best NARX models can capture the original aircraft engine's dynamic characteristic well with the high accuracy. For every type of engine, the relative identification errors of its best NARX model and the component level model are no more than 3.5 % and most of them are within 1 %.

Fractals for Geoengineering

NASA Astrophysics Data System (ADS)

Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga

2016-04-01

The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established for the reservoir' hydraulic units distribution in space and time, as well as for the corresponding well testing data. References: 1. Mandelbrot, B., 1995. Foreword to Fractals in Petroleum Geology and Earth Processes, Edited by: Christopher C. Barton and Paul R. La Pointe, Plenum Press, New York: vii-xii. 2. Jin-Zhou Zhao, Cui-Cui Sheng, Yong_Ming Li, and Shun-Chu Li, 2015. A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir. J. of Chemistry, ID 596597, 8p. 3. Siler, T. , 2007. Fractal Reactor. International Conference Series on Emerging Nuclear Energy Systems 4. Corbett, P. W. M., 2012. The Role of Geoengineering in field development. INTECH, Chapter 8: 181- 198. 5. Nelson, P.H. and J. Kibler, 2003. A Catalog of Porosity and Permeability from core plugs in siliciclastic rocks. U.S. Geological Survey. 6. Per Bak and Kan Chen, 1989. The Physics of Fractals. Physica D 38: 5-12.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks. PMID:21423355

Wavelet-based scalable L-infinity-oriented compression.

PubMed

Alecu, Alin; Munteanu, Adrian; Cornelis, Jan P H; Schelkens, Peter

2006-09-01

Among the different classes of coding techniques proposed in literature, predictive schemes have proven their outstanding performance in near-lossless compression. However, these schemes are incapable of providing embedded L(infinity)-oriented compression, or, at most, provide a very limited number of potential L(infinity) bit-stream truncation points. We propose a new multidimensional wavelet-based L(infinity)-constrained scalable coding framework that generates a fully embedded L(infinity)-oriented bit stream and that retains the coding performance and all the scalability options of state-of-the-art L2-oriented wavelet codecs. Moreover, our codec instantiation of the proposed framework clearly outperforms JPEG2000 in L(infinity) coding sense.

Prediction of welding shrinkage deformation of bridge steel box girder based on wavelet neural network

NASA Astrophysics Data System (ADS)

Tao, Yulong; Miao, Yunshui; Han, Jiaqi; Yan, Feiyun

2018-05-01

Aiming at the low accuracy of traditional forecasting methods such as linear regression method, this paper presents a prediction method for predicting the relationship between bridge steel box girder and its displacement with wavelet neural network. Compared with traditional forecasting methods, this scheme has better local characteristics and learning ability, which greatly improves the prediction ability of deformation. Through analysis of the instance and found that after compared with the traditional prediction method based on wavelet neural network, the rigid beam deformation prediction accuracy is higher, and is superior to the BP neural network prediction results, conform to the actual demand of engineering design.

Image restoration by minimizing zero norm of wavelet frame coefficients

NASA Astrophysics Data System (ADS)

Bao, Chenglong; Dong, Bin; Hou, Likun; Shen, Zuowei; Zhang, Xiaoqun; Zhang, Xue

2016-11-01

In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the {{\\ell }}0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of {{\\ell }}0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

Enhancing hyperspectral spatial resolution using multispectral image fusion: A wavelet approach

NASA Astrophysics Data System (ADS)

Jazaeri, Amin

High spectral and spatial resolution images have a significant impact in remote sensing applications. Because both spatial and spectral resolutions of spaceborne sensors are fixed by design and it is not possible to further increase the spatial or spectral resolution, techniques such as image fusion must be applied to achieve such goals. This dissertation introduces the concept of wavelet fusion between hyperspectral and multispectral sensors in order to enhance the spectral and spatial resolution of a hyperspectral image. To test the robustness of this concept, images from Hyperion (hyperspectral sensor) and Advanced Land Imager (multispectral sensor) were first co-registered and then fused using different wavelet algorithms. A regression-based fusion algorithm was also implemented for comparison purposes. The results show that the fused images using a combined bi-linear wavelet-regression algorithm have less error than other methods when compared to the ground truth. In addition, a combined regression-wavelet algorithm shows more immunity to misalignment of the pixels due to the lack of proper registration. The quantitative measures of average mean square error show that the performance of wavelet-based methods degrades when the spatial resolution of hyperspectral images becomes eight times less than its corresponding multispectral image. Regardless of what method of fusion is utilized, the main challenge in image fusion is image registration, which is also a very time intensive process. Because the combined regression wavelet technique is computationally expensive, a hybrid technique based on regression and wavelet methods was also implemented to decrease computational overhead. However, the gain in faster computation was offset by the introduction of more error in the outcome. The secondary objective of this dissertation is to examine the feasibility and sensor requirements for image fusion for future NASA missions in order to be able to perform onboard image fusion. In this process, the main challenge of image registration was resolved by registering the input images using transformation matrices of previously acquired data. The composite image resulted from the fusion process remarkably matched the ground truth, indicating the possibility of real time onboard fusion processing.

Continuous Wavelet Transform Analysis of Acceleration Signals Measured from a Wave Buoy

PubMed Central

Chuang, Laurence Zsu-Hsin; Wu, Li-Chung; Wang, Jong-Hao

2013-01-01

Accelerometers, which can be installed inside a floating platform on the sea, are among the most commonly used sensors for operational ocean wave measurements. To examine the non-stationary features of ocean waves, this study was conducted to derive a wavelet spectrum of ocean waves and to synthesize sea surface elevations from vertical acceleration signals of a wave buoy through the continuous wavelet transform theory. The short-time wave features can be revealed by simultaneously examining the wavelet spectrum and the synthetic sea surface elevations. The in situ wave signals were applied to verify the practicality of the wavelet-based algorithm. We confirm that the spectral leakage and the noise at very-low-frequency bins influenced the accuracies of the estimated wavelet spectrum and the synthetic sea surface elevations. The appropriate thresholds of these two factors were explored. To study the short-time wave features from the wave records, the acceleration signals recorded from an accelerometer inside a discus wave buoy are analysed. The results from the wavelet spectrum show the evidence of short-time nonlinear wave events. Our study also reveals that more surface profiles with higher vertical asymmetry can be found from short-time nonlinear wave with stronger harmonic spectral peak. Finally, we conclude that the algorithms of continuous wavelet transform are practical for revealing the short-time wave features of the buoy acceleration signals. PMID:23966188

3D Wavelet-Based Filter and Method

DOEpatents

Moss, William C.; Haase, Sebastian; Sedat, John W.

2008-08-12

A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.

Wavelet-based audio embedding and audio/video compression

NASA Astrophysics Data System (ADS)

Mendenhall, Michael J.; Claypoole, Roger L., Jr.

2001-12-01

Watermarking, traditionally used for copyright protection, is used in a new and exciting way. An efficient wavelet-based watermarking technique embeds audio information into a video signal. Several effective compression techniques are applied to compress the resulting audio/video signal in an embedded fashion. This wavelet-based compression algorithm incorporates bit-plane coding, index coding, and Huffman coding. To demonstrate the potential of this audio embedding and audio/video compression algorithm, we embed an audio signal into a video signal and then compress. Results show that overall compression rates of 15:1 can be achieved. The video signal is reconstructed with a median PSNR of nearly 33 dB. Finally, the audio signal is extracted from the compressed audio/video signal without error.

Decoding the Margins: What Can the Fractal Geometry of Basaltic Flow Margins Tell Us?

NASA Astrophysics Data System (ADS)

Schaefer, E. I.; Hamilton, C.; Neish, C.; Beard, S. P.; Bramson, A. M.; Sori, M.; Rader, E. L.

2016-12-01

Studying lava flows on other planetary bodies is essential to characterizing eruption styles and constraining the bodies' thermal evolution. Although planetary basaltic flows are common, many key features are not resolvable in orbital imagery. We are thus developing a technique to characterize basaltic flow type, sub-meter roughness, and sediment mantling from these data. We will present the results from upcoming fieldwork at Craters of the Moon National Monument and Preserve with FINESSE (August) and at Hawai'i Volcanoes National Park (September). We build on earlier work that showed that basaltic flow margins are approximately fractal [Bruno et al., 1992; Gaonac'h et al., 1992] and that their fractal dimensions (D) have distinct `a`ā and pāhoehoe ranges under simple conditions [Bruno et al., 1994]. Using a differential GPS rover, we have recently shown that the margin of Iceland's 2014 Holuhraun flow exhibits near-perfect (R2=0.9998) fractality for ≥24 km across dm to km scales [Schaefer et al., 2016]. This finding suggests that a fractal-based technique has significant potential to characterize flows at sub-resolution scales. We are simultaneously seeking to understand how margin fractality can be modified. A preliminary result for an `a'ā flow in Hawaii's Ka'ū Desert suggests that although aeolian mantling obscures the original flow margin, the apparent margin (i.e., sediment-lava interface) remains fractal [Schaefer et al., 2015]. Further, the apparent margin's D is likely significantly modified from that of the original margin. Other factors that we are exploring include erosion, transitional flow types, and topographic confinement. We will also rigorously test the intriguing possibility that margin D correlates with the sub-meter Hurst exponent H of the flow surface, a common metric of roughness scaling [e.g., Shepard et al., 2001]. This hypothesis is based on geometric arguments [Turcotte, 1997] and is qualitatively consistent with all results so far.

Timing of activities of daily life is jaggy: How episodic ultradian changes in body and brain temperature are integrated into this process.

PubMed

Blessing, William; Ootsuka, Youichirou

2016-01-01

Charles Darwin noted that natural selection applies even to the hourly organization of daily life. Indeed, in many species, the day is segmented into active periods when the animal searches for food, and inactive periods when the animal digests and rests. This episodic temporal patterning is conventionally referred to as ultradian (<24 hours) rhythmicity. The average time between ultradian events is approximately 1-2 hours, but the interval is highly variable. The ultradian pattern is stochastic, jaggy rather than smooth, so that although the next event is likely to occur within 1-2 hours, it is not possible to predict the precise timing. When models of circadian timing are applied to the ultradian temporal pattern, the underlying assumption of true periodicity (stationarity) has distorted the analyses, so that the ultradian pattern is frequently averaged away and ignored. Each active ultradian episode commences with an increase in hippocampal theta rhythm, indicating the switch of attention to the external environment. During each active episode, behavioral and physiological processes, including changes in body and brain temperature, occur in an integrated temporal order, confirming organization by programs endogenous to the central nervous system. We describe methods for analyzing episodic ultradian events, including the use of wavelet mathematics to determine their timing and amplitude, and the use of fractal-based procedures to determine their complexity.

Timing of activities of daily life is jaggy: How episodic ultradian changes in body and brain temperature are integrated into this process

PubMed Central

Blessing, William; Ootsuka, Youichirou

2016-01-01

ABSTRACT Charles Darwin noted that natural selection applies even to the hourly organization of daily life. Indeed, in many species, the day is segmented into active periods when the animal searches for food, and inactive periods when the animal digests and rests. This episodic temporal patterning is conventionally referred to as ultradian (<24 hours) rhythmicity. The average time between ultradian events is approximately 1–2 hours, but the interval is highly variable. The ultradian pattern is stochastic, jaggy rather than smooth, so that although the next event is likely to occur within 1–2 hours, it is not possible to predict the precise timing. When models of circadian timing are applied to the ultradian temporal pattern, the underlying assumption of true periodicity (stationarity) has distorted the analyses, so that the ultradian pattern is frequently averaged away and ignored. Each active ultradian episode commences with an increase in hippocampal theta rhythm, indicating the switch of attention to the external environment. During each active episode, behavioral and physiological processes, including changes in body and brain temperature, occur in an integrated temporal order, confirming organization by programs endogenous to the central nervous system. We describe methods for analyzing episodic ultradian events, including the use of wavelet mathematics to determine their timing and amplitude, and the use of fractal-based procedures to determine their complexity. PMID:28349079

[Fractal research of neurite growth in immunofluorescent images].

PubMed

Tang, Min; Wang, Huinan

2008-12-01

Fractal dimension has been widely used in medical images processing and analysis. The neurite growth of cultured dorsal root ganglion (DRG) was detected by fluorescent immunocytochemistry treated with nerve regeneration factor (0.1, 0.5, 2.0 mg/L). A novel method based on triangular prism surface area (TPSA) was introduced and adopted to calculate the fractal dimension of the two-dimensional immunofluorescent images. Experimental results demonstrate that this method is easy to understand and convenient to operate, and the quantititve results are concordant with the observational findings under microscope. This method can be guidelines for analyzing and deciding experimental results.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder.

PubMed

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E; Bertoldo, Alessandra

2015-02-21

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

New methodology for evaluating osteoclastic activity induced by orthodontic load

PubMed Central

ARAÚJO, Adriele Silveira; FERNANDES, Alline Birra Nolasco; MACIEL, José Vinicius Bolognesi; NETTO, Juliana de Noronha Santos; BOLOGNESE, Ana Maria

2015-01-01

Orthodontic tooth movement (OTM) is a dynamic process of bone modeling involving osteoclast-driven resorption on the compression side. Consequently, to estimate the influence of various situations on tooth movement, experimental studies need to analyze this cell. Objectives The aim of this study was to test and validate a new method for evaluating osteoclastic activity stimulated by mechanical loading based on the fractal analysis of the periodontal ligament (PDL)-bone interface. Material and Methods The mandibular right first molars of 14 rabbits were tipped mesially by a coil spring exerting a constant force of 85 cN. To evaluate the actual influence of osteoclasts on fractal dimension of bone surface, alendronate (3 mg/Kg) was injected weekly in seven of those rabbits. After 21 days, the animals were killed and their jaws were processed for histological evaluation. Osteoclast counts and fractal analysis (by the box counting method) of the PDL-bone interface were performed in histological sections of the right and left sides of the mandible. Results An increase in the number of osteoclasts and in fractal dimension after OTM only happened when alendronate was not administered. Strong correlation was found between the number of osteoclasts and fractal dimension. Conclusions Our results suggest that osteoclastic activity leads to an increase in bone surface irregularity, which can be quantified by its fractal dimension. This makes fractal analysis by the box counting method a potential tool for the assessment of osteoclastic activity on bone surfaces in microscopic examination. PMID:25760264

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

NASA Astrophysics Data System (ADS)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Wavelet Analyses of Oil Prices, USD Variations and Impact on Logistics

NASA Astrophysics Data System (ADS)

Melek, M.; Tokgozlu, A.; Aslan, Z.

2009-07-01

This paper is related with temporal variations of historical oil prices and Dollar and Euro in Turkey. Daily data based on OECD and Central Bank of Turkey records beginning from 1946 has been considered. 1D-continuous wavelets and wavelet packets analysis techniques have been applied on data. Wavelet techniques help to detect abrupt changing's, increasing and decreasing trends of data. Estimation of variables has been presented by using linear regression estimation techniques. The results of this study have been compared with the small and large scale effects. Transportation costs of track show a similar variation with fuel prices. The second part of the paper is related with estimation of imports, exports, costs, total number of vehicles and annual variations by considering temporal variation of oil prices and Dollar currency in Turkey. Wavelet techniques offer a user friendly methodology to interpret some local effects on increasing trend of imports and exports data.

Wavelet based analysis of multi-electrode EEG-signals in epilepsy

NASA Astrophysics Data System (ADS)

Hein, Daniel A.; Tetzlaff, Ronald

2005-06-01

For many epilepsy patients seizures cannot sufficiently be controlled by an antiepileptic pharmacatherapy. Furthermore, only in small number of cases a surgical treatment may be possible. The aim of this work is to contribute to the realization of an implantable seizure warning device. By using recordings of electroenzephalographical(EEG) signals obtained from the department of epileptology of the University of Bonn we studied a recently proposed algorithm for the detection of parameter changes in nonlinear systems. Firstly, after calculating the crosscorrelation function between the signals of two electrodes near the epileptic focus, a wavelet-analysis follows using a sliding window with the so called Mexican-Hat wavelet. Then the Shannon-Entropy of the wavelet-transformed data has been determined providing the information content on a time scale in subject to the dilation of the wavelet-transformation. It shows distinct changes at the seizure onset for all dilations and for all patients.

A study on multiresolution lossless video coding using inter/intra frame adaptive prediction

NASA Astrophysics Data System (ADS)

Nakachi, Takayuki; Sawabe, Tomoko; Fujii, Tetsuro

2003-06-01

Lossless video coding is required in the fields of archiving and editing digital cinema or digital broadcasting contents. This paper combines a discrete wavelet transform and adaptive inter/intra-frame prediction in the wavelet transform domain to create multiresolution lossless video coding. The multiresolution structure offered by the wavelet transform facilitates interchange among several video source formats such as Super High Definition (SHD) images, HDTV, SDTV, and mobile applications. Adaptive inter/intra-frame prediction is an extension of JPEG-LS, a state-of-the-art lossless still image compression standard. Based on the image statistics of the wavelet transform domains in successive frames, inter/intra frame adaptive prediction is applied to the appropriate wavelet transform domain. This adaptation offers superior compression performance. This is achieved with low computational cost and no increase in additional information. Experiments on digital cinema test sequences confirm the effectiveness of the proposed algorithm.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

Fractal modeling of fluidic leakage through metal sealing surfaces

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong

2018-04-01

This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.

Definition of a temporal distribution index for high temporal resolution precipitation data over Peninsular Spain and the Balearic Islands: the fractal dimension; and its synoptic implications

NASA Astrophysics Data System (ADS)

Meseguer-Ruiz, Oliver; Osborn, Timothy J.; Sarricolea, Pablo; Jones, Philip D.; Cantos, Jorge Olcina; Serrano-Notivoli, Roberto; Martin-Vide, Javier

2018-03-01

Precipitation on the Spanish mainland and in the Balearic archipelago exhibits a high degree of spatial and temporal variability, regardless of the temporal resolution of the data considered. The fractal dimension indicates the property of self-similarity, and in the case of this study, wherein it is applied to the temporal behaviour of rainfall at a fine (10-min) resolution from a total of 48 observatories, it provides insights into its more or less convective nature. The methodology of Jenkinson & Collison which automatically classifies synoptic situations at the surface, as well as an adaptation of this methodology at 500 hPa, was applied in order to gain insights into the synoptic implications of extreme values of the fractal dimension. The highest fractal dimension values in the study area were observed in places with precipitation that has a more random behaviour over time with generally high totals. Four different regions in which the atmospheric mechanisms giving rise to precipitation at the surface differ from the corresponding above-ground mechanisms have been identified in the study area based on the fractal dimension. In the north of the Iberian Peninsula, high fractal dimension values are linked to a lower frequency of anticyclonic situations, whereas the opposite occurs in the central region. In the Mediterranean, higher fractal dimension values are associated with a higher frequency of the anticyclonic type and a lower frequency of the advective type from the east. In the south, lower fractal dimension values indicate higher frequency with respect to the anticyclonic type from the east and lower frequency with respect to the cyclonic type.

On the fractal morphology of combustion-generated soot aggregates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koylu, U.O.

1995-12-31

The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of sootmore » was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.« less

A physically based connection between fractional calculus and fractal geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Bio-inspired patterned networks (BIPS) for development of wearable/disposable biosensors

NASA Astrophysics Data System (ADS)

McLamore, E. S.; Convertino, M.; Hondred, John; Das, Suprem; Claussen, J. C.; Vanegas, D. C.; Gomes, C.

2016-05-01

Here we demonstrate a novel approach for fabricating point of care (POC) wearable electrochemical biosensors based on 3D patterning of bionanocomposite networks. To create Bio-Inspired Patterned network (BIPS) electrodes, we first generate fractal network in silico models that optimize transport of network fluxes according to an energy function. Network patterns are then inkjet printed onto flexible substrate using conductive graphene ink. We then deposit fractal nanometal structures onto the graphene to create a 3D nanocomposite network. Finally, we biofunctionalize the surface with biorecognition agents using covalent bonding. In this paper, BIPS are used to develop high efficiency, low cost biosensors for measuring glucose as a proof of concept. Our results on the fundamental performance of BIPS sensors show that the biomimetic nanostructures significantly enhance biosensor sensitivity, accuracy, response time, limit of detection, and hysteresis compared to conventional POC non fractal electrodes (serpentine, interdigitated, and screen printed electrodes). BIPs, in particular Apollonian patterned BIPS, represent a new generation of POC biosensors based on nanoscale and microscale fractal networks that significantly improve electrical connectivity, leading to enhanced sensor performance.

A Quantitative Approach to Scar Analysis

PubMed Central

Khorasani, Hooman; Zheng, Zhong; Nguyen, Calvin; Zara, Janette; Zhang, Xinli; Wang, Joyce; Ting, Kang; Soo, Chia

2011-01-01

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology. PMID:21281794

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

NASA Astrophysics Data System (ADS)

Shepherd, I. G.; Cheng, Robert K.; Talbot, L.

1992-10-01

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 μm/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.

Ozone treatment of coal- and coffee grounds-based active carbons: Water vapor adsorption and surface fractal micropores

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsunoda, Ryoichi; Ozawa, Takayoshi; Ando, Junichi

1998-09-15

Characteristics of the adsorption iostherms of water vapor on active carbons from coal and coffee grounds and those ozonized ones from the surface fractal dimension analysis are discussed. The upswing of the adsorption isotherms in the low relative pressure of coffee grounds-based active carbon, of which isotherms were not scarcely affected on ozonization, was attributed to the adsorption of water molecules on the metallic oxides playing the role of oxygen-surface complexes, which formed the corrugated surfaces on the basal planes of micropore walls with the surface fractal dimension D{sub s} > 2. On the other hand, coal-based active carbon withmore » D{sub s} < 2, which indicated the flat surfaces of micropore walls, showed little effect on the upswing even on ozonization, even though the adsorption amounts of water vapor were increased in the low relative pressure.« less

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

NASA Technical Reports Server (NTRS)

Kiely, Aaron; Xie, Hua; Klimesh, matthew; Aranki, Nazeeh

2010-01-01

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Multiresolution MAP despeckling of SAR images based on locally adaptive generalized Gaussian pdf modeling.

PubMed

Argenti, Fabrizio; Bianchi, Tiziano; Alparone, Luciano

2006-11-01

In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori MIAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation.

Centrifugal compressor surge detecting method based on wavelet analysis of unsteady pressure fluctuations in typical stages

NASA Astrophysics Data System (ADS)

Izmaylov, R.; Lebedev, A.

2015-08-01

Centrifugal compressors are complex energy equipment. Automotive control and protection system should meet the requirements: of operation reliability and durability. In turbocompressors there are at least two dangerous areas: surge and rotating stall. Antisurge protecting systems usually use parametric or feature methods. As a rule industrial system are parametric. The main disadvantages of anti-surge parametric systems are difficulties in mass flow measurements in natural gas pipeline compressor. The principal idea of feature method is based on the experimental fact: as a rule just before the onset of surge rotating or precursor stall established in compressor. In this case the problem consists in detecting of unsteady pressure or velocity fluctuations characteristic signals. Wavelet analysis is the best method for detecting onset of rotating stall in spite of high level of spurious signals (rotating wakes, turbulence, etc.). This method is compatible with state of the art DSP systems of industrial control. Examples of wavelet analysis application for detecting onset of rotating stall in typical stages centrifugal compressor are presented. Experimental investigations include unsteady pressure measurement and sophisticated data acquisition system. Wavelet transforms used biorthogonal wavelets in Mathlab systems.

Rank Determination of Mental Functions by 1D Wavelets and Partial Correlation.

PubMed

Karaca, Y; Aslan, Z; Cattani, C; Galletta, D; Zhang, Y

2017-01-01

The main aim of this paper is to classify mental functions by the Wechsler Adult Intelligence Scale-Revised tests with a mixed method based on wavelets and partial correlation. The Wechsler Adult Intelligence Scale-Revised is a widely used test designed and applied for the classification of the adults cognitive skills in a comprehensive manner. In this paper, many different intellectual profiles have been taken into consideration to measure the relationship between the mental functioning and psychological disorder. We propose a method based on wavelets and correlation analysis for classifying mental functioning, by the analysis of some selected parameters measured by the Wechsler Adult Intelligence Scale-Revised tests. In particular, 1-D Continuous Wavelet Analysis, 1-D Wavelet Coefficient Method and Partial Correlation Method have been analyzed on some Wechsler Adult Intelligence Scale-Revised parameters such as School Education, Gender, Age, Performance Information Verbal and Full Scale Intelligence Quotient. In particular, we will show that gender variable has a negative but a significant role on age and Performance Information Verbal factors. The age parameters also has a significant relation in its role on Performance Information Verbal and Full Scale Intelligence Quotient change.

Exploration of EEG features of Alzheimer's disease using continuous wavelet transform.

PubMed

Ghorbanian, Parham; Devilbiss, David M; Hess, Terry; Bernstein, Allan; Simon, Adam J; Ashrafiuon, Hashem

2015-09-01

We have developed a novel approach to elucidate several discriminating EEG features of Alzheimer's disease. The approach is based on the use of a variety of continuous wavelet transforms, pairwise statistical tests with multiple comparison correction, and several decision tree algorithms, in order to choose the most prominent EEG features from a single sensor. A pilot study was conducted to record EEG signals from Alzheimer's disease (AD) patients and healthy age-matched control (CTL) subjects using a single dry electrode device during several eyes-closed (EC) and eyes-open (EO) resting conditions. We computed the power spectrum distribution properties and wavelet and sample entropy of the wavelet coefficients time series at scale ranges approximately corresponding to the major brain frequency bands. A predictive index was developed using the results from statistical tests and decision tree algorithms to identify the most reliable significant features of the AD patients when compared to healthy controls. The three most dominant features were identified as larger absolute mean power and larger standard deviation of the wavelet scales corresponding to 4-8 Hz (θ) during EO and lower wavelet entropy of the wavelet scales corresponding to 8-12 Hz (α) during EC, respectively. The fourth reliable set of distinguishing features of AD patients was lower relative power of the wavelet scales corresponding to 12-30 Hz (β) followed by lower skewness of the wavelet scales corresponding to 2-4 Hz (upper δ), both during EO. In general, the results indicate slowing and lower complexity of EEG signal in AD patients using a very easy-to-use and convenient single dry electrode device.

Fractal Electronic Circuits Assembled From Nanoclusters

NASA Astrophysics Data System (ADS)

Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.

2009-07-01

Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.

Segmentation of dermoscopy images using wavelet networks.

PubMed

Sadri, Amir Reza; Zekri, Maryam; Sadri, Saeed; Gheissari, Niloofar; Mokhtari, Mojgan; Kolahdouzan, Farzaneh

2013-04-01

This paper introduces a new approach for the segmentation of skin lesions in dermoscopic images based on wavelet network (WN). The WN presented here is a member of fixed-grid WNs that is formed with no need of training. In this WN, after formation of wavelet lattice, determining shift and scale parameters of wavelets with two screening stage and selecting effective wavelets, orthogonal least squares algorithm is used to calculate the network weights and to optimize the network structure. The existence of two stages of screening increases globality of the wavelet lattice and provides a better estimation of the function especially for larger scales. R, G, and B values of a dermoscopy image are considered as the network inputs and the network structure formation. Then, the image is segmented and the skin lesions exact boundary is determined accordingly. The segmentation algorithm were applied to 30 dermoscopic images and evaluated with 11 different metrics, using the segmentation result obtained by a skilled pathologist as the ground truth. Experimental results show that our method acts more effectively in comparison with some modern techniques that have been successfully used in many medical imaging problems.

A Hierarchical Approach to Fracture Mechanics

NASA Technical Reports Server (NTRS)

Saether, Erik; Taasan, Shlomo

2004-01-01

Recent research conducted under NASA LaRC's Creativity and Innovation Program has led to the development of an initial approach for a hierarchical fracture mechanics. This methodology unites failure mechanisms occurring at different length scales and provides a framework for a physics-based theory of fracture. At the nanoscale, parametric molecular dynamic simulations are used to compute the energy associated with atomic level failure mechanisms. This information is used in a mesoscale percolation model of defect coalescence to obtain statistics of fracture paths and energies through Monte Carlo simulations. The mathematical structure of predicted crack paths is described using concepts of fractal geometry. The non-integer fractal dimension relates geometric and energy measures between meso- and macroscales. For illustration, a fractal-based continuum strain energy release rate is derived for inter- and transgranular fracture in polycrystalline metals.

Experimental Study and Fractal Analysis on the Anisotropic Performance of Explosively Welded Interfaces of 304 Stainless Steel/245 Carbon Steel

NASA Astrophysics Data System (ADS)

Fu, Yanshu; Qiu, Yaohui; Li, Yulong

2018-03-01

The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.

Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale

NASA Astrophysics Data System (ADS)

Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian

2018-06-01

Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.

Experimental Study and Fractal Analysis on the Anisotropic Performance of Explosively Welded Interfaces of 304 Stainless Steel/245 Carbon Steel

NASA Astrophysics Data System (ADS)

Fu, Yanshu; Qiu, Yaohui; Li, Yulong

2018-05-01

The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.

The wavelet/scalar quantization compression standard for digital fingerprint images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bradley, J.N.; Brislawn, C.M.

1994-04-01

A new digital image compression standard has been adopted by the US Federal Bureau of Investigation for use on digitized gray-scale fingerprint images. The algorithm is based on adaptive uniform scalar quantization of a discrete wavelet transform image decomposition and is referred to as the wavelet/scalar quantization standard. The standard produces archival quality images at compression ratios of around 20:1 and will allow the FBI to replace their current database of paper fingerprint cards with digital imagery.

[A wavelet neural network algorithm of EEG signals data compression and spikes recognition].

PubMed

Zhang, Y; Liu, A; Yu, K

1999-06-01

A novel method of EEG signals compression representation and epileptiform spikes recognition based on wavelet neural network and its algorithm is presented. The wavelet network not only can compress data effectively but also can recover original signal. In addition, the characters of the spikes and the spike-slow rhythm are auto-detected from the time-frequency isoline of EEG signal. This method is well worth using in the field of the electrophysiological signal processing and time-frequency analyzing.

A study of renal blood flow regulation using the discrete wavelet transform

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Pavlova, Olga N.; Mosekilde, Erik; Sosnovtseva, Olga V.

2010-02-01

In this paper we provide a way to distinguish features of renal blood flow autoregulation mechanisms in normotensive and hypertensive rats based on the discrete wavelet transform. Using the variability of the wavelet coefficients we show distinctions that occur between the normal and pathological states. A reduction of this variability in hypertension is observed on the microscopic level of the blood flow in efferent arteriole of single nephrons. This reduction is probably associated with higher flexibility of healthy cardiovascular system.

Special issue of selected papers from the second UK-Japan bilateral Workshop and First ERCOFTAC Workshop on Turbulent Flows Generated/Designed in Multiscale/Fractal Ways, London, March 2012

NASA Astrophysics Data System (ADS)

Laizet, Sylvain; Sakai, Yasuhiko; Christos Vassilicos, J.

2013-12-01

This special issue of Fluid Dynamics Research includes nine papers which are based on nine of the presentations at the Second UK-Japan bilateral Workshop and First ERCOFTAC Workshop on 'Turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications' held from 26 to 27 March 2012 at Imperial College London, UK. The research area of fractal-generated turbulent flows started with a chapter published in 2001 in one of the conference proceedings which came out of the 1999 Isaac Newton Institute 6 month Programme on Turbulence in Cambridge (UK). However, the first results which formed the basis of much of the work reported in this special issue started appearing from 2007 onwards and progress since then could perhaps be described as not insignificant. Research in this area has resulted in the following six notable advances: (a) the definition of two new length-scales characterizing grid-generated turbulence; (b) enhanced and energy-efficient stirring and scalar transfer by fractal grid and fractal openings/flanges with applications, in particular, to improved turbulence generation for combustion; (c) the non-equilibrium turbulent dissipation law; (d) non-equilibrium axisymmetric wake laws; (e) insights into the dependence of drag forces and vortex shedding on the fractal geometry of fractal objects and simulation methods for the calculation of drag of fractal trees; and (f) the invention and successful proof of concept of fractal spoilers and fractal fences. The present special issue contains papers directly related to these advances and can be seen as a reflection of the current research in the field of fractal-generated turbulent flows and their differences and commonalities with other turbulent flows. The financial support from the Japan Society for the Promotion of Science has been decisive for the organization and success of this workshop. We are also grateful to ERCOFTAC who put in place the EU-wide Special Interest Group on multiscale-generated turbulence and for supporting the workshop both financially and by way of advertisement. Last but by no means least, we express our deep gratitude to the editors of FDR who handled this issue: M Funakoshi, A D Gilbert, L B Mydlarski and K Suga.

Music and fractals

NASA Astrophysics Data System (ADS)

Wuorinen, Charles

2015-03-01

Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...

Analysis of swallowing sounds using hidden Markov models.

PubMed

Aboofazeli, Mohammad; Moussavi, Zahra

2008-04-01

In recent years, acoustical analysis of the swallowing mechanism has received considerable attention due to its diagnostic potentials. This paper presents a hidden Markov model (HMM) based method for the swallowing sound segmentation and classification. Swallowing sound signals of 15 healthy and 11 dysphagic subjects were studied. The signals were divided into sequences of 25 ms segments each of which were represented by seven features. The sequences of features were modeled by HMMs. Trained HMMs were used for segmentation of the swallowing sounds into three distinct phases, i.e., initial quiet period, initial discrete sounds (IDS) and bolus transit sounds (BTS). Among the seven features, accuracy of segmentation by the HMM based on multi-scale product of wavelet coefficients was higher than that of the other HMMs and the linear prediction coefficient (LPC)-based HMM showed the weakest performance. In addition, HMMs were used for classification of the swallowing sounds of healthy subjects and dysphagic patients. Classification accuracy of different HMM configurations was investigated. When we increased the number of states of the HMMs from 4 to 8, the classification error gradually decreased. In most cases, classification error for N=9 was higher than that of N=8. Among the seven features used, root mean square (RMS) and waveform fractal dimension (WFD) showed the best performance in the HMM-based classification of swallowing sounds. When the sequences of the features of IDS segment were modeled separately, the accuracy reached up to 85.5%. As a second stage classification, a screening algorithm was used which correctly classified all the subjects but one healthy subject when RMS was used as characteristic feature of the swallowing sounds and the number of states was set to N=8.

Embedded wavelet-based face recognition under variable position

NASA Astrophysics Data System (ADS)

Cotret, Pascal; Chevobbe, Stéphane; Darouich, Mehdi

2015-02-01

For several years, face recognition has been a hot topic in the image processing field: this technique is applied in several domains such as CCTV, electronic devices delocking and so on. In this context, this work studies the efficiency of a wavelet-based face recognition method in terms of subject position robustness and performance on various systems. The use of wavelet transform has a limited impact on the position robustness of PCA-based face recognition. This work shows, for a well-known database (Yale face database B*), that subject position in a 3D space can vary up to 10% of the original ROI size without decreasing recognition rates. Face recognition is performed on approximation coefficients of the image wavelet transform: results are still satisfying after 3 levels of decomposition. Furthermore, face database size can be divided by a factor 64 (22K with K = 3). In the context of ultra-embedded vision systems, memory footprint is one of the key points to be addressed; that is the reason why compression techniques such as wavelet transform are interesting. Furthermore, it leads to a low-complexity face detection stage compliant with limited computation resources available on such systems. The approach described in this work is tested on three platforms from a standard x86-based computer towards nanocomputers such as RaspberryPi and SECO boards. For K = 3 and a database with 40 faces, the execution mean time for one frame is 0.64 ms on a x86-based computer, 9 ms on a SECO board and 26 ms on a RaspberryPi (B model).

Wavelet-based clustering of resting state MRI data in the rat.

PubMed

Medda, Alessio; Hoffmann, Lukas; Magnuson, Matthew; Thompson, Garth; Pan, Wen-Ju; Keilholz, Shella

2016-01-01

While functional connectivity has typically been calculated over the entire length of the scan (5-10min), interest has been growing in dynamic analysis methods that can detect changes in connectivity on the order of cognitive processes (seconds). Previous work with sliding window correlation has shown that changes in functional connectivity can be observed on these time scales in the awake human and in anesthetized animals. This exciting advance creates a need for improved approaches to characterize dynamic functional networks in the brain. Previous studies were performed using sliding window analysis on regions of interest defined based on anatomy or obtained from traditional steady-state analysis methods. The parcellation of the brain may therefore be suboptimal, and the characteristics of the time-varying connectivity between regions are dependent upon the length of the sliding window chosen. This manuscript describes an algorithm based on wavelet decomposition that allows data-driven clustering of voxels into functional regions based on temporal and spectral properties. Previous work has shown that different networks have characteristic frequency fingerprints, and the use of wavelets ensures that both the frequency and the timing of the BOLD fluctuations are considered during the clustering process. The method was applied to resting state data acquired from anesthetized rats, and the resulting clusters agreed well with known anatomical areas. Clusters were highly reproducible across subjects. Wavelet cross-correlation values between clusters from a single scan were significantly higher than the values from randomly matched clusters that shared no temporal information, indicating that wavelet-based analysis is sensitive to the relationship between areas. Copyright © 2015 Elsevier Inc. All rights reserved.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart.

PubMed

Cluitmans, Matthijs; Karel, Joël; Bonizzi, Pietro; Volders, Paul; Westra, Ronald; Peeters, Ralf

2018-05-12

We investigated a novel sparsity-based regularization method in the wavelet domain of the inverse problem of electrocardiography that aims at preserving the spatiotemporal characteristics of heart-surface potentials. In three normal, anesthetized dogs, electrodes were implanted around the epicardium and body-surface electrodes were attached to the torso. Potential recordings were obtained simultaneously on the body surface and on the epicardium. A CT scan was used to digitize a homogeneous geometry which consisted of the body-surface electrodes and the epicardial surface. A novel multitask elastic-net-based method was introduced to regularize the ill-posed inverse problem. The method simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Performance was assessed in terms of quality of reconstructed epicardial potentials, estimated activation and recovery time, and estimated locations of pacing, and compared with performance of Tikhonov zeroth-order regularization. Results in the wavelet domain obtained higher sparsity than those in the time domain. Epicardial potentials were non-invasively reconstructed with higher accuracy than with Tikhonov zeroth-order regularization (p < 0.05), and recovery times were improved (p < 0.05). No significant improvement was found in terms of activation times and localization of origin of pacing. Next to improved estimation of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias, this novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions. Graphical Abstract The inverse problem of electrocardiography is to reconstruct heart-surface potentials from recorded bodysurface electrocardiograms (ECGs) and a torso-heart geometry. However, it is ill-posed and solving it requires additional constraints for regularization. We introduce a regularization method that simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Our approach reconstructs epicardial (heart-surface) potentials with higher accuracy than common methods. It also improves the reconstruction of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias. This novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions.

Wavelet multiresolution complex network for decoding brain fatigued behavior from P300 signals

NASA Astrophysics Data System (ADS)

Gao, Zhong-Ke; Wang, Zi-Bo; Yang, Yu-Xuan; Li, Shan; Dang, Wei-Dong; Mao, Xiao-Qian

2018-09-01

Brain-computer interface (BCI) enables users to interact with the environment without relying on neural pathways and muscles. P300 based BCI systems have been extensively used to achieve human-machine interaction. However, the appearance of fatigue symptoms during operation process leads to the decline in classification accuracy of P300. Characterizing brain cognitive process underlying normal and fatigue conditions constitutes a problem of vital importance in the field of brain science. We in this paper propose a novel wavelet decomposition based complex network method to efficiently analyze the P300 signals recorded in the image stimulus test based on classical 'Oddball' paradigm. Initially, multichannel EEG signals are decomposed into wavelet coefficient series. Then we construct complex network by treating electrodes as nodes and determining the connections according to the 2-norm distances between wavelet coefficient series. The analysis of topological structure and statistical index indicates that the properties of brain network demonstrate significant distinctions between normal status and fatigue status. More specifically, the brain network reconfiguration in response to the cognitive task in fatigue status is reflected as the enhancement of the small-worldness.

A Wavelet-based Fast Discrimination of Transformer Magnetizing Inrush Current

NASA Astrophysics Data System (ADS)

Kitayama, Masashi

Recently customers who need electricity of higher quality have been installing co-generation facilities. They can avoid voltage sags and other distribution system related disturbances by supplying electricity to important load from their generators. For another example, FRIENDS, highly reliable distribution system using semiconductor switches or storage devices based on power electronics technology, is proposed. These examples illustrates that the request for high reliability in distribution system is increasing. In order to realize these systems, fast relaying algorithms are indispensable. The author proposes a new method of detecting magnetizing inrush current using discrete wavelet transform (DWT). DWT provides the function of detecting discontinuity of current waveform. Inrush current occurs when transformer core becomes saturated. The proposed method detects spikes of DWT components derived from the discontinuity of the current waveform at both the beginning and the end of inrush current. Wavelet thresholding, one of the wavelet-based statistical modeling, was applied to detect the DWT component spikes. The proposed method is verified using experimental data using single-phase transformer and the proposed method is proved to be effective.

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations

NASA Technical Reports Server (NTRS)

Sjoegreen, B.; Yee, H. C.

2001-01-01

The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme independent and can be stand alone options for numerical algorithm other than the Yee et al. scheme.

Effective degrees of freedom of a random walk on a fractal

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Multiresolution With Super-Compact Wavelets

NASA Technical Reports Server (NTRS)

Lee, Dohyung

2000-01-01

The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.

Texture feature extraction based on wavelet transform and gray-level co-occurrence matrices applied to osteosarcoma diagnosis.

PubMed

Hu, Shan; Xu, Chao; Guan, Weiqiao; Tang, Yong; Liu, Yana

2014-01-01

Osteosarcoma is the most common malignant bone tumor among children and adolescents. In this study, image texture analysis was made to extract texture features from bone CR images to evaluate the recognition rate of osteosarcoma. To obtain the optimal set of features, Sym4 and Db4 wavelet transforms and gray-level co-occurrence matrices were applied to the image, with statistical methods being used to maximize the feature selection. To evaluate the performance of these methods, a support vector machine algorithm was used. The experimental results demonstrated that the Sym4 wavelet had a higher classification accuracy (93.44%) than the Db4 wavelet with respect to osteosarcoma occurrence in the epiphysis, whereas the Db4 wavelet had a higher classification accuracy (96.25%) for osteosarcoma occurrence in the diaphysis. Results including accuracy, sensitivity, specificity and ROC curves obtained using the wavelets were all higher than those obtained using the features derived from the GLCM method. It is concluded that, a set of texture features can be extracted from the wavelets and used in computer-aided osteosarcoma diagnosis systems. In addition, this study also confirms that multi-resolution analysis is a useful tool for texture feature extraction during bone CR image processing.

Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition

NASA Astrophysics Data System (ADS)

Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.

2005-12-01

Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.

Cloud-scale genomic signals processing classification analysis for gene expression microarray data.

PubMed

Harvey, Benjamin; Soo-Yeon Ji

2014-01-01

As microarray data available to scientists continues to increase in size and complexity, it has become overwhelmingly important to find multiple ways to bring inference though analysis of DNA/mRNA sequence data that is useful to scientists. Though there have been many attempts to elucidate the issue of bringing forth biological inference by means of wavelet preprocessing and classification, there has not been a research effort that focuses on a cloud-scale classification analysis of microarray data using Wavelet thresholding in a Cloud environment to identify significantly expressed features. This paper proposes a novel methodology that uses Wavelet based Denoising to initialize a threshold for determination of significantly expressed genes for classification. Additionally, this research was implemented and encompassed within cloud-based distributed processing environment. The utilization of Cloud computing and Wavelet thresholding was used for the classification 14 tumor classes from the Global Cancer Map (GCM). The results proved to be more accurate than using a predefined p-value for differential expression classification. This novel methodology analyzed Wavelet based threshold features of gene expression in a Cloud environment, furthermore classifying the expression of samples by analyzing gene patterns, which inform us of biological processes. Moreover, enabling researchers to face the present and forthcoming challenges that may arise in the analysis of data in functional genomics of large microarray datasets.

Wavelet-based multiscale analysis of minimum toe clearance variability in the young and elderly during walking.

PubMed

Khandoker, Ahsan H; Karmakar, Chandan K; Begg, Rezaul K; Palaniswami, Marimuthu

2007-01-01

As humans age or are influenced by pathology of the neuromuscular system, gait patterns are known to adjust, accommodating for reduced function in the balance control system. The aim of this study was to investigate the effectiveness of a wavelet based multiscale analysis of a gait variable [minimum toe clearance (MTC)] in deriving indexes for understanding age-related declines in gait performance and screening of balance impairments in the elderly. MTC during walking on a treadmill for 30 healthy young, 27 healthy elderly and 10 falls risk elderly subjects with a history of tripping falls were analyzed. The MTC signal from each subject was decomposed to eight detailed signals at different wavelet scales by using the discrete wavelet transform. The variances of detailed signals at scales 8 to 1 were calculated. The multiscale exponent (beta) was then estimated from the slope of the variance progression at successive scales. The variance at scale 5 was significantly (p<0.01) different between young and healthy elderly group. Results also suggest that the Beta between scales 1 to 2 are effective for recognizing falls risk gait patterns. Results have implication for quantifying gait dynamics in normal, ageing and pathological conditions. Early detection of gait pattern changes due to ageing and balance impairments using wavelet-based multiscale analysis might provide the opportunity to initiate preemptive measures to be undertaken to avoid injurious falls.

Wavelet transform based on inner product in fault diagnosis of rotating machinery: A review

NASA Astrophysics Data System (ADS)

Chen, Jinglong; Li, Zipeng; Pan, Jun; Chen, Gaige; Zi, Yanyang; Yuan, Jing; Chen, Binqiang; He, Zhengjia

2016-03-01

As a significant role in industrial equipment, rotating machinery fault diagnosis (RMFD) always draws lots of attention for guaranteeing product quality and improving economic benefit. But non-stationary vibration signal with a large amount of noise on abnormal condition of weak fault or compound fault in many cases would lead to this task challenging. As one of the most powerful non-stationary signal processing techniques, wavelet transform (WT) has been extensively studied and widely applied in RMFD. Numerous publications about the study and applications of WT for RMFD have been presented to academic journals, technical reports and conference proceedings. Many previous publications admit that WT can be realized by means of inner product principle of signal and wavelet base. This paper verifies the essence on inner product operation of WT by simulation and field experiments. Then the development process of WT based on inner product is concluded and the applications of major developments in RMFD are also summarized. Finally, super wavelet transform as an important prospect of WT based on inner product are presented and discussed. It is expected that this paper can offer an in-depth and comprehensive references for researchers and help them with finding out further research topics.

Target Identification Using Harmonic Wavelet Based ISAR Imaging

NASA Astrophysics Data System (ADS)

Shreyamsha Kumar, B. K.; Prabhakar, B.; Suryanarayana, K.; Thilagavathi, V.; Rajagopal, R.

2006-12-01

A new approach has been proposed to reduce the computations involved in the ISAR imaging, which uses harmonic wavelet-(HW) based time-frequency representation (TFR). Since the HW-based TFR falls into a category of nonparametric time-frequency (T-F) analysis tool, it is computationally efficient compared to parametric T-F analysis tools such as adaptive joint time-frequency transform (AJTFT), adaptive wavelet transform (AWT), and evolutionary AWT (EAWT). Further, the performance of the proposed method of ISAR imaging is compared with the ISAR imaging by other nonparametric T-F analysis tools such as short-time Fourier transform (STFT) and Choi-Williams distribution (CWD). In the ISAR imaging, the use of HW-based TFR provides similar/better results with significant (92%) computational advantage compared to that obtained by CWD. The ISAR images thus obtained are identified using a neural network-based classification scheme with feature set invariant to translation, rotation, and scaling.

The Application of Continuous Wavelet Transform Based Foreground Subtraction Method in 21 cm Sky Surveys

NASA Astrophysics Data System (ADS)

Gu, Junhua; Xu, Haiguang; Wang, Jingying; An, Tao; Chen, Wen

2013-08-01

We propose a continuous wavelet transform based non-parametric foreground subtraction method for the detection of redshifted 21 cm signal from the epoch of reionization. This method works based on the assumption that the foreground spectra are smooth in frequency domain, while the 21 cm signal spectrum is full of saw-tooth-like structures, thus their characteristic scales are significantly different. We can distinguish them in the wavelet coefficient space easily and perform the foreground subtraction. Compared with the traditional spectral fitting based method, our method is more tolerant to complex foregrounds. Furthermore, we also find that when the instrument has uncorrected response error, our method can also work significantly better than the spectral fitting based method. Our method can obtain similar results with the Wp smoothing method, which is also a non-parametric method, but our method consumes much less computing time.

Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

PubMed Central

Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing

2014-01-01

Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680

An Approach to Study Elastic Vibrations of Fractal Cylinders

NASA Astrophysics Data System (ADS)

Steinberg, Lev; Zepeda, Mario

2016-11-01

This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.