Discrete Haar transform and protein structure.

PubMed

Morosetti, S

1997-12-01

The discrete Haar transform of the sequence of the backbone dihedral angles (phi and psi) was performed over a set of X-ray protein structures of high resolution from the Brookhaven Protein Data Bank. Afterwards, the new dihedral angles were calculated by the inverse transform, using a growing number of Haar functions, from the lower to the higher degree. New structures were obtained using these dihedral angles, with standard values for bond lengths and angles, and with omega = 0 degree. The reconstructed structures were compared with the experimental ones, and analyzed by visual inspection and statistical analysis. When half of the Haar coefficients were used, all the reconstructed structures were not yet collapsed to a tertiary folding, but they showed yet realized most of the secondary motifs. These results indicate a substantial separation of structural information in the space of Haar transform, with the secondary structural information mainly present in the Haar coefficients of lower degrees, and the tertiary one present in the higher degree coefficients. Because of this separation, the representation of the folded structures in the space of Haar transform seems a promising candidate to encompass the problem of premature convergence in genetic algorithms.

Fast Poisson noise removal by biorthogonal Haar domain hypothesis testing

NASA Astrophysics Data System (ADS)

Zhang, B.; Fadili, M. J.; Starck, J.-L.; Digel, S. W.

2008-07-01

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. Facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong “staircase” artifacts. In this paper, we propose to combine the HT framework with the decimated biorthogonal Haar (Bi-Haar) transform instead of the classical Haar. The Bi-Haar filter bank is normalized such that the p-values of Bi-Haar coefficients (p) provide good approximation to those of Haar (pH) for high-intensity settings or large scales; for low-intensity settings and small scales, we show that p are essentially upper-bounded by pH. Thus, we may apply the Haar-based HTs to Bi-Haar coefficients to control a prefixed false positive rate. By doing so, we benefit from the regular Bi-Haar filter bank to gain a smooth estimate while always maintaining a low computational complexity. A Fisher-approximation-based threshold implementing the HTs is also established. The efficiency of this method is illustrated on an example of hyperspectral-source-flux estimation.

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.

Use of local noise power spectrum and wavelet analysis in quantitative image quality assurance for EPIDs

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

Lee, Soyoung

Purpose: To investigate the use of local noise power spectrum (NPS) to characterize image noise and wavelet analysis to isolate defective pixels and inter-subpanel flat-fielding artifacts for quantitative quality assurance (QA) of electronic portal imaging devices (EPIDs). Methods: A total of 93 image sets including custom-made bar-pattern images and open exposure images were collected from four iViewGT a-Si EPID systems over three years. Global quantitative metrics such as modulation transform function (MTF), NPS, and detective quantum efficiency (DQE) were computed for each image set. Local NPS was also calculated for individual subpanels by sampling region of interests within each subpanelmore » of the EPID. The 1D NPS, obtained by radially averaging the 2D NPS, was fitted to a power-law function. The r-square value of the linear regression analysis was used as a singular metric to characterize the noise properties of individual subpanels of the EPID. The sensitivity of the local NPS was first compared with the global quantitative metrics using historical image sets. It was then compared with two commonly used commercial QA systems with images collected after applying two different EPID calibration methods (single-level gain and multilevel gain). To detect isolated defective pixels and inter-subpanel flat-fielding artifacts, Haar wavelet transform was applied on the images. Results: Global quantitative metrics including MTF, NPS, and DQE showed little change over the period of data collection. On the contrary, a strong correlation between the local NPS (r-square values) and the variation of the EPID noise condition was observed. The local NPS analysis indicated image quality improvement with the r-square values increased from 0.80 ± 0.03 (before calibration) to 0.85 ± 0.03 (after single-level gain calibration) and to 0.96 ± 0.03 (after multilevel gain calibration), while the commercial QA systems failed to distinguish the image quality improvement between

Structural health monitoring approach for detecting ice accretion on bridge cable using the Haar Wavelet Transform

NASA Astrophysics Data System (ADS)

Andre, Julia; Kiremidjian, Anne; Liao, Yizheng; Georgakis, Christos; Rajagopal, Ram

2016-04-01

Ice accretion on cables of bridge structures poses serious risk to the structure as well as to vehicular traffic when the ice falls onto the road. Detection of ice formation, quantification of the amount of ice accumulated, and prediction of icefalls will increase the safety and serviceability of the structure. In this paper, an ice accretion detection algorithm is presented based on the Continuous Wavelet Transform (CWT). In the proposed algorithm, the acceleration signals obtained from bridge cables are transformed using wavelet method. The damage sensitive features (DSFs) are defined as a function of the wavelet energy at specific wavelet scales. It is found that as ice accretes on the cables, the mass of cable increases, thus changing the wavelet energies. Hence, the DSFs can be used to track the change of cables mass. To validate the proposed algorithm, we use the data collected from a laboratory experiment conducted at the Technical University of Denmark (DTU). In this experiment, a cable was placed in a wind tunnel as ice volume grew progressively. Several accelerometers were installed at various locations along the testing cable to collect vibration signals.

The brain MRI classification problem from wavelets perspective

NASA Astrophysics Data System (ADS)

Bendib, Mohamed M.; Merouani, Hayet F.; Diaba, Fatma

2015-02-01

Haar and Daubechies 4 (DB4) are the most used wavelets for brain MRI (Magnetic Resonance Imaging) classification. The former is simple and fast to compute while the latter is more complex and offers a better resolution. This paper explores the potential of both of them in performing Normal versus Pathological discrimination on the one hand, and Multiclassification on the other hand. The Whole Brain Atlas is used as a validation database, and the Random Forest (RF) algorithm is employed as a learning approach. The achieved results are discussed and statistically compared.

Harmonic analysis of traction power supply system based on wavelet decomposition

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, AC drive electric locomotive and EMU large-scale operation in the country on the ground, the electrified railway has become the main harmonic source of China's power grid. In response to this phenomenon, the need for timely monitoring of power quality problems of electrified railway, assessment and governance. Wavelet transform is developed on the basis of Fourier analysis, the basic idea comes from the harmonic analysis, with a rigorous theoretical model, which has inherited and developed the local thought of Garbor transformation, and has overcome the disadvantages such as window fixation and lack of discrete orthogonally, so as to become a more recently studied spectral analysis tool. The wavelet analysis takes the gradual and precise time domain step in the high frequency part so as to focus on any details of the signal being analyzed, thereby comprehensively analyzing the harmonics of the traction power supply system meanwhile use the pyramid algorithm to increase the speed of wavelet decomposition. The matlab simulation shows that the use of wavelet decomposition of the traction power supply system for harmonic spectrum analysis is effective.

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.

Obscenity Detection Using Haar-Like Features and Gentle Adaboost Classifier

PubMed Central

Min, Yang; Zhu, Dingju

2014-01-01

Large exposure of skin area of an image is considered obscene. This only fact may lead to many false images having skin-like objects and may not detect those images which have partially exposed skin area but have exposed erotogenic human body parts. This paper presents a novel method for detecting nipples from pornographic image contents. Nipple is considered as an erotogenic organ to identify pornographic contents from images. In this research Gentle Adaboost (GAB) haar-cascade classifier and haar-like features used for ensuring detection accuracy. Skin filter prior to detection made the system more robust. The experiment showed that, considering accuracy, haar-cascade classifier performs well, but in order to satisfy detection time, train-cascade classifier is suitable. To validate the results, we used 1198 positive samples containing nipple objects and 1995 negative images. The detection rates for haar-cascade and train-cascade classifiers are 0.9875 and 0.8429, respectively. The detection time for haar-cascade is 0.162 seconds and is 0.127 seconds for train-cascade classifier. PMID:25003153

Obscenity detection using haar-like features and Gentle Adaboost classifier.

PubMed

Mustafa, Rashed; Min, Yang; Zhu, Dingju

2014-01-01

Large exposure of skin area of an image is considered obscene. This only fact may lead to many false images having skin-like objects and may not detect those images which have partially exposed skin area but have exposed erotogenic human body parts. This paper presents a novel method for detecting nipples from pornographic image contents. Nipple is considered as an erotogenic organ to identify pornographic contents from images. In this research Gentle Adaboost (GAB) haar-cascade classifier and haar-like features used for ensuring detection accuracy. Skin filter prior to detection made the system more robust. The experiment showed that, considering accuracy, haar-cascade classifier performs well, but in order to satisfy detection time, train-cascade classifier is suitable. To validate the results, we used 1198 positive samples containing nipple objects and 1995 negative images. The detection rates for haar-cascade and train-cascade classifiers are 0.9875 and 0.8429, respectively. The detection time for haar-cascade is 0.162 seconds and is 0.127 seconds for train-cascade classifier.

Wavelet detection of coherent structures in interplanetary magnetic flux ropes and its role in the intermittent turbulence

NASA Astrophysics Data System (ADS)

Muñoz, P. R.; Chian, A. C.

2013-12-01

We implement a method to detect coherent magnetic structures using the Haar discrete wavelet transform (Salem et al., ApJ 702, 537, 2009), and apply it to an event detected by Cluster at the turbulent boundary layer of an interplanetary magnetic flux rope. The wavelet method is able to detect magnetic coherent structures and extract main features of solar wind intermittent turbulence, such as the power spectral density and the scaling exponent of structure functions. Chian and Muñoz (ApJL 733, L34, 2011) investigated the relation between current sheets, turbulence, and magnetic reconnections at the leading edge of an interplanetary coronal mass ejection measured by Cluster upstream of the Earth's bow shock on 2005 January 21. We found observational evidence of two magnetically reconnected current sheets in the vicinity of a front magnetic cloud boundary layer, where the scaling exponent of structure functions of magnetic fluctuations exhibits multifractal behavior. Using the wavelet technique, we show that the current sheets associated to magnetic reconnection are part of the set of magnetic coherent structures responsible for multifractality. By removing them using a filtering criteria, it is possible to recover a self-similar scaling exponent predicted for homogeneous turbulence. Finally, we discuss an extension of the wavelet technique to study coherent structures in two-dimensional solar magnetograms.

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.

Generalized exact holographic mapping with wavelets

NASA Astrophysics Data System (ADS)

Lee, Ching Hua

2017-12-01

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.

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

Classification of epileptic seizures using wavelet packet log energy and norm entropies with recurrent Elman neural network classifier.

PubMed

Raghu, S; Sriraam, N; Kumar, G Pradeep

2017-02-01

Electroencephalogram shortly termed as EEG is considered as the fundamental segment for the assessment of the neural activities in the brain. In cognitive neuroscience domain, EEG-based assessment method is found to be superior due to its non-invasive ability to detect deep brain structure while exhibiting superior spatial resolutions. Especially for studying the neurodynamic behavior of epileptic seizures, EEG recordings reflect the neuronal activity of the brain and thus provide required clinical diagnostic information for the neurologist. This specific proposed study makes use of wavelet packet based log and norm entropies with a recurrent Elman neural network (REN) for the automated detection of epileptic seizures. Three conditions, normal, pre-ictal and epileptic EEG recordings were considered for the proposed study. An adaptive Weiner filter was initially applied to remove the power line noise of 50 Hz from raw EEG recordings. Raw EEGs were segmented into 1 s patterns to ensure stationarity of the signal. Then wavelet packet using Haar wavelet with a five level decomposition was introduced and two entropies, log and norm were estimated and were applied to REN classifier to perform binary classification. The non-linear Wilcoxon statistical test was applied to observe the variation in the features under these conditions. The effect of log energy entropy (without wavelets) was also studied. It was found from the simulation results that the wavelet packet log entropy with REN classifier yielded a classification accuracy of 99.70 % for normal-pre-ictal, 99.70 % for normal-epileptic and 99.85 % for pre-ictal-epileptic.

UV Spectrophotometric Simultaneous Determination of Paracetamol and Ibuprofen in Combined Tablets by Derivative and Wavelet Transforms

PubMed Central

Hoang, Vu Dang; Ly, Dong Thi Ha; Tho, Nguyen Huu; Minh Thi Nguyen, Hue

2014-01-01

The application of first-order derivative and wavelet transforms to UV spectra and ratio spectra was proposed for the simultaneous determination of ibuprofen and paracetamol in their combined tablets. A new hybrid approach on the combined use of first-order derivative and wavelet transforms to spectra was also discussed. In this application, DWT (sym6 and haar), CWT (mexh), and FWT were optimized to give the highest spectral recoveries. Calibration graphs in the linear concentration ranges of ibuprofen (12–32 mg/L) and paracetamol (20–40 mg/L) were obtained by measuring the amplitudes of the transformed signals. Our proposed spectrophotometric methods were statistically compared to HPLC in terms of precision and accuracy. PMID:24949492

UV spectrophotometric simultaneous determination of paracetamol and ibuprofen in combined tablets by derivative and wavelet transforms.

PubMed

Hoang, Vu Dang; Ly, Dong Thi Ha; Tho, Nguyen Huu; Nguyen, Hue Minh Thi

2014-01-01

The application of first-order derivative and wavelet transforms to UV spectra and ratio spectra was proposed for the simultaneous determination of ibuprofen and paracetamol in their combined tablets. A new hybrid approach on the combined use of first-order derivative and wavelet transforms to spectra was also discussed. In this application, DWT (sym6 and haar), CWT (mexh), and FWT were optimized to give the highest spectral recoveries. Calibration graphs in the linear concentration ranges of ibuprofen (12-32 mg/L) and paracetamol (20-40 mg/L) were obtained by measuring the amplitudes of the transformed signals. Our proposed spectrophotometric methods were statistically compared to HPLC in terms of precision and accuracy.

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.

Fault Analysis of Space Station DC Power Systems-Using Neural Network Adaptive Wavelets to Detect Faults

NASA Technical Reports Server (NTRS)

Momoh, James A.; Wang, Yanchun; Dolce, James L.

1997-01-01

This paper describes the application of neural network adaptive wavelets for fault diagnosis of space station power system. The method combines wavelet transform with neural network by incorporating daughter wavelets into weights. Therefore, the wavelet transform and neural network training procedure become one stage, which avoids the complex computation of wavelet parameters and makes the procedure more straightforward. The simulation results show that the proposed method is very efficient for the identification of fault locations.

Directional filtering for block recovery using wavelet features

NASA Astrophysics Data System (ADS)

Hyun, Seung H.; Eom, Il K.; Kim, Yoo S.

2005-07-01

When images compressed with block-based compression techniques are transmitted over a noisy channel, unexpected block losses occur. Conventional methods that do not consider edge directions can cause blocked blurring artifacts. In this paper, we present a post-processing-based block recovery scheme using Haar wavelet features. The adaptive selection of neighboring blocks is performed based on the energy of wavelet subbands (EWS) and difference between DC values (DDC). The lost blocks are recovered by linear interpolation in the spatial domain using selected blocks. The method using only EWS performs well for horizontal and vertical edges, but not as well for diagonal edges. Conversely, only using DDC performs well for diagonal edges with the exception of line- or roof-type edge profiles. Therefore, we combine EWS and DDC for better results. The proposed directional recovery method is effective for the strong edge because exploit the varying neighboring blocks adaptively according to the edges and the directional information in the image. The proposed method outperforms the previous methods that used only fixed blocks.

Multiresolution analysis (discrete wavelet transform) through Daubechies family for emotion recognition in speech.

NASA Astrophysics Data System (ADS)

Campo, D.; Quintero, O. L.; Bastidas, M.

2016-04-01

We propose a study of the mathematical properties of voice as an audio signal. This work includes signals in which the channel conditions are not ideal for emotion recognition. Multiresolution analysis- discrete wavelet transform - was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states. ANNs proved to be a system that allows an appropriate classification of such states. This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features. Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify.

Wavelet analysis of poorly-focused ultrasonic signal of pressure tube inspection in nuclear industry

NASA Astrophysics Data System (ADS)

Zhao, Huan; Gachagan, Anthony; Dobie, Gordon; Lardner, Timothy

2018-04-01

Pressure tube fabrication and installment challenges combined with natural sagging over time can produce issues with probe alignment for pressure tube inspection of the primary circuit of CANDU reactors. The ability to extract accurate defect depth information from poorly focused ultrasonic signals would reduce additional inspection procedures, which leads to a significant time and cost saving. Currently, the defect depth measurement protocol is to simply calculate the time difference between the peaks of the echo signals from the tube surface and the defect from a single element probe focused at the back-wall depth. When alignment issues are present, incorrect focusing results in interference within the returning echo signal. This paper proposes a novel wavelet analysis method that employs the Haar wavelet to decompose the original poorly focused A-scan signal and reconstruct detailed information based on a selected high frequency component range within the bandwidth of the transducer. Compared to the original signal, the wavelet analysis method provides additional characteristic defect information and an improved estimate of defect depth with errors less than 5%.

Fractal markets hypothesis and the global financial crisis: wavelet power evidence.

PubMed

Kristoufek, Ladislav

2013-10-04

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.

Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav

2013-10-01

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.

Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence

PubMed Central

Kristoufek, Ladislav

2013-01-01

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis. PMID:24091386

Preprocessing of PHERMEX flash radiographic images with Haar and adaptive filtering

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

Brolley, J.E.

1978-11-01

Work on image preparation has continued with the application of high-sequency boosting via Haar filtering. This is useful in developing line or edge structures. Widrow LMS adaptive filtering has also been shown to be useful in developing edge structure in special problems. Shadow effects can be obtained with the latter which may be useful for some problems. Combined Haar and adaptive filtering is illustrated for a PHERMEX image.

Univariate Time Series Prediction of Solar Power Using a Hybrid Wavelet-ARMA-NARX Prediction Method

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

Nazaripouya, Hamidreza; Wang, Yubo; Chu, Chi-Cheng

This paper proposes a new hybrid method for super short-term solar power prediction. Solar output power usually has a complex, nonstationary, and nonlinear characteristic due to intermittent and time varying behavior of solar radiance. In addition, solar power dynamics is fast and is inertia less. An accurate super short-time prediction is required to compensate for the fluctuations and reduce the impact of solar power penetration on the power system. The objective is to predict one step-ahead solar power generation based only on historical solar power time series data. The proposed method incorporates discrete wavelet transform (DWT), Auto-Regressive Moving Average (ARMA)more » models, and Recurrent Neural Networks (RNN), while the RNN architecture is based on Nonlinear Auto-Regressive models with eXogenous inputs (NARX). The wavelet transform is utilized to decompose the solar power time series into a set of richer-behaved forming series for prediction. ARMA model is employed as a linear predictor while NARX is used as a nonlinear pattern recognition tool to estimate and compensate the error of wavelet-ARMA prediction. The proposed method is applied to the data captured from UCLA solar PV panels and the results are compared with some of the common and most recent solar power prediction methods. The results validate the effectiveness of the proposed approach and show a considerable improvement in the prediction precision.« less

The convergence of double Fourier-Haar series over homothetic copies of sets

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

Oniani, G. G., E-mail: oniani@atsu.edu.ge

The paper is concerned with the convergence of double Fourier- Haar series with partial sums taken over homothetic copies of a given bounded set W⊂R{sub +}{sup 2} containing the intersection of some neighbourhood of the origin with R{sub +}{sup 2}. It is proved that for a set W from a fairly broad class (in particular, for convex W) there are two alternatives: either the Fourier-Haar series of an arbitrary function f∈L([0,1]{sup 2}) converges almost everywhere or Lln{sup +} L([0,1]{sup 2}) is the best integral class in which the double Fourier-Haar series converges almost everywhere. Furthermore, a characteristic property is obtained, whichmore » distinguishes which of the two alternatives is realized for a given W. Bibliography: 12 titles. (paper)« less

Wavelet Algorithms for Illumination Computations

NASA Astrophysics Data System (ADS)

Schroder, Peter

One of the core problems of computer graphics is the computation of the equilibrium distribution of light in a scene. This distribution is given as the solution to a Fredholm integral equation of the second kind involving an integral over all surfaces in the scene. In the general case such solutions can only be numerically approximated, and are generally costly to compute, due to the geometric complexity of typical computer graphics scenes. For this computation both Monte Carlo and finite element techniques (or hybrid approaches) are typically used. A simplified version of the illumination problem is known as radiosity, which assumes that all surfaces are diffuse reflectors. For this case hierarchical techniques, first introduced by Hanrahan et al. (32), have recently gained prominence. The hierarchical approaches lead to an asymptotic improvement when only finite precision is required. The resulting algorithms have cost proportional to O(k^2 + n) versus the usual O(n^2) (k is the number of input surfaces, n the number of finite elements into which the input surfaces are meshed). Similarly a hierarchical technique has been introduced for the more general radiance problem (which allows glossy reflectors) by Aupperle et al. (6). In this dissertation we show the equivalence of these hierarchical techniques to the use of a Haar wavelet basis in a general Galerkin framework. By so doing, we come to a deeper understanding of the properties of the numerical approximations used and are able to extend the hierarchical techniques to higher orders. In particular, we show the correspondence of the geometric arguments underlying hierarchical methods to the theory of Calderon-Zygmund operators and their sparse realization in wavelet bases. The resulting wavelet algorithms for radiosity and radiance are analyzed and numerical results achieved with our implementation are reported. We find that the resulting algorithms achieve smaller and smoother errors at equivalent work.

[The algorithm based on wavelet for canceling muscle electricity and wide range frequency of power line hum in ECG].

PubMed

Zhao, Jie; Hua, Mei

2004-06-01

To develop a wavelet noise canceller that cancels muscle electricity and power line hum in wide range of frequency. According to the feature that the QRS complex has higher frequency components, and the T, P wave have lower frequency components, the biorthogonal wavelet was selected to decompose the original signals. An interference-eliminated signal ECG was formed by reconstruction from the changed coefficients of wavelet. By using the canceller, muscle electricity and power line interference between 49 Hz and 61 Hz were eliminated from the ECG signals. This canceller works well in canceling muscle electricity, and basic and harmonic frequencies of power line hum. The canceller is also insensitive to the frequency change of power line, the same procedure is good for both 50 and 60 Hz power line hum.

Wavelets and Multifractal Analysis

DTIC Science & Technology

2004-07-01

distribution unlimited 13. SUPPLEMENTARY NOTES See also ADM001750, Wavelets and Multifractal Analysis (WAMA) Workshop held on 19-31 July 2004., The original...f)] . . . 16 2.5.4 Detrended Fluctuation Analysis [DFA(m)] . . . . . . . . . . . . . . . 17 2.6 Scale-Independent Measures...18 2.6.1 Detrended -Fluctuation- Analysis Power-Law Exponent (αD) . . . . . . 18 2.6.2 Wavelet-Transform Power-Law Exponent

Testing of Haar-Like Feature in Region of Interest Detection for Automated Target Recognition (ATR) System

NASA Technical Reports Server (NTRS)

Zhang, Yuhan; Lu, Dr. Thomas

2010-01-01

The objectives of this project were to develop a ROI (Region of Interest) detector using Haar-like feature similar to the face detection in Intel's OpenCV library, implement it in Matlab code, and test the performance of the new ROI detector against the existing ROI detector that uses Optimal Trade-off Maximum Average Correlation Height filter (OTMACH). The ROI detector included 3 parts: 1, Automated Haar-like feature selection in finding a small set of the most relevant Haar-like features for detecting ROIs that contained a target. 2, Having the small set of Haar-like features from the last step, a neural network needed to be trained to recognize ROIs with targets by taking the Haar-like features as inputs. 3, using the trained neural network from the last step, a filtering method needed to be developed to process the neural network responses into a small set of regions of interests. This needed to be coded in Matlab. All the 3 parts needed to be coded in Matlab. The parameters in the detector needed to be trained by machine learning and tested with specific datasets. Since OpenCV library and Haar-like feature were not available in Matlab, the Haar-like feature calculation needed to be implemented in Matlab. The codes for Adaptive Boosting and max/min filters in Matlab could to be found from the Internet but needed to be integrated to serve the purpose of this project. The performance of the new detector was tested by comparing the accuracy and the speed of the new detector against the existing OTMACH detector. The speed was referred as the average speed to find the regions of interests in an image. The accuracy was measured by the number of false positives (false alarms) at the same detection rate between the two detectors.

Fractal properties and denoising of lidar signals from cirrus clouds

NASA Astrophysics Data System (ADS)

van den Heuvel, J. C.; Driesenaar, M. L.; Lerou, R. J. L.

2000-02-01

Airborne lidar signals of cirrus clouds are analyzed to determine the cloud structure. Climate modeling and numerical weather prediction benefit from accurate modeling of cirrus clouds. Airborne lidar measurements of the European Lidar in Space Technology Experiment (ELITE) campaign were analyzed by combining shots to obtain the backscatter at constant altitude. The signal at high altitude was analyzed for horizontal structure of cirrus clouds. The power spectrum and the structure function show straight lines on a double logarithmic plot. This behavior is characteristic for a Brownian fractal. Wavelet analysis using the Haar wavelet confirms the fractal aspects. It is shown that the horizontal structure of cirrus can be described by a fractal with a dimension of 1.8 over length scales that vary 4 orders of magnitude. We use the fractal properties in a new denoising method. Denoising is required for future lidar measurements from space that have a low signal to noise ratio. Our wavelet denoising is based on the Haar wavelet and uses the statistical fractal properties of cirrus clouds in a method based on the maximum a posteriori (MAP) probability. This denoising based on wavelets is tested on airborne lidar signals from ELITE using added Gaussian noise. Superior results with respect to averaging are obtained.

Synthesis of wavelet envelope in 2-D random media having power-law spectra: comparison with FD simulations

NASA Astrophysics Data System (ADS)

Sato, Haruo; Fehler, Michael C.

2016-10-01

The envelope broadening and the peak delay of the S-wavelet of a small earthquake with increasing travel distance are results of scattering by random velocity inhomogeneities in the earth medium. As a simple mathematical model, Sato proposed a new stochastic synthesis of the scalar wavelet envelope in 3-D von Kármán type random media when the centre wavenumber of the wavelet is in the power-law spectral range of the random velocity fluctuation. The essential idea is to split the random medium spectrum into two components using the centre wavenumber as a reference: the long-scale (low-wavenumber spectral) component produces the peak delay and the envelope broadening by multiple scattering around the forward direction; the short-scale (high-wavenumber spectral) component attenuates wave amplitude by wide angle scattering. The former is calculated by the Markov approximation based on the parabolic approximation and the latter is calculated by the Born approximation. Here, we extend the theory for the envelope synthesis of a wavelet in 2-D random media, which makes it easy to compare with finite difference (FD) simulation results. The synthetic wavelet envelope is analytically written by using the random medium parameters in the angular frequency domain. For the case that the power spectral density function of the random velocity fluctuation has a steep roll-off at large wavenumbers, the envelope broadening is small and frequency independent, and scattering attenuation is weak. For the case of a small roll-off, however, the envelope broadening is large and increases with frequency, and the scattering attenuation is strong and increases with frequency. As a preliminary study, we compare synthetic wavelet envelopes with the average of FD simulation wavelet envelopes in 50 synthesized random media, which are characterized by the RMS fractional velocity fluctuation ε = 0.05, correlation scale a = 5 km and the background wave velocity V0 = 4 km s-1. We use the radiation

Secure annotation for medical images based on reversible watermarking in the Integer Fibonacci-Haar transform domain

NASA Astrophysics Data System (ADS)

Battisti, F.; Carli, M.; Neri, A.

2011-03-01

The increasing use of digital image-based applications is resulting in huge databases that are often difficult to use and prone to misuse and privacy concerns. These issues are especially crucial in medical applications. The most commonly adopted solution is the encryption of both the image and the patient data in separate files that are then linked. This practice results to be inefficient since, in order to retrieve patient data or analysis details, it is necessary to decrypt both files. In this contribution, an alternative solution for secure medical image annotation is presented. The proposed framework is based on the joint use of a key-dependent wavelet transform, the Integer Fibonacci-Haar transform, of a secure cryptographic scheme, and of a reversible watermarking scheme. The system allows: i) the insertion of the patient data into the encrypted image without requiring the knowledge of the original image, ii) the encryption of annotated images without causing loss in the embedded information, and iii) due to the complete reversibility of the process, it allows recovering the original image after the mark removal. Experimental results show the effectiveness of the proposed scheme.

Computer-aided diagnosis of breast microcalcifications based on dual-tree complex wavelet transform.

PubMed

Jian, Wushuai; Sun, Xueyan; Luo, Shuqian

2012-12-19

Digital mammography is the most reliable imaging modality for breast carcinoma diagnosis and breast micro-calcifications is regarded as one of the most important signs on imaging diagnosis. In this paper, a computer-aided diagnosis (CAD) system is presented for breast micro-calcifications based on dual-tree complex wavelet transform (DT-CWT) to facilitate radiologists like double reading. Firstly, 25 abnormal ROIs were extracted according to the center and diameter of the lesions manually and 25 normal ROIs were selected randomly. Then micro-calcifications were segmented by combining space and frequency domain techniques. We extracted three texture features based on wavelet (Haar, DB4, DT-CWT) transform. Totally 14 descriptors were introduced to define the characteristics of the suspicious micro-calcifications. Principal Component Analysis (PCA) was used to transform these descriptors to a compact and efficient vector expression. Support Vector Machine (SVM) classifier was used to classify potential micro-calcifications. Finally, we used the receiver operating characteristic (ROC) curve and free-response operating characteristic (FROC) curve to evaluate the performance of the CAD system. The results of SVM classifications based on different wavelets shows DT-CWT has a better performance. Compared with other results, DT-CWT method achieved an accuracy of 96% and 100% for the classification of normal and abnormal ROIs, and the classification of benign and malignant micro-calcifications respectively. In FROC analysis, our CAD system for clinical dataset detection achieved a sensitivity of 83.5% at a false positive per image of 1.85. Compared with general wavelets, DT-CWT could describe the features more effectively, and our CAD system had a competitive performance.

Computer-aided diagnosis of breast microcalcifications based on dual-tree complex wavelet transform

PubMed Central

2012-01-01

Background Digital mammography is the most reliable imaging modality for breast carcinoma diagnosis and breast micro-calcifications is regarded as one of the most important signs on imaging diagnosis. In this paper, a computer-aided diagnosis (CAD) system is presented for breast micro-calcifications based on dual-tree complex wavelet transform (DT-CWT) to facilitate radiologists like double reading. Methods Firstly, 25 abnormal ROIs were extracted according to the center and diameter of the lesions manually and 25 normal ROIs were selected randomly. Then micro-calcifications were segmented by combining space and frequency domain techniques. We extracted three texture features based on wavelet (Haar, DB4, DT-CWT) transform. Totally 14 descriptors were introduced to define the characteristics of the suspicious micro-calcifications. Principal Component Analysis (PCA) was used to transform these descriptors to a compact and efficient vector expression. Support Vector Machine (SVM) classifier was used to classify potential micro-calcifications. Finally, we used the receiver operating characteristic (ROC) curve and free-response operating characteristic (FROC) curve to evaluate the performance of the CAD system. Results The results of SVM classifications based on different wavelets shows DT-CWT has a better performance. Compared with other results, DT-CWT method achieved an accuracy of 96% and 100% for the classification of normal and abnormal ROIs, and the classification of benign and malignant micro-calcifications respectively. In FROC analysis, our CAD system for clinical dataset detection achieved a sensitivity of 83.5% at a false positive per image of 1.85. Conclusions Compared with general wavelets, DT-CWT could describe the features more effectively, and our CAD system had a competitive performance. PMID:23253202

Developing a multi-Kinect-system for monitoring in dairy cows: object recognition and surface analysis using wavelets.

PubMed

Salau, J; Haas, J H; Thaller, G; Leisen, M; Junge, W

2016-09-01

Camera-based systems in dairy cattle were intensively studied over the last years. Different from this study, single camera systems with a limited range of applications were presented, mostly using 2D cameras. This study presents current steps in the development of a camera system comprising multiple 3D cameras (six Microsoft Kinect cameras) for monitoring purposes in dairy cows. An early prototype was constructed, and alpha versions of software for recording, synchronizing, sorting and segmenting images and transforming the 3D data in a joint coordinate system have already been implemented. This study introduced the application of two-dimensional wavelet transforms as method for object recognition and surface analyses. The method was explained in detail, and four differently shaped wavelets were tested with respect to their reconstruction error concerning Kinect recorded depth maps from different camera positions. The images' high frequency parts reconstructed from wavelet decompositions using the haar and the biorthogonal 1.5 wavelet were statistically analyzed with regard to the effects of image fore- or background and of cows' or persons' surface. Furthermore, binary classifiers based on the local high frequencies have been implemented to decide whether a pixel belongs to the image foreground and if it was located on a cow or a person. Classifiers distinguishing between image regions showed high (⩾0.8) values of Area Under reciever operation characteristic Curve (AUC). The classifications due to species showed maximal AUC values of 0.69.

Applications of Wavelet Transform and Fuzzy Neural Network on Power Quality Recognition

NASA Astrophysics Data System (ADS)

Liao, Chiung-Chou; Yang, Hong-Tzer; Lin, Ying-Chun

2008-10-01

The wavelet transform coefficients (WTCs) contain plenty of information needed for transient event identification of power quality (PQ) events. However, adopting WTCs directly has the drawbacks of taking a longer time and too much memory for the recognition system. To solve the abovementioned recognition problems and to effectively reduce the number of features representing power transients, spectrum energies of WTCs in different scales are calculated by Parseval's Theorem. Through the proposed approach, features of the original power signals can be reserved and not influenced by occurring points of PQ events. The fuzzy neural classification systems are then used for signal recognition and fuzzy rule construction. Success rates of recognizing PQ events from noise-riding signals are proven to be feasible in power system applications in this paper.

Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

NASA Astrophysics Data System (ADS)

Wei, H. L.; Billings, S. A.

2009-09-01

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.

Wavelets analysis for differentiating solid, non-macroscopic fat containing, enhancing renal masses: a pilot study

NASA Astrophysics Data System (ADS)

Varghese, Bino; Hwang, Darryl; Mohamed, Passant; Cen, Steven; Deng, Christopher; Chang, Michael; Duddalwar, Vinay

2017-11-01

Purpose: To evaluate potential use of wavelets analysis in discriminating benign and malignant renal masses (RM) Materials and Methods: Regions of interest of the whole lesion were manually segmented and co-registered from multiphase CT acquisitions of 144 patients (98 malignant RM: renal cell carcinoma (RCC) and 46 benign RM: oncocytoma, lipid-poor angiomyolipoma). Here, the Haar wavelet was used to analyze the grayscale images of the largest segmented tumor in the axial direction. Six metrics (energy, entropy, homogeneity, contrast, standard deviation (SD) and variance) derived from 3-levels of image decomposition in 3 directions (horizontal, vertical and diagonal) respectively, were used to quantify tumor texture. Independent t-test or Wilcoxon rank sum test depending on data normality were used as exploratory univariate analysis. Stepwise logistic regression and receiver operator characteristics (ROC) curve analysis were used to select predictors and assess prediction accuracy, respectively. Results: Consistently, 5 out of 6 wavelet-based texture measures (except homogeneity) were higher for malignant tumors compared to benign, when accounting for individual texture direction. Homogeneity was consistently lower in malignant than benign tumors irrespective of direction. SD and variance measured in the diagonal direction on the corticomedullary phase showed significant (p<0.05) difference between benign versus malignant tumors. The multivariate model with variance (3 directions) and SD (vertical direction) extracted from the excretory and pre-contrast phase, respectively showed an area under the ROC curve (AUC) of 0.78 (p < 0.05) in discriminating malignant from benign. Conclusion: Wavelet analysis is a valuable texture evaluation tool to add to a radiomics platforms geared at reliably characterizing and stratifying renal masses.

Repeatability and Reliability Characterization of Phonocardiograph Systems Using Wavelet and Backpropagation Neural Network

NASA Astrophysics Data System (ADS)

Sumarna; Astono, J.; Purwanto, A.; Agustika, D. K.

2018-04-01

Phonocardiograph (PCG) system consisting of an electronic stethoscope, mic condenser, mic preamp, and the battery has been developed. PCG system is used to detect heart abnormalities. Although PCG is not popular because of many things that affect its performance, in this research we try to reduce the factors that affecting its consistency To find out whether the system is repeatable and reliable the system have to be characterized first. This research aims to see whether the PCG system can provide the same results for measurements of the same patient. Characterization of the system is done by analyzing whether the PCG system can recognize the S1 and S2 part of the same person. From the recording result, S1 and S2 then transformed by using Discrete Wavelet Transform of Haar mother wavelet of level 1 and extracted the feature by using data range of approximation coefficients. The result was analyzed by using pattern recognition system of backpropagation neural network. Partially obtained data used as training data and partly used as test data. From the results of the pattern recognition system, it can be concluded that the system accuracy in recognizing S1 reach 87.5% and S2 only hit 67%.

Exploratory study and application of the angular wavelet analysis for assessing the spatial distribution of breakdown spots in Pt/HfO2/Pt structures

NASA Astrophysics Data System (ADS)

Muñoz-Gorriz, J.; Monaghan, S.; Cherkaoui, K.; Suñé, J.; Hurley, P. K.; Miranda, E.

2017-12-01

The angular wavelet analysis is applied for assessing the spatial distribution of breakdown spots in Pt/HfO2/Pt capacitors with areas ranging from 104 to 105 μm2. The breakdown spot lateral sizes are in the range from 1 to 3 μm, and they appear distributed on the top metal electrode as a point pattern. The spots are generated by ramped and constant voltage stresses and are the consequence of microexplosions caused by the formation of shorts spanning the dielectric film. This kind of pattern was analyzed in the past using the conventional spatial analysis tools such as intensity plots, distance histograms, pair correlation function, and nearest neighbours. Here, we show that the wavelet analysis offers an alternative and complementary method for testing whether or not the failure site distribution departs from a complete spatial randomness process in the angular domain. The effect of using different wavelet functions, such as the Haar, Sine, French top hat, Mexican hat, and Morlet, as well as the roles played by the process intensity, the location of the voltage probe, and the aspect ratio of the device, are all discussed.

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

Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

PubMed Central

Wiedenhoeft, John; Brugel, Eric; Schliep, Alexander

2016-01-01

By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings. PMID:27177143

A Comparative Analysis for Selection of Appropriate Mother Wavelet for Detection of Stationary Disturbances

NASA Astrophysics Data System (ADS)

Kamble, Saurabh Prakash; Thawkar, Shashank; Gaikwad, Vinayak G.; Kothari, D. P.

2017-12-01

Detection of disturbances is the first step of mitigation. Power electronics plays a crucial role in modern power system which makes system operation efficient but it also bring stationary disturbances in the power system and added impurities to the supply. It happens because of the non-linear loads used in modern day power system which inject disturbances like harmonic disturbances, flickers, sag etc. in power grid. These impurities can damage equipments so it is necessary to mitigate these impurities present in the supply very quickly. So, digital signal processing techniques are incorporated for detection purpose. Signal processing techniques like fast Fourier transform, short-time Fourier transform, Wavelet transform etc. are widely used for the detection of disturbances. Among all, wavelet transform is widely used because of its better detection capabilities. But, which mother wavelet has to use for detection is still a mystery. Depending upon the periodicity, the disturbances are classified as stationary and non-stationary disturbances. This paper presents the importance of selection of mother wavelet for analyzing stationary disturbances using discrete wavelet transform. Signals with stationary disturbances of various frequencies are generated using MATLAB. The analysis of these signals is done using various mother wavelets like Daubechies and bi-orthogonal wavelets and the measured root mean square value of stationary disturbance is obtained. The measured value obtained by discrete wavelet transform is compared with the exact RMS value of the frequency component and the percentage differences are presented which helps to select optimum mother wavelet.

On orthogonal projectors induced by compact groups and Haar measures

NASA Astrophysics Data System (ADS)

Niezgoda, Marek

2008-02-01

We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered.

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.

Wavelets

NASA Astrophysics Data System (ADS)

Strang, Gilbert

1994-06-01

Several methods are compared that are used to analyze and synthesize a signal. Three ways are mentioned to transform a symphony: into cosine waves (Fourier transform), into pieces of cosines (short-time Fourier transform), and into wavelets (little waves that start and stop). Choosing the best basis, higher dimensions, fast wavelet transform, and Daubechies wavelets are discussed. High-definition television is described. The use of wavelets in identifying fingerprints in the future is related.

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.

An Analog Circuit Approximation of the Discrete Wavelet Transform for Ultra Low Power Signal Processing in Wearable Sensor Nodes

PubMed Central

Casson, Alexander J.

2015-01-01

Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via gmC circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans. PMID:26694414

An Analog Circuit Approximation of the Discrete Wavelet Transform for Ultra Low Power Signal Processing in Wearable Sensor Nodes.

PubMed

Casson, Alexander J

2015-12-17

Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g(m)C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans.

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.

Assessment of Power Quality based on Fuzzy Logic and Discrete Wavelet Transform for Nonstationary Disturbances

NASA Astrophysics Data System (ADS)

Sinha, Pampa; Nath, Sudipta

2010-10-01

The main aspects of power system delivery are reliability and quality. If all the customers of a power system get uninterrupted power through the year then the system is considered to be reliable. The term power quality may be referred to as maintaining near sinusoidal voltage at rated frequency at the consumers end. The power component definitions are defined according to the IEEE Standard 1459-2000 both for single phase and three phase unbalanced systems based on Fourier Transform (FFT). In the presence of nonstationary power quality (PQ) disturbances results in accurate values due to its sensitivity to the spectral leakage problem. To overcome these limitations the power quality components are calculated using Discrete Wavelet Transform (DWT). In order to handle the uncertainties associated with electric power systems operations fuzzy logic has been incorporated in this paper. A new power quality index has been introduced here which can assess the power quality under nonstationary disturbances.

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.

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.

On-Line Loss of Control Detection Using Wavelets

NASA Technical Reports Server (NTRS)

Brenner, Martin J. (Technical Monitor); Thompson, Peter M.; Klyde, David H.; Bachelder, Edward N.; Rosenthal, Theodore J.

2005-01-01

Wavelet transforms are used for on-line detection of aircraft loss of control. Wavelet transforms are compared with Fourier transform methods and shown to more rapidly detect changes in the vehicle dynamics. This faster response is due to a time window that decreases in length as the frequency increases. New wavelets are defined that further decrease the detection time by skewing the shape of the envelope. The wavelets are used for power spectrum and transfer function estimation. Smoothing is used to tradeoff the variance of the estimate with detection time. Wavelets are also used as front-end to the eigensystem reconstruction algorithm. Stability metrics are estimated from the frequency response and models, and it is these metrics that are used for loss of control detection. A Matlab toolbox was developed for post-processing simulation and flight data using the wavelet analysis methods. A subset of these methods was implemented in real time and named the Loss of Control Analysis Tool Set or LOCATS. A manual control experiment was conducted using a hardware-in-the-loop simulator for a large transport aircraft, in which the real time performance of LOCATS was demonstrated. The next step is to use these wavelet analysis tools for flight test support.

A wavelet-fuzzy logic based energy management strategy for a fuel cell/battery/ultra-capacitor hybrid vehicular power system

NASA Astrophysics Data System (ADS)

Erdinc, O.; Vural, B.; Uzunoglu, M.

Due to increasing concerns on environmental pollution and depleting fossil fuels, fuel cell (FC) vehicle technology has received considerable attention as an alternative to the conventional vehicular systems. However, a FC system combined with an energy storage system (ESS) can display a preferable performance for vehicle propulsion. As the additional ESS can fulfill the transient power demand fluctuations, the fuel cell can be downsized to fit the average power demand without facing peak loads. Besides, braking energy can be recovered by the ESS. This study focuses on a vehicular system powered by a fuel cell and equipped with two secondary energy storage devices: battery and ultra-capacitor (UC). However, an advanced energy management strategy is quite necessary to split the power demand of a vehicle in a suitable way for the on-board power sources in order to maximize the performance while promoting the fuel economy and endurance of hybrid system components. In this study, a wavelet and fuzzy logic based energy management strategy is proposed for the developed hybrid vehicular system. Wavelet transform has great capability for analyzing signals consisting of instantaneous changes like a hybrid electric vehicle (HEV) power demand. Besides, fuzzy logic has a quite suitable structure for the control of hybrid systems. The mathematical and electrical models of the hybrid vehicular system are developed in detail and simulated using MATLAB ®, Simulink ® and SimPowerSystems ® environments.

Multiscale wavelet representations for mammographic feature analysis

NASA Astrophysics Data System (ADS)

Laine, Andrew F.; Song, Shuwu

1992-12-01

This paper introduces a novel approach for accomplishing mammographic feature analysis through multiresolution representations. We show that efficient (nonredundant) representations may be identified from digital mammography and used to enhance specific mammographic features within a continuum of scale space. The multiresolution decomposition of wavelet transforms provides a natural hierarchy in which to embed an interactive paradigm for accomplishing scale space feature analysis. Choosing wavelets (or analyzing functions) that are simultaneously localized in both space and frequency, results in a powerful methodology for image analysis. Multiresolution and orientation selectivity, known biological mechanisms in primate vision, are ingrained in wavelet representations and inspire the techniques presented in this paper. Our approach includes local analysis of complete multiscale representations. Mammograms are reconstructed from wavelet coefficients, enhanced by linear, exponential and constant weight functions localized in scale space. By improving the visualization of breast pathology we can improve the changes of early detection of breast cancers (improve quality) while requiring less time to evaluate mammograms for most patients (lower costs).

Fourier and Wavelet Analysis of Coronal Time Series

NASA Astrophysics Data System (ADS)

Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.

2016-10-01

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

Indirect adaptive soft computing based wavelet-embedded control paradigms for WT/PV/SOFC in a grid/charging station connected hybrid power system.

PubMed

Mumtaz, Sidra; Khan, Laiq; Ahmed, Saghir; Bader, Rabiah

2017-01-01

This paper focuses on the indirect adaptive tracking control of renewable energy sources in a grid-connected hybrid power system. The renewable energy systems have low efficiency and intermittent nature due to unpredictable meteorological conditions. The domestic load and the conventional charging stations behave in an uncertain manner. To operate the renewable energy sources efficiently for harvesting maximum power, instantaneous nonlinear dynamics should be captured online. A Chebyshev-wavelet embedded NeuroFuzzy indirect adaptive MPPT (maximum power point tracking) control paradigm is proposed for variable speed wind turbine-permanent synchronous generator (VSWT-PMSG). A Hermite-wavelet incorporated NeuroFuzzy indirect adaptive MPPT control strategy for photovoltaic (PV) system to extract maximum power and indirect adaptive tracking control scheme for Solid Oxide Fuel Cell (SOFC) is developed. A comprehensive simulation test-bed for a grid-connected hybrid power system is developed in Matlab/Simulink. The robustness of the suggested indirect adaptive control paradigms are evaluated through simulation results in a grid-connected hybrid power system test-bed by comparison with conventional and intelligent control techniques. The simulation results validate the effectiveness of the proposed control paradigms.

Indirect adaptive soft computing based wavelet-embedded control paradigms for WT/PV/SOFC in a grid/charging station connected hybrid power system

PubMed Central

Khan, Laiq; Ahmed, Saghir; Bader, Rabiah

2017-01-01

This paper focuses on the indirect adaptive tracking control of renewable energy sources in a grid-connected hybrid power system. The renewable energy systems have low efficiency and intermittent nature due to unpredictable meteorological conditions. The domestic load and the conventional charging stations behave in an uncertain manner. To operate the renewable energy sources efficiently for harvesting maximum power, instantaneous nonlinear dynamics should be captured online. A Chebyshev-wavelet embedded NeuroFuzzy indirect adaptive MPPT (maximum power point tracking) control paradigm is proposed for variable speed wind turbine-permanent synchronous generator (VSWT-PMSG). A Hermite-wavelet incorporated NeuroFuzzy indirect adaptive MPPT control strategy for photovoltaic (PV) system to extract maximum power and indirect adaptive tracking control scheme for Solid Oxide Fuel Cell (SOFC) is developed. A comprehensive simulation test-bed for a grid-connected hybrid power system is developed in Matlab/Simulink. The robustness of the suggested indirect adaptive control paradigms are evaluated through simulation results in a grid-connected hybrid power system test-bed by comparison with conventional and intelligent control techniques. The simulation results validate the effectiveness of the proposed control paradigms. PMID:28877191

Wavelet library for constrained devices

NASA Astrophysics Data System (ADS)

Ehlers, Johan Hendrik; Jassim, Sabah A.

2007-04-01

The wavelet transform is a powerful tool for image and video processing, useful in a range of applications. This paper is concerned with the efficiency of a certain fast-wavelet-transform (FWT) implementation and several wavelet filters, more suitable for constrained devices. Such constraints are typically found on mobile (cell) phones or personal digital assistants (PDA). These constraints can be a combination of; limited memory, slow floating point operations (compared to integer operations, most often as a result of no hardware support) and limited local storage. Yet these devices are burdened with demanding tasks such as processing a live video or audio signal through on-board capturing sensors. In this paper we present a new wavelet software library, HeatWave, that can be used efficiently for image/video processing/analysis tasks on mobile phones and PDA's. We will demonstrate that HeatWave is suitable for realtime applications with fine control and range to suit transform demands. We shall present experimental results to substantiate these claims. Finally this library is intended to be of real use and applied, hence we considered several well known and common embedded operating system platform differences; such as a lack of common routines or functions, stack limitations, etc. This makes HeatWave suitable for a range of applications and research projects.

Shoulder muscles recruitment during a power backward giant swing on high bar: a wavelet-EMG-analysis.

PubMed

Frère, Julien; Göpfert, Beat; Slawinski, Jean; Tourny-Chollet, Claire

2012-04-01

This study aimed at determining the upper limb muscles coordination during a power backward giant swing (PBGS) and the recruitment pattern of motor units (MU) of co-activated muscles. The wavelet transformation (WT) was applied to the surface electromyographic (EMG) signal of eight shoulder muscles. Total gymnast's body energy and wavelet synergies extracted from the WT-EMG by using a non-negative matrix factorization were analyzed as a function of the body position angle of the gymnast. A cross-correlation analysis of the EMG patterns allowed determining two main groups of co-activated muscles. Two wavelet synergies representing the main spectral features (82% of the variance accounted for) discriminated the recruitment of MU. Although no task-group of MU was found among the muscles, it appeared that a higher proportion of fast MU was recruited within the muscles of the first group during the upper part of the PBGS. The last increase of total body energy before bar release was induced by the recruitment of the muscles of the second group but did not necessitate the recruitment of a higher proportion of fast MU. Such muscle coordination agreed with previous simulations of elements on high bar as well as the findings related to the recruitment of MU. Copyright © 2012 Elsevier B.V. All rights reserved.

Wavelet processing techniques for digital mammography

NASA Astrophysics Data System (ADS)

Laine, Andrew F.; Song, Shuwu

1992-09-01

This paper introduces a novel approach for accomplishing mammographic feature analysis through multiresolution representations. We show that efficient (nonredundant) representations may be identified from digital mammography and used to enhance specific mammographic features within a continuum of scale space. The multiresolution decomposition of wavelet transforms provides a natural hierarchy in which to embed an interactive paradigm for accomplishing scale space feature analysis. Similar to traditional coarse to fine matching strategies, the radiologist may first choose to look for coarse features (e.g., dominant mass) within low frequency levels of a wavelet transform and later examine finer features (e.g., microcalcifications) at higher frequency levels. In addition, features may be extracted by applying geometric constraints within each level of the transform. Choosing wavelets (or analyzing functions) that are simultaneously localized in both space and frequency, results in a powerful methodology for image analysis. Multiresolution and orientation selectivity, known biological mechanisms in primate vision, are ingrained in wavelet representations and inspire the techniques presented in this paper. Our approach includes local analysis of complete multiscale representations. Mammograms are reconstructed from wavelet representations, enhanced by linear, exponential and constant weight functions through scale space. By improving the visualization of breast pathology we can improve the chances of early detection of breast cancers (improve quality) while requiring less time to evaluate mammograms for most patients (lower costs).

Filtering of the Radon transform to enhance linear signal features via wavelet pyramid decomposition

NASA Astrophysics Data System (ADS)

Meckley, John R.

1995-09-01

The information content in many signal processing applications can be reduced to a set of linear features in a 2D signal transform. Examples include the narrowband lines in a spectrogram, ship wakes in a synthetic aperture radar image, and blood vessels in a medical computer-aided tomography scan. The line integrals that generate the values of the projections of the Radon transform can be characterized as a bank of matched filters for linear features. This localization of energy in the Radon transform for linear features can be exploited to enhance these features and to reduce noise by filtering the Radon transform with a filter explicitly designed to pass only linear features, and then reconstructing a new 2D signal by inverting the new filtered Radon transform (i.e., via filtered backprojection). Previously used methods for filtering the Radon transform include Fourier based filtering (a 2D elliptical Gaussian linear filter) and a nonlinear filter ((Radon xfrm)**y with y >= 2.0). Both of these techniques suffer from the mismatch of the filter response to the true functional form of the Radon transform of a line. The Radon transform of a line is not a point but is a function of the Radon variables (rho, theta) and the total line energy. This mismatch leads to artifacts in the reconstructed image and a reduction in achievable processing gain. The Radon transform for a line is computed as a function of angle and offset (rho, theta) and the line length. The 2D wavelet coefficients are then compared for the Haar wavelets and the Daubechies wavelets. These filter responses are used as frequency filters for the Radon transform. The filtering is performed on the wavelet pyramid decomposition of the Radon transform by detecting the most likely positions of lines in the transform and then by convolving the local area with the appropriate response and zeroing the pyramid coefficients outside of the response area. The response area is defined to contain 95% of the total

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

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.

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.

Method and system for determining precursors of health abnormalities from processing medical records

DOEpatents

None, None

2013-06-25

Medical reports are converted to document vectors in computing apparatus and sampled by applying a maximum variation sampling function including a fitness function to the document vectors to reduce a number of medical records being processed and to increase the diversity of the medical records being processed. Linguistic phrases are extracted from the medical records and converted to s-grams. A Haar wavelet function is applied to the s-grams over the preselected time interval; and the coefficient results of the Haar wavelet function are examined for patterns representing the likelihood of health abnormalities. This confirms certain s-grams as precursors of the health abnormality and a parameter can be calculated in relation to the occurrence of such a health abnormality.

Motion compensation via redundant-wavelet multihypothesis.

PubMed

Fowler, James E; Cui, Suxia; Wang, Yonghui

2006-10-01

Multihypothesis motion compensation has been widely used in video coding with previous attention focused on techniques employing predictions that are diverse spatially or temporally. In this paper, the multihypothesis concept is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase. The corresponding multiple-phase inverse transform implicitly combines the phase-diverse predictions into a single spatial-domain prediction for motion compensation. The performance advantage of this redundant-wavelet-multihypothesis approach is investigated analytically, invoking the fact that the multiple-phase inverse involves a projection that significantly reduces the power of a dense-motion residual modeled as additive noise. The analysis shows that redundant-wavelet multihypothesis is capable of up to a 7-dB reduction in prediction-residual variance over an equivalent single-phase, single-hypothesis approach. Experimental results substantiate the performance advantage for a block-based implementation.

Four-dimensional wavelet compression of arbitrarily sized echocardiographic data.

PubMed

Zeng, Li; Jansen, Christian P; Marsch, Stephan; Unser, Michael; Hunziker, Patrick R

2002-09-01

Wavelet-based methods have become most popular for the compression of two-dimensional medical images and sequences. The standard implementations consider data sizes that are powers of two. There is also a large body of literature treating issues such as the choice of the "optimal" wavelets and the performance comparison of competing algorithms. With the advent of telemedicine, there is a strong incentive to extend these techniques to higher dimensional data such as dynamic three-dimensional (3-D) echocardiography [four-dimensional (4-D) datasets]. One of the practical difficulties is that the size of this data is often not a multiple of a power of two, which can lead to increased computational complexity and impaired compression power. Our contribution in this paper is to present a genuine 4-D extension of the well-known zerotree algorithm for arbitrarily sized data. The key component of our method is a one-dimensional wavelet algorithm that can handle arbitrarily sized input signals. The method uses a pair of symmetric/antisymmetric wavelets (10/6) together with some appropriate midpoint symmetry boundary conditions that reduce border artifacts. The zerotree structure is also adapted so that it can accommodate noneven data splitting. We have applied our method to the compression of real 3-D dynamic sequences from clinical cardiac ultrasound examinations. Our new algorithm compares very favorably with other more ad hoc adaptations (image extension and tiling) of the standard powers-of-two methods, in terms of both compression performance and computational cost. It is vastly superior to slice-by-slice wavelet encoding. This was seen not only in numerical image quality parameters but also in expert ratings, where significant improvement using the new approach could be documented. Our validation experiments show that one can safely compress 4-D data sets at ratios of 128:1 without compromising the diagnostic value of the images. We also display some more extreme

Wavelet transform processing applied to partial discharge evaluation

NASA Astrophysics Data System (ADS)

Macedo, E. C. T.; Araújo, D. B.; da Costa, E. G.; Freire, R. C. S.; Lopes, W. T. A.; Torres, I. S. M.; de Souza Neto, J. M. R.; Bhatti, S. A.; Glover, I. A.

2012-05-01

Partial Discharge (PD) is characterized by high frequency current pulses that occur in high voltage (HV) electrical equipments originated from gas ionization process when damaged insulation is submitted to high values of electric field [1]. PD monitoring is a useful method of assessing the aging degree of the insulation, manufacturing defects or chemical/mechanical damage. Many sources of noise (e.g. radio transmissions, commutator noise from rotating machines, power electronics switching circuits, corona discharge, etc.) can directly affect the PD estimation. Among the many mathematical techniques that can be applied to de-noise PD signals, the wavelet transform is one of the most powerful. It can simultaneously supply information about the pulse occurrence, time and pulse spectrum, and also de-noise in-field measured PD signals. In this paper is described the application of wavelet transform in the suppression of the main types of noise that can affect the observation and analysis of PD signals in high voltage apparatus. In addition, is presented a study that indicates the appropriated mother-wavelet for this application based on the cross-correlation factor.

Wavelet extractor: A Bayesian well-tie and wavelet extraction program

NASA Astrophysics Data System (ADS)

Gunning, James; Glinsky, Michael E.

2006-06-01

We introduce a new open-source toolkit for the well-tie or wavelet extraction problem of estimating seismic wavelets from seismic data, time-to-depth information, and well-log suites. The wavelet extraction model is formulated as a Bayesian inverse problem, and the software will simultaneously estimate wavelet coefficients, other parameters associated with uncertainty in the time-to-depth mapping, positioning errors in the seismic imaging, and useful amplitude-variation-with-offset (AVO) related parameters in multi-stack extractions. It is capable of multi-well, multi-stack extractions, and uses continuous seismic data-cube interpolation to cope with the problem of arbitrary well paths. Velocity constraints in the form of checkshot data, interpreted markers, and sonic logs are integrated in a natural way. The Bayesian formulation allows computation of full posterior uncertainties of the model parameters, and the important problem of the uncertain wavelet span is addressed uses a multi-model posterior developed from Bayesian model selection theory. The wavelet extraction tool is distributed as part of the Delivery seismic inversion toolkit. A simple log and seismic viewing tool is included in the distribution. The code is written in Java, and thus platform independent, but the Seismic Unix (SU) data model makes the inversion particularly suited to Unix/Linux environments. It is a natural companion piece of software to Delivery, having the capacity to produce maximum likelihood wavelet and noise estimates, but will also be of significant utility to practitioners wanting to produce wavelet estimates for other inversion codes or purposes. The generation of full parameter uncertainties is a crucial function for workers wishing to investigate questions of wavelet stability before proceeding to more advanced inversion studies.

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.

Rate-distortion analysis of directional wavelets.

PubMed

Maleki, Arian; Rajaei, Boshra; Pourreza, Hamid Reza

2012-02-01

The inefficiency of separable wavelets in representing smooth edges has led to a great interest in the study of new 2-D transformations. The most popular criterion for analyzing these transformations is the approximation power. Transformations with near-optimal approximation power are useful in many applications such as denoising and enhancement. However, they are not necessarily good for compression. Therefore, most of the nearly optimal transformations such as curvelets and contourlets have not found any application in image compression yet. One of the most promising schemes for image compression is the elegant idea of directional wavelets (DIWs). While these algorithms outperform the state-of-the-art image coders in practice, our theoretical understanding of them is very limited. In this paper, we adopt the notion of rate-distortion and calculate the performance of the DIW on a class of edge-like images. Our theoretical analysis shows that if the edges are not "sharp," the DIW will compress them more efficiently than the separable wavelets. It also demonstrates the inefficiency of the quadtree partitioning that is often used with the DIW. To solve this issue, we propose a new partitioning scheme called megaquad partitioning. Our simulation results on real-world images confirm the benefits of the proposed partitioning algorithm, promised by our theoretical analysis. © 2011 IEEE

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.

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.

Induction motors airgap-eccentricity detection through the discrete wavelet transform of the apparent power signal under non-stationary operating conditions.

PubMed

Yahia, K; Cardoso, A J M; Ghoggal, A; Zouzou, S E

2014-03-01

Fast Fourier transform (FFT) analysis has been successfully used for fault diagnosis in induction machines. However, this method does not always provide good results for the cases of load torque, speed and voltages variation, leading to a variation of the motor-slip and the consequent FFT problems that appear due to the non-stationary nature of the involved signals. In this paper, the discrete wavelet transform (DWT) of the apparent-power signal for the airgap-eccentricity fault detection in three-phase induction motors is presented in order to overcome the above FFT problems. The proposed method is based on the decomposition of the apparent-power signal from which wavelet approximation and detail coefficients are extracted. The energy evaluation of a known bandwidth permits to define a fault severity factor (FSF). Simulation as well as experimental results are provided to illustrate the effectiveness and accuracy of the proposed method presented even for the case of load torque variations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Response of Autonomic Nervous System to Body Positions:

NASA Astrophysics Data System (ADS)

Xu, Aiguo; Gonnella, G.; Federici, A.; Stramaglia, S.; Simone, F.; Zenzola, A.; Santostasi, R.

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1) and the second parts (HD2) of 90° head down tilt, and during recovery (REC). The wavelet transform was performed using the Haar function of period T=2j (j=1,2,...,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident differences than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work.

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

ON THE FOURIER AND WAVELET ANALYSIS OF CORONAL TIME SERIES

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

Auchère, F.; Froment, C.; Bocchialini, K.

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence and Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causingmore » false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence and Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.« less

On the Fourier and Wavelet Analysis of Coronal Time Series

NASA Astrophysics Data System (ADS)

Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.

2016-07-01

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

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.

Fuzzy wavelet plus a quantum neural network as a design base for power system stability enhancement.

PubMed

Ganjefar, Soheil; Tofighi, Morteza; Karami, Hamidreza

2015-11-01

In this study, we introduce an indirect adaptive fuzzy wavelet neural controller (IAFWNC) as a power system stabilizer to damp inter-area modes of oscillations in a multi-machine power system. Quantum computing is an efficient method for improving the computational efficiency of neural networks, so we developed an identifier based on a quantum neural network (QNN) to train the IAFWNC in the proposed scheme. All of the controller parameters are tuned online based on the Lyapunov stability theory to guarantee the closed-loop stability. A two-machine, two-area power system equipped with a static synchronous series compensator as a series flexible ac transmission system was used to demonstrate the effectiveness of the proposed controller. The simulation and experimental results demonstrated that the proposed IAFWNC scheme can achieve favorable control performance. Copyright © 2015 Elsevier Ltd. All rights reserved.

Wavelets and distributed approximating functionals

NASA Astrophysics Data System (ADS)

Wei, G. W.; Kouri, D. J.; Hoffman, D. K.

1998-07-01

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

ECG Signal Analysis and Arrhythmia Detection using Wavelet Transform

NASA Astrophysics Data System (ADS)

Kaur, Inderbir; Rajni, Rajni; Marwaha, Anupma

2016-12-01

Electrocardiogram (ECG) is used to record the electrical activity of the heart. The ECG signal being non-stationary in nature, makes the analysis and interpretation of the signal very difficult. Hence accurate analysis of ECG signal with a powerful tool like discrete wavelet transform (DWT) becomes imperative. In this paper, ECG signal is denoised to remove the artifacts and analyzed using Wavelet Transform to detect the QRS complex and arrhythmia. This work is implemented in MATLAB software for MIT/BIH Arrhythmia database and yields the sensitivity of 99.85 %, positive predictivity of 99.92 % and detection error rate of 0.221 % with wavelet transform. It is also inferred that DWT outperforms principle component analysis technique in detection of ECG signal.

Detecting trace components in liquid chromatography/mass spectrometry data sets with two-dimensional wavelets

NASA Astrophysics Data System (ADS)

Compton, Duane C.; Snapp, Robert R.

2007-09-01

TWiGS (two-dimensional wavelet transform with generalized cross validation and soft thresholding) is a novel algorithm for denoising liquid chromatography-mass spectrometry (LC-MS) data for use in "shot-gun" proteomics. Proteomics, the study of all proteins in an organism, is an emerging field that has already proven successful for drug and disease discovery in humans. There are a number of constraints that limit the effectiveness of liquid chromatography-mass spectrometry (LC-MS) for shot-gun proteomics, where the chemical signals are typically weak, and data sets are computationally large. Most algorithms suffer greatly from a researcher driven bias, making the results irreproducible and unusable by other laboratories. We thus introduce a new algorithm, TWiGS, that removes electrical (additive white) and chemical noise from LC-MS data sets. TWiGS is developed to be a true two-dimensional algorithm, which operates in the time-frequency domain, and minimizes the amount of researcher bias. It is based on the traditional discrete wavelet transform (DWT), which allows for fast and reproducible analysis. The separable two-dimensional DWT decomposition is paired with generalized cross validation and soft thresholding. The Haar, Coiflet-6, Daubechie-4 and the number of decomposition levels are determined based on observed experimental results. Using a synthetic LC-MS data model, TWiGS accurately retains key characteristics of the peaks in both the time and m/z domain, and can detect peaks from noise of the same intensity. TWiGS is applied to angiotensin I and II samples run on a LC-ESI-TOF-MS (liquid-chromatography-electrospray-ionization) to demonstrate its utility for the detection of low-lying peaks obscured by noise.

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.

ON THE UNIQUENESS OF HAAR SERIES CONVERGENT IN THE METRICS OF L_p\\lbrack0,\\,1\\rbrack, 0, AND IN MEASURE

NASA Astrophysics Data System (ADS)

Talalyan, A. A.

1986-02-01

It is established that if the partial sums S_n(x) of a Haar series \\sum a_n\\chi_n(x) converge to f(x)\\in L_p\\lbrack0,\\,1\\rbrack, 0, at the rate \\int_0^1\\vert S_n-f\\vert^p dx=o(1/n^{1/p}), then f(x) is A-integrable and a_n=(A)\\int_0^1 f(x)\\chi_n(x)dx, for n=1,\\,2,\\,\\dots. Analogous theorems are proved also for the case where Haar series converge in the metric of L_p\\lbrack0,\\,1\\rbrack, 0, over some subsequences of partial sums. The sharpness of these theorems is also proved.Bibliography: 10 titles.

A modified multiscale peak alignment method combined with trilinear decomposition to study the volatile/heat-labile components in Ligusticum chuanxiong Hort - Cyperus rotundus rhizomes by HS-SPME-GC/MS.

PubMed

He, Min; Yan, Pan; Yang, Zhi-Yu; Zhang, Zhi-Min; Yang, Tian-Biao; Hong, Liang

2018-03-15

Head Space/Solid Phase Micro-Extraction (HS-SPME) coupled with Gas Chromatography/Mass Spectrometer (GC/MS) was used to determine the volatile/heat-labile components in Ligusticum chuanxiong Hort - Cyperus rotundus rhizomes. Facing co-eluting peaks in k samples, a trilinear structure was reconstructed to obtain the second-order advantage. The retention time (RT) shift with multi-channel detection signals for different samples has been vital in maintaining the trilinear structure, thus a modified multiscale peak alignment (mMSPA) method was proposed in this paper. The peak position and peak width of representative ion profile were firstly detected by mMSPA using Continuous Wavelet Transform with Haar wavelet as the mother wavelet (Haar CWT). Then, the raw shift was confirmed by Fast Fourier Transform (FFT) cross correlation calculation. To obtain the optimal shift, Haar CWT was again used to detect the subtle deviations and be amalgamated in calculation. Here, to ensure there is no peaks shape alternation, the alignment was performed in local domains of data matrices, and all data points in the peak zone were moved via linear interpolation in non-peak parts. Finally, chemical components of interest in Ligusticum chuanxiong Hort - Cyperus rotundus rhizomes were analyzed by HS-SPME-GCMS and mMSPA-alternating trilinear decomposition (ATLD) resolution. As a result, the concentration variation between herbs and their pharmaceutical products can provide a scientific basic for the quality standard establishment of traditional Chinese medicines. Copyright © 2018 Elsevier B.V. All rights reserved.

Wavelet Transforms using VTK-m

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

Li, Shaomeng; Sewell, Christopher Meyer

2016-09-27

These are a set of slides that deal with the topics of wavelet transforms using VTK-m. First, wavelets are discussed and detailed, then VTK-m is discussed and detailed, then wavelets and VTK-m are looked at from a performance comparison, then from an accuracy comparison, and finally lessons learned, conclusion, and what is next. Lessons learned are the following: Launching worklets is expensive; Natural logic of performing 2D wavelet transform: Repeat the same 1D wavelet transform on every row, repeat the same 1D wavelet transform on every column, invoke the 1D wavelet worklet every time: num_rows x num_columns; VTK-m approach ofmore » performing 2D wavelet transform: Create a worklet for 2D that handles both rows and columns, invoke this new worklet only one time; Fast calculation, but cannot reuse 1D implementations.« less

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.

Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty

NASA Astrophysics Data System (ADS)

Xu, Shengli; Jiang, Xiaomo; Huang, Jinzhi; Yang, Shuhua; Wang, Xiaofang

2016-12-01

Centrifugal compressor often suffers various defects such as impeller cracking, resulting in forced outage of the total plant. Damage diagnostics and condition monitoring of such a turbomachinery system has become an increasingly important and powerful tool to prevent potential failure in components and reduce unplanned forced outage and further maintenance costs, while improving reliability, availability and maintainability of a turbomachinery system. This paper presents a probabilistic signal processing methodology for damage diagnostics using multiple time history data collected from different locations of a turbomachine, considering data uncertainty and multivariate correlation. The proposed methodology is based on the integration of three advanced state-of-the-art data mining techniques: discrete wavelet packet transform, Bayesian hypothesis testing, and probabilistic principal component analysis. The multiresolution wavelet analysis approach is employed to decompose a time series signal into different levels of wavelet coefficients. These coefficients represent multiple time-frequency resolutions of a signal. Bayesian hypothesis testing is then applied to each level of wavelet coefficient to remove possible imperfections. The ratio of posterior odds Bayesian approach provides a direct means to assess whether there is imperfection in the decomposed coefficients, thus avoiding over-denoising. Power spectral density estimated by the Welch method is utilized to evaluate the effectiveness of Bayesian wavelet cleansing method. Furthermore, the probabilistic principal component analysis approach is developed to reduce dimensionality of multiple time series and to address multivariate correlation and data uncertainty for damage diagnostics. The proposed methodology and generalized framework is demonstrated with a set of sensor data collected from a real-world centrifugal compressor with impeller cracks, through both time series and contour analyses of vibration

"NONLINEAR DYNAMIC SYSTEMS RESPONSE TO NON-STATIONARY EXCITATION USING THE WAVELET TRANSFORM"

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

SPANOS, POL D.

2006-01-15

The objective of this research project has been the development of techniques for estimating the power spectra of stochastic processes using wavelet transform, and the development of related techniques for determining the response of linear/nonlinear systems to excitations which are described via the wavelet transform. Both of the objectives have been achieved, and the research findings have been disseminated in papers in archival journals and technical conferences.

Time frequency power profile of QRS complex obtained with wavelet transform in spontaneously hypertensive rats.

PubMed

Takano, Nami K; Tsutsumi, Takeshi; Suzuki, Hiroshi; Okamoto, Yoshiwo; Nakajima, Toshiaki

2012-02-01

We evaluated whether frequency analysis could detect the development of interstitial fibrosis in rats. SHR/Izm and age-matched WKY/Izm were used. Limb lead II electrocardiograms were recorded. Continuous wavelet transform (CWT) was applied for the time-frequency analysis. The integrated time-frequency power (ITFP) between QRS complexes was measured and compared between groups. The ITFP at low-frequency bands (≤125Hz) was significantly higher in SHR/Izm. The percent change of ITFP showed the different patterns between groups. Prominent interstitial fibrosis with an increase in TIMP-1 mRNA expression was also observed in SHR/Izm. These results were partly reproduced in a computer simulation. Copyright © 2011 Elsevier Ltd. All rights reserved.

Periodized Daubechies wavelets

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

Restrepo, J.M.; Leaf, G.K.; Schlossnagle, G.

1996-03-01

The properties of periodized Daubechies wavelets on [0,1] are detailed and counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrated by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators. The periodization of the connection coefficients in Galerkin schemes is presented in detail.

Automated corresponding point candidate selection for image registration using wavelet transformation neurla network with rotation invariant inputs and context information about neighboring candidates

NASA Astrophysics Data System (ADS)

Okumura, Hiroshi; Suezaki, Masashi; Sueyasu, Hideki; Arai, Kohei

2003-03-01

An automated method that can select corresponding point candidates is developed. This method has the following three features: 1) employment of the RIN-net for corresponding point candidate selection; 2) employment of multi resolution analysis with Haar wavelet transformation for improvement of selection accuracy and noise tolerance; 3) employment of context information about corresponding point candidates for screening of selected candidates. Here, the 'RIN-net' means the back-propagation trained feed-forward 3-layer artificial neural network that feeds rotation invariants as input data. In our system, pseudo Zernike moments are employed as the rotation invariants. The RIN-net has N x N pixels field of view (FOV). Some experiments are conducted to evaluate corresponding point candidate selection capability of the proposed method by using various kinds of remotely sensed images. The experimental results show the proposed method achieves fewer training patterns, less training time, and higher selection accuracy than conventional method.

Multidimensional signaling via wavelet packets

NASA Astrophysics Data System (ADS)

Lindsey, Alan R.

1995-04-01

This work presents a generalized signaling strategy for orthogonally multiplexed communication. Wavelet packet modulation (WPM) employs the basis functions from an arbitrary pruning of a full dyadic tree structured filter bank as orthogonal pulse shapes for conventional QAM symbols. The multi-scale modulation (MSM) and M-band wavelet modulation (MWM) schemes which have been recently introduced are handled as special cases, with the added benefit of an entire library of potentially superior sets of basis functions. The figures of merit are derived and it is shown that the power spectral density is equivalent to that for QAM (in fact, QAM is another special case) and hence directly applicable in existing systems employing this standard modulation. Two key advantages of this method are increased flexibility in time-frequency partitioning and an efficient all-digital filter bank implementation, making the WPM scheme more robust to a larger set of interferences (both temporal and sinusoidal) and computationally attractive as well.

FPGA Based Wavelet Trigger in Radio Detection of Cosmic Rays

NASA Astrophysics Data System (ADS)

Szadkowski, Zbigniew; Szadkowska, Anna

2014-12-01

Experiments which show coherent radio emission from extensive air showers induced by ultra-high-energy cosmic rays are designed for a detailed study of the development of the electromagnetic part of air showers. Radio detectors can operate with 100 % up time as, e.g., surface detectors based on water-Cherenkov tanks. They are being developed for ground-based experiments (e.g., the Pierre Auger Observatory) as another type of air-shower detector in addition to fluorescence detectors, which operate with only ˜10 % of duty on dark nights. The radio signals from air showers are caused by coherent emission from geomagnetic radiation and charge-excess processes. The self-triggers in radio detectors currently in use often generate a dense stream of data, which is analyzed afterwards. Huge amounts of registered data require significant manpower for off-line analysis. Improvement of trigger efficiency is a relevant factor. The wavelet trigger, which investigates on-line the power of radio signals (˜ V2/ R), is promising; however, it requires some improvements with respect to current designs. In this work, Morlet wavelets with various scaling factors were used for an analysis of real data from the Auger Engineering Radio Array and for optimization of the utilization of the resources in an FPGA. The wavelet analysis showed that the power of events is concentrated mostly in a limited range of the frequency spectrum (consistent with a range imposed by the input analog band-pass filter). However, we found several events with suspicious spectral characteristics, where the signal power is spread over the full band-width sampled by a 200 MHz digitizer with significant contribution of very high and very low frequencies. These events may not originate from cosmic ray showers but could be the result of human contamination. The engine of the wavelet analysis can be implemented in the modern powerful FPGAs and can remove suspicious events on-line to reduce the trigger rate.

Wavelet denoising during optical coherence tomography of the prostate nerves using the complex wavelet transform.

PubMed

Chitchian, Shahab; Fiddy, Michael; Fried, Nathaniel M

2008-01-01

Preservation of the cavernous nerves during prostate cancer surgery is critical in preserving sexual function after surgery. Optical coherence tomography (OCT) of the prostate nerves has recently been studied for potential use in nerve-sparing prostate surgery. In this study, the discrete wavelet transform and complex dual-tree wavelet transform are implemented for wavelet shrinkage denoising in OCT images of the rat prostate. Applying the complex dual-tree wavelet transform provides improved results for speckle noise reduction in the OCT prostate image. Image quality metrics of the cavernous nerves and signal-to-noise ratio (SNR) were improved significantly using this complex wavelet denoising technique.

Wavelet-Based Motion Artifact Removal for Electrodermal Activity

PubMed Central

Chen, Weixuan; Jaques, Natasha; Taylor, Sara; Sano, Akane; Fedor, Szymon; Picard, Rosalind W.

2017-01-01

Electrodermal activity (EDA) recording is a powerful, widely used tool for monitoring psychological or physiological arousal. However, analysis of EDA is hampered by its sensitivity to motion artifacts. We propose a method for removing motion artifacts from EDA, measured as skin conductance (SC), using a stationary wavelet transform (SWT). We modeled the wavelet coefficients as a Gaussian mixture distribution corresponding to the underlying skin conductance level (SCL) and skin conductance responses (SCRs). The goodness-of-fit of the model was validated on ambulatory SC data. We evaluated the proposed method in comparison with three previous approaches. Our method achieved a greater reduction of artifacts while retaining motion-artifact-free data. PMID:26737714

Multiscale Medical Image Fusion in Wavelet Domain

PubMed Central

Khare, Ashish

2013-01-01

Wavelet transforms have emerged as a powerful tool in image fusion. However, the study and analysis of medical image fusion is still a challenging area of research. Therefore, in this paper, we propose a multiscale fusion of multimodal medical images in wavelet domain. Fusion of medical images has been performed at multiple scales varying from minimum to maximum level using maximum selection rule which provides more flexibility and choice to select the relevant fused images. The experimental analysis of the proposed method has been performed with several sets of medical images. Fusion results have been evaluated subjectively and objectively with existing state-of-the-art fusion methods which include several pyramid- and wavelet-transform-based fusion methods and principal component analysis (PCA) fusion method. The comparative analysis of the fusion results has been performed with edge strength (Q), mutual information (MI), entropy (E), standard deviation (SD), blind structural similarity index metric (BSSIM), spatial frequency (SF), and average gradient (AG) metrics. The combined subjective and objective evaluations of the proposed fusion method at multiple scales showed the effectiveness and goodness of the proposed approach. PMID:24453868

Wavelets and their applications past and future

NASA Astrophysics Data System (ADS)

Coifman, Ronald R.

2009-04-01

As this is a conference on mathematical tools for defense, I would like to dedicate this talk to the memory of Louis Auslander, who through his insights and visionary leadership, brought powerful new mathematics into DARPA, he has provided the main impetus to the development and insertion of wavelet based processing in defense. My goal here is to describe the evolution of a stream of ideas in Harmonic Analysis, ideas which in the past have been mostly applied for the analysis and extraction of information from physical data, and which now are increasingly applied to organize and extract information and knowledge from any set of digital documents, from text to music to questionnaires. This form of signal processing on digital data, is part of the future of wavelet analysis.

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

Wavelet median denoising of ultrasound images

NASA Astrophysics Data System (ADS)

Macey, Katherine E.; Page, Wyatt H.

2002-05-01

Ultrasound images are contaminated with both additive and multiplicative noise, which is modeled by Gaussian and speckle noise respectively. Distinguishing small features such as fallopian tubes in the female genital tract in the noisy environment is problematic. A new method for noise reduction, Wavelet Median Denoising, is presented. Wavelet Median Denoising consists of performing a standard noise reduction technique, median filtering, in the wavelet domain. The new method is tested on 126 images, comprised of 9 original images each with 14 levels of Gaussian or speckle noise. Results for both separable and non-separable wavelets are evaluated, relative to soft-thresholding in the wavelet domain, using the signal-to-noise ratio and subjective assessment. The performance of Wavelet Median Denoising is comparable to that of soft-thresholding. Both methods are more successful in removing Gaussian noise than speckle noise. Wavelet Median Denoising outperforms soft-thresholding for a larger number of cases of speckle noise reduction than of Gaussian noise reduction. Noise reduction is more successful using non-separable wavelets than separable wavelets. When both methods are applied to ultrasound images obtained from a phantom of the female genital tract a small improvement is seen; however, a substantial improvement is required prior to clinical use.

Time-frequency wavelet analysis of the interrelationship between the global macro assets and the fear indexes

NASA Astrophysics Data System (ADS)

Abid, Fathi; Kaffel, Bilel

2018-01-01

Understanding the interrelationships of the global macro assets is crucial for global macro investing. This paper investigates the local variance and the interconnection between the stock, gold, oil, Forex and the implied volatility markets in the time/frequency domains using the wavelet methodology, including the wavelet power spectrum, the wavelet squared coherence and phase difference, the wavelet multiple correlation and cross-correlation. The univariate analysis reveals that, in some crisis periods, underlying asset markets present the same pattern in terms of the wavelet power spectrum indicating high volatility for the medium scale, and that for the other market stress periods, volatility behaves differently. Moreover, unlike the underlying asset markets, the implied volatility markets are characterized by high power regions across the entire period, even in the absence of economic events. Bivariate results show a bidirectional relationship between the underlying assets and their corresponding implied volatility indexes, and a steady co-movement between the stock index and its corresponding fear index. Multiple correlation analysis indicates a strong correlation between markets at high scales with evidence of a nearly perfect integration for a period longer than a year. In addition, the hedging strategies based on the volatility index lead to an increase in portfolio correlation. On the other hand, the results from multiple cross-correlations reveal that the lead-lag effect starts from the medium scale and that the VIX (stock market volatility index) index is the potential leader or follower of the other markets.

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.

A Wavelet Polarization Decomposition Net Model for Polarimetric SAR Image Classification

NASA Astrophysics Data System (ADS)

He, Chu; Ou, Dan; Yang, Teng; Wu, Kun; Liao, Mingsheng; Chen, Erxue

2014-11-01

In this paper, a deep model based on wavelet texture has been proposed for Polarimetric Synthetic Aperture Radar (PolSAR) image classification inspired by recent successful deep learning method. Our model is supposed to learn powerful and informative representations to improve the generalization ability for the complex scene classification tasks. Given the influence of speckle noise in Polarimetric SAR image, wavelet polarization decomposition is applied first to obtain basic and discriminative texture features which are then embedded into a Deep Neural Network (DNN) in order to compose multi-layer higher representations. We demonstrate that the model can produce a powerful representation which can capture some untraceable information from Polarimetric SAR images and show a promising achievement in comparison with other traditional SAR image classification methods for the SAR image dataset.

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.

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.

Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data

NASA Technical Reports Server (NTRS)

Komm, R. W.; Gu, Y.; Hill, F.; Stark, P. B.; Fodor, I. K.

1999-01-01

Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10.

Application of wavelet packet transform to compressing Raman spectra data

NASA Astrophysics Data System (ADS)

Chen, Chen; Peng, Fei; Cheng, Qinghua; Xu, Dahai

2008-12-01

Abstract The Wavelet transform has been established with the Fourier transform as a data-processing method in analytical fields. The main fields of application are related to de-noising, compression, variable reduction, and signal suppression. Raman spectroscopy (RS) is characterized by the frequency excursion that can show the information of molecule. Every substance has its own feature Raman spectroscopy, which can analyze the structure, components, concentrations and some other properties of samples easily. RS is a powerful analytical tool for detection and identification. There are many databases of RS. But the data of Raman spectrum needs large space to storing and long time to searching. In this paper, Wavelet packet is chosen to compress Raman spectra data of some benzene series. The obtained results show that the energy retained is as high as 99.9% after compression, while the percentage for number of zeros is 87.50%. It was concluded that the Wavelet packet has significance in compressing the RS data.

Efficient hemodynamic event detection utilizing relational databases and wavelet analysis

NASA Technical Reports Server (NTRS)

Saeed, M.; Mark, R. G.

2001-01-01

Development of a temporal query framework for time-oriented medical databases has hitherto been a challenging problem. We describe a novel method for the detection of hemodynamic events in multiparameter trends utilizing wavelet coefficients in a MySQL relational database. Storage of the wavelet coefficients allowed for a compact representation of the trends, and provided robust descriptors for the dynamics of the parameter time series. A data model was developed to allow for simplified queries along several dimensions and time scales. Of particular importance, the data model and wavelet framework allowed for queries to be processed with minimal table-join operations. A web-based search engine was developed to allow for user-defined queries. Typical queries required between 0.01 and 0.02 seconds, with at least two orders of magnitude improvement in speed over conventional queries. This powerful and innovative structure will facilitate research on large-scale time-oriented medical databases.

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.

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.

Application of wavelet analysis for monitoring the hydrologic effects of dam operation: Glen canyon dam and the Colorado River at lees ferry, Arizona

USGS Publications Warehouse

White, M.A.; Schmidt, J.C.; Topping, D.J.

2005-01-01

Wavelet analysis is a powerful tool with which to analyse the hydrologic effects of dam construction and operation on river systems. Using continuous records of instantaneous discharge from the Lees Ferry gauging station and records of daily mean discharge from upstream tributaries, we conducted wavelet analyses of the hydrologic structure of the Colorado River in Grand Canyon. The wavelet power spectrum (WPS) of daily mean discharge provided a highly compressed and integrative picture of the post-dam elimination of pronounced annual and sub-annual flow features. The WPS of the continuous record showed the influence of diurnal and weekly power generation cycles, shifts in discharge management, and the 1996 experimental flood in the post-dam period. Normalization of the WPS by local wavelet spectra revealed the fine structure of modulation in discharge scale and amplitude and provides an extremely efficient tool with which to assess the relationships among hydrologic cycles and ecological and geomorphic systems. We extended our analysis to sections of the Snake River and showed how wavelet analysis can be used as a data mining technique. The wavelet approach is an especially promising tool with which to assess dam operation in less well-studied regions and to evaluate management attempts to reconstruct desired flow characteristics. Copyright ?? 2005 John Wiley & Sons, Ltd.

An accuracy improvement method for the topology measurement of an atomic force microscope using a 2D wavelet transform.

PubMed

Yoon, Yeomin; Noh, Suwoo; Jeong, Jiseong; Park, Kyihwan

2018-05-01

The topology image is constructed from the 2D matrix (XY directions) of heights Z captured from the force-feedback loop controller. For small height variations, nonlinear effects such as hysteresis or creep of the PZT-driven Z nano scanner can be neglected and its calibration is quite straightforward. For large height variations, the linear approximation of the PZT-driven Z nano scanner fail and nonlinear behaviors must be considered because this would cause inaccuracies in the measurement image. In order to avoid such inaccuracies, an additional strain gauge sensor is used to directly measure displacement of the PZT-driven Z nano scanner. However, this approach also has a disadvantage in its relatively low precision. In order to obtain high precision data with good linearity, we propose a method of overcoming the low precision problem of the strain gauge while its feature of good linearity is maintained. We expect that the topology image obtained from the strain gauge sensor showing significant noise at high frequencies. On the other hand, the topology image obtained from the controller output showing low noise at high frequencies. If the low and high frequency signals are separable from both topology images, the image can be constructed so that it is represented with high accuracy and low noise. In order to separate the low frequencies from high frequencies, a 2D Haar wavelet transform is used. Our proposed method use the 2D wavelet transform for obtaining good linearity from strain gauge sensor and good precision from controller output. The advantages of the proposed method are experimentally validated by using topology images. Copyright © 2018 Elsevier B.V. All rights reserved.

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.

The ssWavelets package

Treesearch

Jeffrey H. Gove

2017-01-01

This package adds several classes, generics and associated methods as well as a few various functions to help with wavelet decomposition of sampling surfaces generated using sampSurf. As such, it can be thought of as an extension to sampSurf for wavelet analysis.

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

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

Basis Selection for Wavelet Regression

NASA Technical Reports Server (NTRS)

Wheeler, Kevin R.; Lau, Sonie (Technical Monitor)

1998-01-01

A wavelet basis selection procedure is presented for wavelet regression. Both the basis and the threshold are selected using cross-validation. The method includes the capability of incorporating prior knowledge on the smoothness (or shape of the basis functions) into the basis selection procedure. The results of the method are demonstrated on sampled functions widely used in the wavelet regression literature. The results of the method are contrasted with other published methods.

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

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

Davis, A.B.; Clothiaux, E.

Because of Earth`s gravitational field, its atmosphere is strongly anisotropic with respect to the vertical; the effect of the Earth`s rotation on synoptic wind patterns also causes a more subtle form of anisotropy in the horizontal plane. The authors survey various approaches to statistically robust anisotropy from a wavelet perspective and present a new one adapted to strongly non-isotropic fields that are sampled on a rectangular grid with a large aspect ratio. This novel technique uses an anisotropic version of Multi-Resolution Analysis (MRA) in image analysis; the authors form a tensor product of the standard dyadic Haar basis, where themore » dividing ratio is {lambda}{sub z} = 2, and a nonstandard triadic counterpart, where the dividing ratio is {lambda}{sub x} = 3. The natural support of the field is therefore 2{sup n} pixels (vertically) by 3{sup n} pixels (horizontally) where n is the number of levels in the MRA. The natural triadic basis includes the French top-hat wavelet which resonates with bumps in the field whereas the Haar wavelet responds to ramps or steps. The complete 2D basis has one scaling function and five wavelets. The resulting anisotropic MRA is designed for application to the liquid water content (LWC) field in boundary-layer clouds, as the prevailing wind advects them by a vertically pointing mm-radar system. Spatial correlations are notoriously long-range in cloud structure and the authors use the wavelet coefficients from the new MRA to characterize these correlations in a multifractal analysis scheme. In the present study, the MRA is used (in synthesis mode) to generate fields that mimic cloud structure quite realistically although only a few parameters are used to control the randomness of the LWC`s wavelet coefficients.« less

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.

Wavelet Packet Entropy for Heart Murmurs Classification

PubMed Central

Safara, Fatemeh; Doraisamy, Shyamala; Azman, Azreen; Jantan, Azrul; Ranga, Sri

2012-01-01

Heart murmurs are the first signs of cardiac valve disorders. Several studies have been conducted in recent years to automatically differentiate normal heart sounds, from heart sounds with murmurs using various types of audio features. Entropy was successfully used as a feature to distinguish different heart sounds. In this paper, new entropy was introduced to analyze heart sounds and the feasibility of using this entropy in classification of five types of heart sounds and murmurs was shown. The entropy was previously introduced to analyze mammograms. Four common murmurs were considered including aortic regurgitation, mitral regurgitation, aortic stenosis, and mitral stenosis. Wavelet packet transform was employed for heart sound analysis, and the entropy was calculated for deriving feature vectors. Five types of classification were performed to evaluate the discriminatory power of the generated features. The best results were achieved by BayesNet with 96.94% accuracy. The promising results substantiate the effectiveness of the proposed wavelet packet entropy for heart sounds classification. PMID:23227043

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.

Innovative second-generation wavelets construction with recurrent neural networks for solar radiation forecasting.

PubMed

Capizzi, Giacomo; Napoli, Christian; Bonanno, Francesco

2012-11-01

Solar radiation prediction is an important challenge for the electrical engineer because it is used to estimate the power developed by commercial photovoltaic modules. This paper deals with the problem of solar radiation prediction based on observed meteorological data. A 2-day forecast is obtained by using novel wavelet recurrent neural networks (WRNNs). In fact, these WRNNS are used to exploit the correlation between solar radiation and timescale-related variations of wind speed, humidity, and temperature. The input to the selected WRNN is provided by timescale-related bands of wavelet coefficients obtained from meteorological time series. The experimental setup available at the University of Catania, Italy, provided this information. The novelty of this approach is that the proposed WRNN performs the prediction in the wavelet domain and, in addition, also performs the inverse wavelet transform, giving the predicted signal as output. The obtained simulation results show a very low root-mean-square error compared to the results of the solar radiation prediction approaches obtained by hybrid neural networks reported in the recent literature.

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.

Analyze the dynamic features of rat EEG using wavelet entropy.

PubMed

Feng, Zhouyan; Chen, Hang

2005-01-01

Wavelet entropy (WE), a new method of complexity measure for non-stationary signals, was used to investigate the dynamic features of rat EEGs under three vigilance states. The EEGs of the freely moving rats were recorded with implanted electrodes and were decomposed into four components of delta, theta, alpha and beta by using multi-resolution wavelet transform. Then, the wavelet entropy curves were calculated as a function of time. The results showed that there were significant differences among the average WEs of EEGs recorded under the vigilance states of waking, slow wave sleep (SWS) and rapid eye movement (REM) sleep. The changes of WE had different relationships with the four power components under different states. Moreover, there was evident rhythm in EEG WEs of SWS sleep for most experimental rats, which indicated a reciprocal relationship between slow waves and sleep spindles in the micro-states of SWS sleep. Therefore, WE can be used not only to distinguish the long-term changes in EEG complexity, but also to reveal the short-term changes in EEG micro-state.

Comparison between wavelet and wavelet packet transform features for classification of faults in distribution system

NASA Astrophysics Data System (ADS)

Arvind, Pratul

2012-11-01

The ability to identify and classify all ten types of faults in a distribution system is an important task for protection engineers. Unlike transmission system, distribution systems have a complex configuration and are subjected to frequent faults. In the present work, an algorithm has been developed for identifying all ten types of faults in a distribution system by collecting current samples at the substation end. The samples are subjected to wavelet packet transform and artificial neural network in order to yield better classification results. A comparison of results between wavelet transform and wavelet packet transform is also presented thereby justifying the feature extracted from wavelet packet transform yields promising results. It should also be noted that current samples are collected after simulating a 25kv distribution system in PSCAD software.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

A wavelet ridge extraction method employing a novel cost function in two-dimensional wavelet transform profilometry

NASA Astrophysics Data System (ADS)

Wang, Jianhua; Yang, Yanxi

2018-05-01

We present a new wavelet ridge extraction method employing a novel cost function in two-dimensional wavelet transform profilometry (2-D WTP). First of all, the maximum value point is extracted from two-dimensional wavelet transform coefficient modulus, and the local extreme value points over 90% of maximum value are also obtained, they both constitute wavelet ridge candidates. Then, the gradient of rotate factor is introduced into the Abid's cost function, and the logarithmic Logistic model is used to adjust and improve the cost function weights so as to obtain more reasonable value estimation. At last, the dynamic programming method is used to accurately find the optimal wavelet ridge, and the wrapped phase can be obtained by extracting the phase at the ridge. Its advantage is that, the fringe pattern with low signal-to-noise ratio can be demodulated accurately, and its noise immunity will be better. Meanwhile, only one fringe pattern is needed to projected to measured object, so dynamic three-dimensional (3-D) measurement in harsh environment can be realized. Computer simulation and experimental results show that, for the fringe pattern with noise pollution, the 3-D surface recovery accuracy by the proposed algorithm is increased. In addition, the demodulation phase accuracy of Morlet, Fan and Cauchy mother wavelets are compared.

Wavelet Analyses and Applications

ERIC Educational Resources Information Center

Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.

2009-01-01

It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…

Utilizing Wavelet Analysis to assess hydrograph change in northwestern North America

NASA Astrophysics Data System (ADS)

Tang, W.; Carey, S. K.

2017-12-01

Historical streamflow data in the mountainous regions of northwestern North America suggest that changes flows are driven by warming temperature, declining snowpack and glacier extent, and large-scale teleconnections. However, few sites exist that have robust long-term records for statistical analysis, and pervious research has focussed on high and low-flow indices along with trend analysis using Mann-Kendal test and other similar approaches. Furthermore, there has been less emphasis on ascertaining the drivers of change in changes in shape of the streamflow hydrograph compared with traditional flow metrics. In this work, we utilize wavelet analysis to evaluate changes in hydrograph characteristics for snowmelt driven rivers in northwestern North America across a range of scales. Results suggest that wavelets can be used to detect a lengthening and advancement of freshet with a corresponding decline in peak flows. Furthermore, the gradual transition of flows from nival to pluvial regimes in more southerly catchments is evident in the wavelet spectral power through time. This method of change detection is challenged by evaluating the statistical significance of changes in wavelet spectra as related to hydrograph form, yet ongoing work seeks to link these patters to driving weather and climate along with larger scale teleconnections.

Adaptive Multilinear Tensor Product Wavelets

DOE PAGES

Weiss, Kenneth; Lindstrom, Peter

2015-08-12

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how tomore » generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.« less

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.

Riding the Right Wavelet: Detecting Fracture and Fault Orientation Scale Transitions Using Morlet Wavelets

NASA Astrophysics Data System (ADS)

Rizzo, R. E.; Healy, D.; Farrell, N. J.; Smith, M.

2016-12-01

The analysis of images through two-dimensional (2D) continuous wavelet transforms makes it possible to acquire local information at different scales of resolution. This characteristic allows us to use wavelet analysis to quantify anisotropic random fields such as networks of fractures. Previous studies [1] have used 2D anisotropic Mexican hat wavelets to analyse the organisation of fracture networks from cm- to km-scales. However, Antoine et al. [2] explained that this technique can have a relatively poor directional selectivity. This suggests the use of a wavelet whose transform is more sensitive to directions of linear features, i.e. 2D Morlet wavelets [3]. In this work, we use a fully-anisotropic Morlet wavelet as implemented by Neupauer & Powell [4], which is anisotropic in its real and imaginary parts and also in its magnitude. We demonstrate the validity of this analytical technique by application to both synthetic - generated according to known distributions of orientations and lengths - and experimentally produced fracture networks. We have analysed SEM Back Scattered Electron images of thin sections of Hopeman Sandstone (Scotland, UK) deformed under triaxial conditions. We find that the Morlet wavelet, compared to the Mexican hat, is more precise in detecting dominant orientations in fracture scale transition at every scale from intra-grain fractures (µm-scale) up to the faults cutting the whole thin section (cm-scale). Through this analysis we can determine the relationship between the initial orientation of tensile microcracks and the final geometry of the through-going shear fault, with total areal coverage of the analysed image. By comparing thin sections from experiments at different confining pressures, we can quantitatively explore the relationship between the observed geometry and the inferred mechanical processes. [1] Ouillon et al., Nonlinear Processes in Geophysics (1995) 2:158 - 177. [2] Antoine et al., Cambridge University Press (2008) 192

Wavelet analysis in two-dimensional tomography

NASA Astrophysics Data System (ADS)

Burkovets, Dimitry N.

2002-02-01

The diagnostic possibilities of wavelet-analysis of coherent images of connective tissue in its pathological changes diagnostics. The effectiveness of polarization selection in obtaining wavelet-coefficients' images is also shown. The wavelet structures, characterizing the process of skin psoriasis, bone-tissue osteoporosis have been analyzed. The histological sections of physiological normal and pathologically changed samples of connective tissue of human skin and spongy bone tissue have been analyzed.

Wavelet analysis of polarization maps of polycrystalline biological fluids networks

NASA Astrophysics Data System (ADS)

Ushenko, Y. A.

2011-12-01

The optical model of human joints synovial fluid is proposed. The statistic (statistic moments), correlation (autocorrelation function) and self-similar (Log-Log dependencies of power spectrum) structure of polarization two-dimensional distributions (polarization maps) of synovial fluid has been analyzed. It has been shown that differentiation of polarization maps of joint synovial fluid with different physiological state samples is expected of scale-discriminative analysis. To mark out of small-scale domain structure of synovial fluid polarization maps, the wavelet analysis has been used. The set of parameters, which characterize statistic, correlation and self-similar structure of wavelet coefficients' distributions of different scales of polarization domains for diagnostics and differentiation of polycrystalline network transformation connected with the pathological processes, has been determined.

A new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Wavelet Based Protection Scheme for Multi Terminal Transmission System with PV and Wind Generation

NASA Astrophysics Data System (ADS)

Manju Sree, Y.; Goli, Ravi kumar; Ramaiah, V.

2017-08-01

A hybrid generation is a part of large power system in which number of sources usually attached to a power electronic converter and loads are clustered can operate independent of the main power system. The protection scheme is crucial against faults based on traditional over current protection since there are adequate problems due to fault currents in the mode of operation. This paper adopts a new approach for detection, discrimination of the faults for multi terminal transmission line protection in presence of hybrid generation. Transient current based protection scheme is developed with discrete wavelet transform. Fault indices of all phase currents at all terminals are obtained by analyzing the detail coefficients of current signals using bior 1.5 mother wavelet. This scheme is tested for different types of faults and is found effective for detection and discrimination of fault with various fault inception angle and fault impedance.

Forecasting of particulate matter time series using wavelet analysis and wavelet-ARMA/ARIMA model in Taiyuan, China.

PubMed

Zhang, Hong; Zhang, Sheng; Wang, Ping; Qin, Yuzhe; Wang, Huifeng

2017-07-01

Particulate matter with aerodynamic diameter below 10 μm (PM 10 ) forecasting is difficult because of the uncertainties in describing the emission and meteorological fields. This paper proposed a wavelet-ARMA/ARIMA model to forecast the short-term series of the PM 10 concentrations. It was evaluated by experiments using a 10-year data set of daily PM 10 concentrations from 4 stations located in Taiyuan, China. The results indicated the following: (1) PM 10 concentrations of Taiyuan had a decreasing trend during 2005 to 2012 but increased in 2013. PM 10 concentrations had an obvious seasonal fluctuation related to coal-fired heating in winter and early spring. (2) Spatial differences among the four stations showed that the PM 10 concentrations in industrial and heavily trafficked areas were higher than those in residential and suburb areas. (3) Wavelet analysis revealed that the trend variation and the changes of the PM 10 concentration of Taiyuan were complicated. (4) The proposed wavelet-ARIMA model could be efficiently and successfully applied to the PM 10 forecasting field. Compared with the traditional ARMA/ARIMA methods, this wavelet-ARMA/ARIMA method could effectively reduce the forecasting error, improve the prediction accuracy, and realize multiple-time-scale prediction. Wavelet analysis can filter noisy signals and identify the variation trend and the fluctuation of the PM 10 time-series data. Wavelet decomposition and reconstruction reduce the nonstationarity of the PM 10 time-series data, and thus improve the accuracy of the prediction. This paper proposed a wavelet-ARMA/ARIMA model to forecast the PM 10 time series. Compared with the traditional ARMA/ARIMA method, this wavelet-ARMA/ARIMA method could effectively reduce the forecasting error, improve the prediction accuracy, and realize multiple-time-scale prediction. The proposed model could be efficiently and successfully applied to the PM 10 forecasting field.

Determination of seasonals using wavelets in terms of noise parameters changeability

NASA Astrophysics Data System (ADS)

Klos, Anna; Bogusz, Janusz; Figurski, Mariusz

2015-04-01

The reliable velocities of GNSS-derived observations are becoming of high importance nowadays. The fact on how we determine and subtract the seasonals may all cause the time series autocorrelation and affect uncertainties of linear parameters. The periodic changes in GNSS time series are commonly assumed as the sum of annual and semi-annual changes with amplitudes and phases being constant in time and the Least-Squares Estimation (LSE) is used in general to model these sine waves. However, not only seasonals' time-changeability, but also their higher harmonics should be considered. In this research, we focused on more than 230 globally distributed IGS stations that were processed at the Military University of Technology EPN Local Analysis Centre (MUT LAC) in Bernese 5.0 software. The network was divided into 7 different sub-networks with few of overlapping stations and processed separately with newest models. Here, we propose a wavelet-based trend and seasonals determination and removal of whole frequency spectrum between Chandler and quarter-annual periods from North, East and Up components and compare it with LSE-determined values. We used a Meyer symmetric, orthogonal wavelet and assumed nine levels of decomposition. The details from 6 up to 9 were analyzed here as periodic components with frequencies between 0.3-2.5 cpy. The characteristic oscillations for each of frequency band were pointed out. The details lower than 6 summed together with detrended approximation were considered as residua. The power spectral densities (PSDs) of original and decomposed data were stacked for North, East and Up components for each of sub-networks so as to show what power was removed with each of decomposition levels. Moreover, the noises that the certain frequency band follows (in terms of spectral indices of power-law dependencies) were estimated here using a spectral method and compared for all processed sub-networks. It seems, that lowest frequencies up to 0.7 cpy are

Design of Passive Power Filter for Hybrid Series Active Power Filter using Estimation, Detection and Classification Method

NASA Astrophysics Data System (ADS)

Swain, Sushree Diptimayee; Ray, Pravat Kumar; Mohanty, K. B.

2016-06-01

This research paper discover the design of a shunt Passive Power Filter (PPF) in Hybrid Series Active Power Filter (HSAPF) that employs a novel analytic methodology which is superior than FFT analysis. This novel approach consists of the estimation, detection and classification of the signals. The proposed method is applied to estimate, detect and classify the power quality (PQ) disturbance such as harmonics. This proposed work deals with three methods: the harmonic detection through wavelet transform method, the harmonic estimation by Kalman Filter algorithm and harmonic classification by decision tree method. From different type of mother wavelets in wavelet transform method, the db8 is selected as suitable mother wavelet because of its potency on transient response and crouched oscillation at frequency domain. In harmonic compensation process, the detected harmonic is compensated through Hybrid Series Active Power Filter (HSAPF) based on Instantaneous Reactive Power Theory (IRPT). The efficacy of the proposed method is verified in MATLAB/SIMULINK domain and as well as with an experimental set up. The obtained results confirm the superiority of the proposed methodology than FFT analysis. This newly proposed PPF is used to make the conventional HSAPF more robust and stable.

Continuous wavelet transforms for the simultaneous quantitative analysis and dissolution testing of lamivudine-zidovudine tablets.

PubMed

Dinç, Erdal; Özdemir, Nurten; Üstündağ, Özgür; Tilkan, Müşerref Günseli

2013-01-01

Dissolution testing has a very vital importance for a quality control test and prediction of the in vivo behavior of the oral dosage formulation. This requires the use of a powerful analytical method to get reliable, accurate and precise results for the dissolution experiments. In this context, new signal processing approaches, continuous wavelet transforms (CWTs) were improved for the simultaneous quantitative estimation and dissolution testing of lamivudine (LAM) and zidovudine (ZID) in a tablet dosage form. The CWT approaches are based on the application of the continuous wavelet functions to the absorption spectra-data vectors of LAM and ZID in the wavelet domain. After applying many wavelet functions, the families consisting of Mexican hat wavelet with the scaling factor a=256, Symlets wavelet with the scaling factor a=512 and the order of 5 and Daubechies wavelet at the scale factor a=450 and the order of 10 were found to be suitable for the quantitative determination of the mentioned drugs. These wavelet applications were named as mexh-CWT, sym5-CWT and db10-CWT methods. Calibration graphs for LAM and ZID in the working range of 2.0-50.0 µg/mL and 2.0-60.0 µg/mL were obtained measuring the mexh-CWT, sym5-CWT and db10-CWT amplitudes at the wavelength points corresponding to zero crossing points. The validity and applicability of the improved mexh-CWT, sym5-CWT and db10-CWT approaches was carried out by the analysis of the synthetic mixtures containing the analyzed drugs. Simultaneous determination of LAM and ZID in tablets was accomplished by the proposed CWT methods and their dissolution profiles were graphically explored.

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

Representation and design of wavelets using unitary circuits

NASA Astrophysics Data System (ADS)

Evenbly, Glen; White, Steven R.

2018-05-01

The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.

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

Wavelet Decomposition for Discrete Probability Maps

DTIC Science & Technology

2007-08-01

using other wavelet basis functions, such as those mentioned in Section 7 15 DSTO–TN–0760 References 1. P. M. Bentley and J . T . E. McDonnell. Wavelet...84, 1995. 0272-1716. 18. E. J . Stollnitz, T . D. DeRose, and D. H. Salesin. Wavelets for computer graphics: a primer. 2. Computer Graphics and...and Computer Modelling in 2006 from the University of South Australia, Mawson Lakes. Part of this de- gree was undertaken at the University of Twente

Peak finding using biorthogonal wavelets

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

Tan, C.Y.

2000-02-01

The authors show in this paper how they can find the peaks in the input data if the underlying signal is a sum of Lorentzians. In order to project the data into a space of Lorentzian like functions, they show explicitly the construction of scaling functions which look like Lorentzians. From this construction, they can calculate the biorthogonal filter coefficients for both the analysis and synthesis functions. They then compare their biorthogonal wavelets to the FBI (Federal Bureau of Investigations) wavelets when used for peak finding in noisy data. They will show that in this instance, their filters perform muchmore » better than the FBI wavelets.« less

Polar Wavelet Transform and the Associated Uncertainty Principles

NASA Astrophysics Data System (ADS)

Shah, Firdous A.; Tantary, Azhar Y.

2018-06-01

The polar wavelet transform- a generalized form of the classical wavelet transform has been extensively used in science and engineering for finding directional representations of signals in higher dimensions. The aim of this paper is to establish new uncertainty principles associated with the polar wavelet transforms in L2(R2). Firstly, we study some basic properties of the polar wavelet transform and then derive the associated generalized version of Heisenberg-Pauli-Weyl inequality. Finally, following the idea of Beckner (Proc. Amer. Math. Soc. 123, 1897-1905 1995), we drive the logarithmic version of uncertainty principle for the polar wavelet transforms in L2(R2).

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

Qiao, Hongzhu; Rao, N.S.V.; Protopopescu, V.

Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical applications. The sample sizes necessary for PAC learning of regressions or functions under sup norm cost are derived for a general orthonormal system. The result covers the widely used estimators based on Haar wavelets, trignometric functions, and Daubechies wavelets.

Wavelet decomposition and radial basis function networks for system monitoring

NASA Astrophysics Data System (ADS)

Ikonomopoulos, A.; Endou, A.

1998-10-01

Two approaches are coupled to develop a novel collection of black box models for monitoring operational parameters in a complex system. The idea springs from the intention of obtaining multiple predictions for each system variable and fusing them before they are used to validate the actual measurement. The proposed architecture pairs the analytical abilities of the discrete wavelet decomposition with the computational power of radial basis function networks. Members of a wavelet family are constructed in a systematic way and chosen through a statistical selection criterion that optimizes the structure of the network. Network parameters are further optimized through a quasi-Newton algorithm. The methodology is demonstrated utilizing data obtained during two transients of the Monju fast breeder reactor. The models developed are benchmarked with respect to similar regressors based on Gaussian basis functions.

Application of wavelet filtering and Barker-coded pulse compression hybrid method to air-coupled ultrasonic testing

NASA Astrophysics Data System (ADS)

Zhou, Zhenggan; Ma, Baoquan; Jiang, Jingtao; Yu, Guang; Liu, Kui; Zhang, Dongmei; Liu, Weiping

2014-10-01

Air-coupled ultrasonic testing (ACUT) technique has been viewed as a viable solution in defect detection of advanced composites used in aerospace and aviation industries. However, the giant mismatch of acoustic impedance in air-solid interface makes the transmission efficiency of ultrasound low, and leads to poor signal-to-noise (SNR) ratio of received signal. The utilisation of signal-processing techniques in non-destructive testing is highly appreciated. This paper presents a wavelet filtering and phase-coded pulse compression hybrid method to improve the SNR and output power of received signal. The wavelet transform is utilised to filter insignificant components from noisy ultrasonic signal, and pulse compression process is used to improve the power of correlated signal based on cross-correction algorithm. For the purpose of reasonable parameter selection, different families of wavelets (Daubechies, Symlet and Coiflet) and decomposition level in discrete wavelet transform are analysed, different Barker codes (5-13 bits) are also analysed to acquire higher main-to-side lobe ratio. The performance of the hybrid method was verified in a honeycomb composite sample. Experimental results demonstrated that the proposed method is very efficient in improving the SNR and signal strength. The applicability of the proposed method seems to be a very promising tool to evaluate the integrity of high ultrasound attenuation composite materials using the ACUT.

Wavelets for sign language translation

NASA Astrophysics Data System (ADS)

Wilson, Beth J.; Anspach, Gretel

1993-10-01

Wavelet techniques are applied to help extract the relevant parameters of sign language from video images of a person communicating in American Sign Language or Signed English. The compression and edge detection features of two-dimensional wavelet analysis are exploited to enhance the algorithms under development to classify the hand motion, hand location with respect to the body, and handshape. These three parameters have different processing requirements and complexity issues. The results are described for applying various quadrature mirror filter designs to a filterbank implementation of the desired wavelet transform. The overall project is to develop a system that will translate sign language to English to facilitate communication between deaf and hearing people.

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.

Wavelets, non-linearity and turbulence in fusion plasmas

NASA Astrophysics Data System (ADS)

van Milligen, B. Ph.

Introduction Linear spectral analysis tools Wavelet analysis Wavelet spectra and coherence Joint wavelet phase-frequency spectra Non-linear spectral analysis tools Wavelet bispectra and bicoherence Interpretation of the bicoherence Analysis of computer-generated data Coupled van der Pol oscillators A large eddy simulation model for two-fluid plasma turbulence A long wavelength plasma drift wave model Analysis of plasma edge turbulence from Langmuir probe data Radial coherence observed on the TJ-IU torsatron Bicoherence profile at the L/H transition on CCT Conclusions

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.

Effective implementation of wavelet Galerkin method

NASA Astrophysics Data System (ADS)

Finěk, Václav; Šimunková, Martina

2012-11-01

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Δu = f on hypercube with homogeneous Dirichlet boundary conditions. In our implementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

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.

Auto-Detection of Partial Discharges in Power Cables by Descrete Wavelet Transform

NASA Astrophysics Data System (ADS)

Yasuda, Yoh; Hara, Takehisa; Urano, Koji; Chen, Min

One of the serious problems that may happen in power XLPE cables is destruction of insulator. The best and conventional way to prevent such a crucial accident is generally supposed to ascertain partial corona discharges occurring at small void in organic insulator. However, there are some difficulties to detect those partial discharges because of existence of external noises in detected data, whose patterns are hardly identified at a glance. By the reason of the problem, there have been a number of researches on the way of development to accomplish detecting partial discharges by employing neural network (NN) system, which is widely known as the system for pattern recognition. We have been developing the NN system of the auto-detection for partial discharges, which we actually input numerical data of waveform itself into and obtained appropriate performance from. In this paper, we employed Descrete Wavelet Transform (DWT) to acquire more detailed transformed data in order to put them into the NN system. Employing DWT, we became able to express the waveform data in time-frequency space, and achieved effective detectiton of partial discharges by NN system. We present here the results using DWT analysis for partial discharges and noise signals which we obtained actually. Moreover, we present results out of the NN system which were dealt with those transformed data.

Wavelet analysis of near-resonant series RLC circuit with time-dependent forcing frequency

NASA Astrophysics Data System (ADS)

Caccamo, M. T.; Cannuli, A.; Magazù, S.

2018-07-01

In this work, the results of an analysis of the response of a near-resonant series resistance‑inductance‑capacitance (RLC) electric circuit with time-dependent forcing frequency by means of a wavelet cross-correlation approach are reported. In particular, it is shown how the wavelet approach enables frequency and time analysis of the circuit response to be carried out simultaneously—this procedure not being possible by Fourier transform, since the frequency is not stationary in time. A series RLC circuit simulation is performed by using the Simulation Program with Integrated Circuits Emphasis (SPICE), in which an oscillatory sinusoidal voltage drive signal of constant amplitude is swept through the resonant condition by progressively increasing the frequency over a 20-second time window, linearly, from 0.32 Hz to 6.69 Hz. It is shown that the wavelet cross-correlation procedure quantifies the common power between the input signal (represented by the electromotive force) and the output signal, which in the present case is a current, highlighting not only which frequencies are present but also when they occur, i.e. providing a simultaneous time-frequency analysis. The work is directed toward graduate Physics, Engineering and Mathematics students, with the main intention of introducing wavelet analysis into their data analysis toolkit.

Parallel object-oriented, denoising system using wavelet multiresolution analysis

DOEpatents

Kamath, Chandrika; Baldwin, Chuck H.; Fodor, Imola K.; Tang, Nu A.

2005-04-12

The present invention provides a data de-noising system utilizing processors and wavelet denoising techniques. Data is read and displayed in different formats. The data is partitioned into regions and the regions are distributed onto the processors. Communication requirements are determined among the processors according to the wavelet denoising technique and the partitioning of the data. The data is transforming onto different multiresolution levels with the wavelet transform according to the wavelet denoising technique, the communication requirements, and the transformed data containing wavelet coefficients. The denoised data is then transformed into its original reading and displaying data format.

A Wavelet Model for Vocalic Speech Coarticulation

DTIC Science & Technology

1994-10-01

control vowel’s signal as the mother wavelet. A practical experiment is conducted to evaluate the coarticulation channel using samples 01 real speech...transformation from a control speech state (input) to an effected speech state (output). Specifically, a vowel produced in isolation is transformed into an...the wavelet transform of the effected vowel’s signal, using the control vowel’s signal as the mother wavelet. A practical experiment is conducted to

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.

Multi-frequency data analysis in AFM by wavelet transform

NASA Astrophysics Data System (ADS)

Pukhova, V.; Ferrini, G.

2017-10-01

Interacting cantilevers in AFM experiments generate non-stationary, multi-frequency signals consisting of numerous excited flexural and torsional modes and their harmonics. The analysis of such signals is challenging, requiring special methodological approaches and a powerful mathematical apparatus. The most common approach to the signal analysis is to apply Fourier transform analysis. However, FT gives accurate spectra for stationary signals, and for signals changing their spectral content over time, FT provides only an averaged spectrum. Hence, for non-stationary and rapidly varying signals, such as those from interacting cantilevers, a method that shows the spectral evolution in time is needed. One of the most powerful techniques, allowing detailed time-frequency representation of signals, is the wavelet transform. It is a method of analysis that allows representation of energy associated to the signal at a particular frequency and time, providing correlation between the spectral and temporal features of the signal, unlike FT. This is particularly important in AFM experiments because signals nonlinearities contains valuable information about tip-sample interactions and consequently surfaces properties. The present work is aimed to show the advantages of wavelet transform in comparison with FT using as an example the force curve analysis in dynamic force spectroscopy.

Morphological and wavelet features towards sonographic thyroid nodules evaluation.

PubMed

Tsantis, Stavros; Dimitropoulos, Nikos; Cavouras, Dionisis; Nikiforidis, George

2009-03-01

This paper presents a computer-based classification scheme that utilized various morphological and novel wavelet-based features towards malignancy risk evaluation of thyroid nodules in ultrasonography. The study comprised 85 ultrasound images-patients that were cytological confirmed (54 low-risk and 31 high-risk). A set of 20 features (12 based on nodules boundary shape and 8 based on wavelet local maxima located within each nodule) has been generated. Two powerful pattern recognition algorithms (support vector machines and probabilistic neural networks) have been designed and developed in order to quantify the power of differentiation of the introduced features. A comparative study has also been held, in order to estimate the impact speckle had onto the classification procedure. The diagnostic sensitivity and specificity of both classifiers was made by means of receiver operating characteristics (ROC) analysis. In the speckle-free feature set, the area under the ROC curve was 0.96 for the support vector machines classifier whereas for the probabilistic neural networks was 0.91. In the feature set with speckle, the corresponding areas under the ROC curves were 0.88 and 0.86 respectively for the two classifiers. The proposed features can increase the classification accuracy and decrease the rate of missing and misdiagnosis in thyroid cancer control.

Visibility of wavelet quantization noise

NASA Technical Reports Server (NTRS)

Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.

1997-01-01

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

Online Wavelet Complementary velocity Estimator.

PubMed

Righettini, Paolo; Strada, Roberto; KhademOlama, Ehsan; Valilou, Shirin

2018-02-01

In this paper, we have proposed a new online Wavelet Complementary velocity Estimator (WCE) over position and acceleration data gathered from an electro hydraulic servo shaking table. This is a batch estimator type that is based on the wavelet filter banks which extract the high and low resolution of data. The proposed complementary estimator combines these two resolutions of velocities which acquired from numerical differentiation and integration of the position and acceleration sensors by considering a fixed moving horizon window as input to wavelet filter. Because of using wavelet filters, it can be implemented in a parallel procedure. By this method the numerical velocity is estimated without having high noise of differentiators, integration drifting bias and with less delay which is suitable for active vibration control in high precision Mechatronics systems by Direct Velocity Feedback (DVF) methods. This method allows us to make velocity sensors with less mechanically moving parts which makes it suitable for fast miniature structures. We have compared this method with Kalman and Butterworth filters over stability, delay and benchmarked them by their long time velocity integration for getting back the initial position data. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A goal-based angular adaptivity method for thermal radiation modelling in non grey media

NASA Astrophysics Data System (ADS)

Soucasse, Laurent; Dargaville, Steven; Buchan, Andrew G.; Pain, Christopher C.

2017-10-01

This paper investigates for the first time a goal-based angular adaptivity method for thermal radiation transport, suitable for non grey media when the radiation field is coupled with an unsteady flow field through an energy balance. Anisotropic angular adaptivity is achieved by using a Haar wavelet finite element expansion that forms a hierarchical angular basis with compact support and does not require any angular interpolation in space. The novelty of this work lies in (1) the definition of a target functional to compute the goal-based error measure equal to the radiative source term of the energy balance, which is the quantity of interest in the context of coupled flow-radiation calculations; (2) the use of different optimal angular resolutions for each absorption coefficient class, built from a global model of the radiative properties of the medium. The accuracy and efficiency of the goal-based angular adaptivity method is assessed in a coupled flow-radiation problem relevant for air pollution modelling in street canyons. Compared to a uniform Haar wavelet expansion, the adapted resolution uses 5 times fewer angular basis functions and is 6.5 times quicker, given the same accuracy in the radiative source term.

Statistical detection of patterns in unidimensional distributions by continuous wavelet transforms

NASA Astrophysics Data System (ADS)

Baluev, R. V.

2018-04-01

Objective detection of specific patterns in statistical distributions, like groupings or gaps or abrupt transitions between different subsets, is a task with a rich range of applications in astronomy: Milky Way stellar population analysis, investigations of the exoplanets diversity, Solar System minor bodies statistics, extragalactic studies, etc. We adapt the powerful technique of the wavelet transforms to this generalized task, making a strong emphasis on the assessment of the patterns detection significance. Among other things, our method also involves optimal minimum-noise wavelets and minimum-noise reconstruction of the distribution density function. Based on this development, we construct a self-closed algorithmic pipeline aimed to process statistical samples. It is currently applicable to single-dimensional distributions only, but it is flexible enough to undergo further generalizations and development.

A user's guide to the ssWavelets package

Treesearch

J.H. ​Gove

2017-01-01

ssWavelets is an R package that is meant to be used in conjunction with the sampSurf package (Gove, 2012) to perform wavelet decomposition on the results of a sampling surface simulation. In general, the wavelet filter decomposes the sampSurf simulation results by scale (distance), with each scale corresponding to a different level of the...

Analysis of autostereoscopic three-dimensional images using multiview wavelets.

PubMed

Saveljev, Vladimir; Palchikova, Irina

2016-08-10

We propose that multiview wavelets can be used in processing multiview images. The reference functions for the synthesis/analysis of multiview images are described. The synthesized binary images were observed experimentally as three-dimensional visual images. The symmetric multiview B-spline wavelets are proposed. The locations recognized in the continuous wavelet transform correspond to the layout of the test objects. The proposed wavelets can be applied to the multiview, integral, and plenoptic images.

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.

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

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.

Wavelet detection of singularities in the presence of fractal noise

NASA Astrophysics Data System (ADS)

Noel, Steven E.; Gohel, Yogesh J.; Szu, Harold H.

1997-04-01

Here we detect singularities with generalized quadrature processing using the recently developed Hermitian Hat wavelet. Our intended application is radar target detection for the optimal fuzzing of ship self-defense munitions. We first develop a wavelet-based fractal noise model to represent sea clutter. We then investigate wavelet shrinkage as a way to reduce and smooth the noise before attempting wavelet detection. Finally, we use the complex phase of the Hermitian Hat wavelet to detect a simulated target singularity in the presence of our fractal noise.

Vector coding of wavelet-transformed images

NASA Astrophysics Data System (ADS)

Zhou, Jun; Zhi, Cheng; Zhou, Yuanhua

1998-09-01

Wavelet, as a brand new tool in signal processing, has got broad recognition. Using wavelet transform, we can get octave divided frequency band with specific orientation which combines well with the properties of Human Visual System. In this paper, we discuss the classified vector quantization method for multiresolution represented image.

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

Wavelet transform: fundamentals, applications, and implementation using acousto-optic correlators

NASA Astrophysics Data System (ADS)

DeCusatis, Casimer M.; Koay, J.; Litynski, Daniel M.; Das, Pankaj K.

1995-10-01

In recent years there has been a great deal of interest in the use of wavelets to supplement or replace conventional Fourier transform signal processing. This paper provides a review of wavelet transforms for signal processing applications, and discusses several emerging applications which benefit from the advantages of wavelets. The wavelet transform can be implemented as an acousto-optic correlator; perfect reconstruction of digital signals may also be achieved using acousto-optic finite impulse response filter banks. Acousto-optic image correlators are discussed as a potential implementation of the wavelet transform, since a 1D wavelet filter bank may be encoded as a 2D image. We discuss applications of the wavelet transform including nondestructive testing of materials, biomedical applications in the analysis of EEG signals, and interference excision in spread spectrum communication systems. Computer simulations and experimental results for these applications are also provided.

Lifting wavelet method of target detection

NASA Astrophysics Data System (ADS)

Han, Jun; Zhang, Chi; Jiang, Xu; Wang, Fang; Zhang, Jin

2009-11-01

Image target recognition plays a very important role in the areas of scientific exploration, aeronautics and space-to-ground observation, photography and topographic mapping. Complex environment of the image noise, fuzzy, all kinds of interference has always been to affect the stability of recognition algorithm. In this paper, the existence of target detection in real-time, accuracy problems, as well as anti-interference ability, using lifting wavelet image target detection methods. First of all, the use of histogram equalization, the goal difference method to obtain the region, on the basis of adaptive threshold and mathematical morphology operations to deal with the elimination of the background error. Secondly, the use of multi-channel wavelet filter wavelet transform of the original image de-noising and enhancement, to overcome the general algorithm of the noise caused by the sensitive issue of reducing the rate of miscarriage of justice will be the multi-resolution characteristics of wavelet and promotion of the framework can be designed directly in the benefits of space-time region used in target detection, feature extraction of targets. The experimental results show that the design of lifting wavelet has solved the movement of the target due to the complexity of the context of the difficulties caused by testing, which can effectively suppress noise, and improve the efficiency and speed of detection.

Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient

PubMed Central

Zhang, Zhenwei; VanSwearingen, Jessie; Brach, Jennifer S.; Perera, Subashan

2016-01-01

Human gait is a complex interaction of many nonlinear systems and stride intervals exhibit self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a biomarker of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of sixteen mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length. PMID:27960102

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.

A human auditory tuning curves matched wavelet function.

PubMed

Abolhassani, Mohammad D; Salimpour, Yousef

2008-01-01

This paper proposes a new quantitative approach to the problem of matching a wavelet function to a human auditory tuning curves. The auditory filter shapes were derived from the psychophysical measurements in normal-hearing listeners using the variant of the notched-noise method for brief signals in forward and simultaneous masking. These filters were used as templates for the designing a wavelet function that has the maximum matching to a tuning curve. The scaling function was calculated from the matched wavelet function and by using these functions, low pass and high pass filters were derived for the implementation of a filter bank. Therefore, new wavelet families were derived.

A clustering-based fuzzy wavelet neural network model for short-term load forecasting.

PubMed

Kodogiannis, Vassilis S; Amina, Mahdi; Petrounias, Ilias

2013-10-01

Load forecasting is a critical element of power system operation, involving prediction of the future level of demand to serve as the basis for supply and demand planning. This paper presents the development of a novel clustering-based fuzzy wavelet neural network (CB-FWNN) model and validates its prediction on the short-term electric load forecasting of the Power System of the Greek Island of Crete. The proposed model is obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with a "multiplication" wavelet neural network (MWNN). Multidimensional Gaussian type of activation functions have been used in the IF part of the fuzzyrules. A Fuzzy Subtractive Clustering scheme is employed as a pre-processing technique to find out the initial set and adequate number of clusters and ultimately the number of multiplication nodes in MWNN, while Gaussian Mixture Models with the Expectation Maximization algorithm are utilized for the definition of the multidimensional Gaussians. The results corresponding to the minimum and maximum power load indicate that the proposed load forecasting model provides significantly accurate forecasts, compared to conventional neural networks models.

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in

Optimal wavelet denoising for smart biomonitor systems

NASA Astrophysics Data System (ADS)

Messer, Sheila R.; Agzarian, John; Abbott, Derek

2001-03-01

Future smart-systems promise many benefits for biomedical diagnostics. The ideal is for simple portable systems that display and interpret information from smart integrated probes or MEMS-based devices. In this paper, we will discuss a step towards this vision with a heart bio-monitor case study. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. In our example of heartbeat analysis, phonocardiograms (PCGs) have many advantages in that they may be replayed and analysed for spectral and frequency information. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. Wavelets can be employed to denoise the PCG. The signal is decomposed by a discrete wavelet transform. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert Transform to heart sound analysis are discussed.

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.

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).

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.

Conjugate Event Study of Geomagnetic ULF Pulsations with Wavelet-based Indices

NASA Astrophysics Data System (ADS)

Xu, Z.; Clauer, C. R.; Kim, H.; Weimer, D. R.; Cai, X.

2013-12-01

The interactions between the solar wind and geomagnetic field produce a variety of space weather phenomena, which can impact the advanced technology systems of modern society including, for example, power systems, communication systems, and navigation systems. One type of phenomena is the geomagnetic ULF pulsation observed by ground-based or in-situ satellite measurements. Here, we describe a wavelet-based index and apply it to study the geomagnetic ULF pulsations observed in Antarctica and Greenland magnetometer arrays. The wavelet indices computed from these data show spectrum, correlation, and magnitudes information regarding the geomagnetic pulsations. The results show that the geomagnetic field at conjugate locations responds differently according to the frequency of pulsations. The index is effective for identification of the pulsation events and measures important characteristics of the pulsations. It could be a useful tool for the purpose of monitoring geomagnetic pulsations.

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.

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

Detection of Heart Sounds in Children with and without Pulmonary Arterial Hypertension―Daubechies Wavelets Approach

PubMed Central

Elgendi, Mohamed; Kumar, Shine; Guo, Long; Rutledge, Jennifer; Coe, James Y.; Zemp, Roger; Schuurmans, Dale; Adatia, Ian

2015-01-01

Background Automatic detection of the 1st (S1) and 2nd (S2) heart sounds is difficult, and existing algorithms are imprecise. We sought to develop a wavelet-based algorithm for the detection of S1 and S2 in children with and without pulmonary arterial hypertension (PAH). Method Heart sounds were recorded at the second left intercostal space and the cardiac apex with a digital stethoscope simultaneously with pulmonary arterial pressure (PAP). We developed a Daubechies wavelet algorithm for the automatic detection of S1 and S2 using the wavelet coefficient ‘D 6’ based on power spectral analysis. We compared our algorithm with four other Daubechies wavelet-based algorithms published by Liang, Kumar, Wang, and Zhong. We annotated S1 and S2 from an audiovisual examination of the phonocardiographic tracing by two trained cardiologists and the observation that in all subjects systole was shorter than diastole. Results We studied 22 subjects (9 males and 13 females, median age 6 years, range 0.25–19). Eleven subjects had a mean PAP < 25 mmHg. Eleven subjects had PAH with a mean PAP ≥ 25 mmHg. All subjects had a pulmonary artery wedge pressure ≤ 15 mmHg. The sensitivity (SE) and positive predictivity (+P) of our algorithm were 70% and 68%, respectively. In comparison, the SE and +P of Liang were 59% and 42%, Kumar 19% and 12%, Wang 50% and 45%, and Zhong 43% and 53%, respectively. Our algorithm demonstrated robustness and outperformed the other methods up to a signal-to-noise ratio (SNR) of 10 dB. For all algorithms, detection errors arose from low-amplitude peaks, fast heart rates, low signal-to-noise ratio, and fixed thresholds. Conclusion Our algorithm for the detection of S1 and S2 improves the performance of existing Daubechies-based algorithms and justifies the use of the wavelet coefficient ‘D 6’ through power spectral analysis. Also, the robustness despite ambient noise may improve real world clinical performance. PMID:26629704

The norms and variances of the Gabor, Morlet and general harmonic wavelet functions

NASA Astrophysics Data System (ADS)

Simonovski, I.; Boltežar, M.

2003-07-01

This paper deals with certain properties of the continuous wavelet transform and wavelet functions. The norms and the spreads in time and frequency of the common Gabor and Morlet wavelet functions are presented. It is shown that the norm of the Morlet wavelet function does not satisfy the normalization condition and that the normalized Morlet wavelet function is identical to the Gabor wavelet function with the parameter σ=1. The general harmonic wavelet function is developed using frequency modulation of the Hanning and Hamming window functions. Several properties of the general harmonic wavelet function are also presented and compared to the Gabor wavelet function. The time and frequency spreads of the general harmonic wavelet function are only slightly higher than the time and frequency spreads of the Gabor wavelet function. However, the general harmonic wavelet function is simpler to use than the Gabor wavelet function. In addition, the general harmonic wavelet function can be constructed in such a way that the zero average condition is truly satisfied. The average value of the Gabor wavelet function can approach a value of zero but it cannot reach it. When calculating the continuous wavelet transform, errors occur at the start- and the end-time indexes. This is called the edge effect and is caused by the fact that the wavelet transform is calculated from a signal of finite length. In this paper, we propose a method that uses signal mirroring to reduce the errors caused by the edge effect. The success of the proposed method is demonstrated by using a simulated signal.

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.

Exact reconstruction with directional wavelets on the sphere

NASA Astrophysics Data System (ADS)

Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.

2008-08-01

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.

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.

Scalets, wavelets and (complex) turning point quantization

NASA Astrophysics Data System (ADS)

Handy, C. R.; Brooks, H. A.

2001-05-01

Despite the many successes of wavelet analysis in image and signal processing, the incorporation of continuous wavelet transform theory within quantum mechanics has lacked a compelling, first principles, motivating analytical framework, until now. For arbitrary one-dimensional rational fraction Hamiltonians, we develop a simple, unified formalism, which clearly underscores the complementary, and mutually interdependent, role played by moment quantization theory (i.e. via scalets, as defined herein) and wavelets. This analysis involves no approximation of the Hamiltonian within the (equivalent) wavelet space, and emphasizes the importance of (complex) multiple turning point contributions in the quantization process. We apply the method to three illustrative examples. These include the (double-well) quartic anharmonic oscillator potential problem, V(x) = Z2x2 + gx4, the quartic potential, V(x) = x4, and the very interesting and significant non-Hermitian potential V(x) = -(ix)3, recently studied by Bender and Boettcher.

On wavelet analysis of auditory evoked potentials.

PubMed

Bradley, A P; Wilson, W J

2004-05-01

To determine a preferred wavelet transform (WT) procedure for multi-resolution analysis (MRA) of auditory evoked potentials (AEP). A number of WT algorithms, mother wavelets, and pre-processing techniques were examined by way of critical theoretical discussion followed by experimental testing of key points using real and simulated auditory brain-stem response (ABR) waveforms. Conclusions from these examinations were then tested on a normative ABR dataset. The results of the various experiments are reported in detail. Optimal AEP WT MRA is most likely to occur when an over-sampled discrete wavelet transformation (DWT) is used, utilising a smooth (regularity >or=3) and symmetrical (linear phase) mother wavelet, and a reflection boundary extension policy. This study demonstrates the practical importance of, and explains how to minimize potential artefacts due to, 4 inter-related issues relevant to AEP WT MRA, namely shift variance, phase distortion, reconstruction smoothness, and boundary artefacts.

Optical phase distribution evaluation by using zero order Generalized Morse Wavelet

NASA Astrophysics Data System (ADS)

Kocahan, Özlem; Elmas, Merve Naz; Durmuş, ćaǧla; Coşkun, Emre; Tiryaki, Erhan; Özder, Serhat

2017-02-01

When determining the phase from the projected fringes by using continuous wavelet transform (CWT), selection of wavelet is an important step. A new wavelet for phase retrieval from the fringe pattern with the spatial carrier frequency in the x direction is presented. As a mother wavelet, zero order generalized Morse wavelet (GMW) is chosen because of the flexible spatial and frequency localization property, and it is exactly analytic. In this study, GMW method is explained and numerical simulations are carried out to show the validity of this technique for finding the phase distributions. Results for the Morlet and Paul wavelets are compared with the results of GMW analysis.

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.

What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

NASA Astrophysics Data System (ADS)

Schaefli, B.; Maraun, D.; Holschneider, M.

2007-12-01

Extreme hydrological events are often triggered by exceptional co-variations of the relevant hydrometeorological processes and in particular by exceptional co-oscillations at various temporal scales. Wavelet and cross wavelet spectral analysis offers promising time-scale resolved analysis methods to detect and analyze such exceptional co-oscillations. This paper presents the state-of-the-art methods of wavelet spectral analysis, discusses related subtleties, potential pitfalls and recently developed solutions to overcome them and shows how wavelet spectral analysis, if combined to a rigorous significance test, can lead to reliable new insights into hydrometeorological processes for real-world applications. The presented methods are applied to detect potentially flood triggering situations in a high Alpine catchment for which a recent re-estimation of design floods encountered significant problems simulating the observed high flows. For this case study, wavelet spectral analysis of precipitation, temperature and discharge offers a powerful tool to help detecting potentially flood producing meteorological situations and to distinguish between different types of floods with respect to the prevailing critical hydrometeorological conditions. This opens very new perspectives for the analysis of model performances focusing on the occurrence and non-occurrence of different types of high flow events. Based on the obtained results, the paper summarizes important recommendations for future applications of wavelet spectral analysis in hydrology.

Pattern recognition by wavelet transforms using macro fibre composites transducers

NASA Astrophysics Data System (ADS)

Ruiz de la Hermosa González-Carrato, Raúl; García Márquez, Fausto Pedro; Dimlaye, Vichaar; Ruiz-Hernández, Diego

2014-10-01

This paper presents a novel pattern recognition approach for a non-destructive test based on macro fibre composite transducers applied in pipes. A fault detection and diagnosis (FDD) method is employed to extract relevant information from ultrasound signals by wavelet decomposition technique. The wavelet transform is a powerful tool that reveals particular characteristics as trends or breakdown points. The FDD developed for the case study provides information about the temperatures on the surfaces of the pipe, leading to monitor faults associated with cracks, leaks or corrosion. This issue may not be noticeable when temperatures are not subject to sudden changes, but it can cause structural problems in the medium and long-term. Furthermore, the case study is completed by a statistical method based on the coefficient of determination. The main purpose will be to predict future behaviours in order to set alarm levels as a part of a structural health monitoring system.

Interframe vector wavelet coding technique

NASA Astrophysics Data System (ADS)

Wus, John P.; Li, Weiping

1997-01-01

Wavelet coding is often used to divide an image into multi- resolution wavelet coefficients which are quantized and coded. By 'vectorizing' scalar wavelet coding and combining this with vector quantization (VQ), vector wavelet coding (VWC) can be implemented. Using a finite number of states, finite-state vector quantization (FSVQ) takes advantage of the similarity between frames by incorporating memory into the video coding system. Lattice VQ eliminates the potential mismatch that could occur using pre-trained VQ codebooks. It also eliminates the need for codebook storage in the VQ process, thereby creating a more robust coding system. Therefore, by using the VWC coding method in conjunction with the FSVQ system and lattice VQ, the formulation of a high quality very low bit rate coding systems is proposed. A coding system using a simple FSVQ system where the current state is determined by the previous channel symbol only is developed. To achieve a higher degree of compression, a tree-like FSVQ system is implemented. The groupings are done in this tree-like structure from the lower subbands to the higher subbands in order to exploit the nature of subband analysis in terms of the parent-child relationship. Class A and Class B video sequences from the MPEG-IV testing evaluations are used in the evaluation of this coding method.

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

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.

Time-localized wavelet multiple regression and correlation

NASA Astrophysics Data System (ADS)

Fernández-Macho, Javier

2018-02-01

This paper extends wavelet methodology to handle comovement dynamics of multivariate time series via moving weighted regression on wavelet coefficients. The concept of wavelet local multiple correlation is used to produce one single set of multiscale correlations along time, in contrast with the large number of wavelet correlation maps that need to be compared when using standard pairwise wavelet correlations with rolling windows. Also, the spectral properties of weight functions are investigated and it is argued that some common time windows, such as the usual rectangular rolling window, are not satisfactory on these grounds. The method is illustrated with a multiscale analysis of the comovements of Eurozone stock markets during this century. It is shown how the evolution of the correlation structure in these markets has been far from homogeneous both along time and across timescales featuring an acute divide across timescales at about the quarterly scale. At longer scales, evidence from the long-term correlation structure can be interpreted as stable perfect integration among Euro stock markets. On the other hand, at intramonth and intraweek scales, the short-term correlation structure has been clearly evolving along time, experiencing a sharp increase during financial crises which may be interpreted as evidence of financial 'contagion'.

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.

Correlation Filtering of Modal Dynamics using the Laplace Wavelet

NASA Technical Reports Server (NTRS)

Freudinger, Lawrence C.; Lind, Rick; Brenner, Martin J.

1997-01-01

Wavelet analysis allows processing of transient response data commonly encountered in vibration health monitoring tasks such as aircraft flutter testing. The Laplace wavelet is formulated as an impulse response of a single mode system to be similar to data features commonly encountered in these health monitoring tasks. A correlation filtering approach is introduced using the Laplace wavelet to decompose a signal into impulse responses of single mode subsystems. Applications using responses from flutter testing of aeroelastic systems demonstrate modal parameters and stability estimates can be estimated by correlation filtering free decay data with a set of Laplace wavelets.

Embedded wavelet packet transform technique for texture compression

NASA Astrophysics Data System (ADS)

Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay

1995-09-01

A highly efficient texture compression scheme is proposed in this research. With this scheme, energy compaction of texture images is first achieved by the wavelet packet transform, and an embedding approach is then adopted for the coding of the wavelet packet transform coefficients. By comparing the proposed algorithm with the JPEG standard, FBI wavelet/scalar quantization standard and the EZW scheme with extensive experimental results, we observe a significant improvement in the rate-distortion performance and visual quality.

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

Wavelets in medical imaging

NASA Astrophysics Data System (ADS)

Zahra, Noor e.; Sevindir, Hulya Kodal; Aslan, Zafer; Siddiqi, A. H.

2012-07-01

The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.

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.

Acoustical Emission Source Location in Thin Rods Through Wavelet Detail Crosscorrelation

DTIC Science & Technology

1998-03-01

NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS ACOUSTICAL EMISSION SOURCE LOCATION IN THIN RODS THROUGH WAVELET DETAIL CROSSCORRELATION...ACOUSTICAL EMISSION SOURCE LOCATION IN THIN RODS THROUGH WAVELET DETAIL CROSSCORRELATION 6. AUTHOR(S) Jerauld, Joseph G. 5. FUNDING NUMBERS Grant...frequency characteristics of Wavelet Analysis. Software implementation now enables the exploration of the Wavelet Transform to identify the time of

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.

Stationary Wavelet-based Two-directional Two-dimensional Principal Component Analysis for EMG Signal Classification

NASA Astrophysics Data System (ADS)

Ji, Yi; Sun, Shanlin; Xie, Hong-Bo

2017-06-01

Discrete wavelet transform (WT) followed by principal component analysis (PCA) has been a powerful approach for the analysis of biomedical signals. Wavelet coefficients at various scales and channels were usually transformed into a one-dimensional array, causing issues such as the curse of dimensionality dilemma and small sample size problem. In addition, lack of time-shift invariance of WT coefficients can be modeled as noise and degrades the classifier performance. In this study, we present a stationary wavelet-based two-directional two-dimensional principal component analysis (SW2D2PCA) method for the efficient and effective extraction of essential feature information from signals. Time-invariant multi-scale matrices are constructed in the first step. The two-directional two-dimensional principal component analysis then operates on the multi-scale matrices to reduce the dimension, rather than vectors in conventional PCA. Results are presented from an experiment to classify eight hand motions using 4-channel electromyographic (EMG) signals recorded in healthy subjects and amputees, which illustrates the efficiency and effectiveness of the proposed method for biomedical signal analysis.

Fast generation of computer-generated holograms using wavelet shrinkage.

PubMed

Shimobaba, Tomoyoshi; Ito, Tomoyoshi

2017-01-09

Computer-generated holograms (CGHs) are generated by superimposing complex amplitudes emitted from a number of object points. However, this superposition process remains very time-consuming even when using the latest computers. We propose a fast calculation algorithm for CGHs that uses a wavelet shrinkage method, eliminating small wavelet coefficient values to express approximated complex amplitudes using only a few representative wavelet coefficients.

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.

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.

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.

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 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

Wavelet synthetic method for turbulent flow.

PubMed

Zhou, Long; Rauh, Cornelia; Delgado, Antonio

2015-07-01

Based on the idea of random cascades on wavelet dyadic trees and the energy cascade model known as the wavelet p model, a series of velocity increments in two-dimensional space are constructed in different levels of scale. The dynamics is imposed on the generated scales by solving the Euler equation in the Lagrangian framework. A dissipation model is used in order to cover the shortage of the p model, which only predicts in inertial range. Wavelet reconstruction as well as the multiresolution analysis are then performed on each scales. As a result, a type of isotropic velocity field is created. The statistical properties show that the constructed velocity fields share many important features with real turbulence. The pertinence of this approach in the prediction of flow intermittency is also discussed.

Image Retrieval using Integrated Features of Binary Wavelet Transform

NASA Astrophysics Data System (ADS)

Agarwal, Megha; Maheshwari, R. P.

2011-12-01

In this paper a new approach for image retrieval is proposed with the application of binary wavelet transform. This new approach facilitates the feature calculation with the integration of histogram and correlogram features extracted from binary wavelet subbands. Experiments are performed to evaluate and compare the performance of proposed method with the published literature. It is verified that average precision and average recall of proposed method (69.19%, 41.78%) is significantly improved compared to optimal quantized wavelet correlogram (OQWC) [6] (64.3%, 38.00%) and Gabor wavelet correlogram (GWC) [10] (64.1%, 40.6%). All the experiments are performed on Corel 1000 natural image database [20].

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.

Wavelet-domain de-noising of OCT images of human brain malignant glioma

NASA Astrophysics Data System (ADS)

Dolganova, I. N.; Aleksandrova, P. V.; Beshplav, S.-I. T.; Chernomyrdin, N. V.; Dubyanskaya, E. N.; Goryaynov, S. A.; Kurlov, V. N.; Reshetov, I. V.; Potapov, A. A.; Tuchin, V. V.; Zaytsev, K. I.

2018-04-01

We have proposed a wavelet-domain de-noising technique for imaging of human brain malignant glioma by optical coherence tomography (OCT). It implies OCT image decomposition using the direct fast wavelet transform, thresholding of the obtained wavelet spectrum and further inverse fast wavelet transform for image reconstruction. By selecting both wavelet basis and thresholding procedure, we have found an optimal wavelet filter, which application improves differentiation of the considered brain tissue classes - i.e. malignant glioma and normal/intact tissue. Namely, it allows reducing the scattering noise in the OCT images and retaining signal decrement for each tissue class. Therefore, the observed results reveals the wavelet-domain de-noising as a prospective tool for improved characterization of biological tissue using the OCT.

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.

A novel method of identifying motor primitives using wavelet decomposition*

PubMed Central

Popov, Anton; Olesh, Erienne V.; Yakovenko, Sergiy; Gritsenko, Valeriya

2018-01-01

This study reports a new technique for extracting muscle synergies using continuous wavelet transform. The method allows to quantify coincident activation of muscle groups caused by the physiological processes of fixed duration, thus enabling the extraction of wavelet modules of arbitrary groups of muscles. Hierarchical clustering and identification of the repeating wavelet modules across subjects and across movements, was used to identify consistent muscle synergies. Results indicate that the most frequently repeated wavelet modules comprised combinations of two muscles that are not traditional agonists and span different joints. We have also found that these wavelet modules were flexibly combined across different movement directions in a pattern resembling directional tuning. This method is extendable to multiple frequency domains and signal modalities.

Effectiveness of the Wavelet Transform on the Surface EMG to Understand the Muscle Fatigue During Walk

NASA Astrophysics Data System (ADS)

Hussain, M. S.; Mamun, Md.

2012-01-01

Muscle fatigue is the decline in ability of a muscle to create force. Electromyography (EMG) is a medical technique for measuring muscle response to nervous stimulation. During a sustained muscle contraction, the power spectrum of the EMG shifts towards lower frequencies. These effects are due to muscle fatigue. Muscle fatigue is often a result of unhealthy work practice. In this research, the effectiveness of the wavelet transform applied to the surface EMG (SEMG) signal as a means of understanding muscle fatigue during walk is presented. Power spectrum and bispectrum analysis on the EMG signal getting from right rectus femoris muscle is executed utilizing various wavelet functions (WFs). It is possible to recognize muscle fatigue appreciably with the proper choice of the WF. The outcome proves that the most momentous changes in the EMG power spectrum are symbolized by WF Daubechies45. Moreover, this research has compared bispectrum properties to the other WFs. To determine muscle fatigue during gait, Daubechies45 is used in this research to analyze the SEMG signal.

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).

Quantification of localized vertebral deformities using a sparse wavelet-based shape model.

PubMed

Zewail, R; Elsafi, A; Durdle, N

2008-01-01

Medical experts often examine hundreds of spine x-ray images to determine existence of various pathologies. Common pathologies of interest are anterior osteophites, disc space narrowing, and wedging. By careful inspection of the outline shapes of the vertebral bodies, experts are able to identify and assess vertebral abnormalities with respect to the pathology under investigation. In this paper, we present a novel method for quantification of vertebral deformation using a sparse shape model. Using wavelets and Independent component analysis (ICA), we construct a sparse shape model that benefits from the approximation power of wavelets and the capability of ICA to capture higher order statistics in wavelet space. The new model is able to capture localized pathology-related shape deformations, hence it allows for quantification of vertebral shape variations. We investigate the capability of the model to predict localized pathology related deformations. Next, using support-vector machines, we demonstrate the diagnostic capabilities of the method through the discrimination of anterior osteophites in lumbar vertebrae. Experiments were conducted using a set of 150 contours from digital x-ray images of lumbar spine. Each vertebra is labeled as normal or abnormal. Results reported in this work focus on anterior osteophites as the pathology of interest.

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.

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.

Segmentation of Polarimetric SAR Images Usig Wavelet Transformation and Texture Features

NASA Astrophysics Data System (ADS)

Rezaeian, A.; Homayouni, S.; Safari, A.

2015-12-01

Polarimetric Synthetic Aperture Radar (PolSAR) sensors can collect useful observations from earth's surfaces and phenomena for various remote sensing applications, such as land cover mapping, change and target detection. These data can be acquired without the limitations of weather conditions, sun illumination and dust particles. As result, SAR images, and in particular Polarimetric SAR (PolSAR) are powerful tools for various environmental applications. Unlike the optical images, SAR images suffer from the unavoidable speckle, which causes the segmentation of this data difficult. In this paper, we use the wavelet transformation for segmentation of PolSAR images. Our proposed method is based on the multi-resolution analysis of texture features is based on wavelet transformation. Here, we use the information of gray level value and the information of texture. First, we produce coherency or covariance matrices and then generate span image from them. In the next step of proposed method is texture feature extraction from sub-bands is generated from discrete wavelet transform (DWT). Finally, PolSAR image are segmented using clustering methods as fuzzy c-means (FCM) and k-means clustering. We have applied the proposed methodology to full polarimetric SAR images acquired by the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) L-band system, during July, in 2012 over an agricultural area in Winnipeg, Canada.

Investigating Neuromagnetic Brain Responses against Chromatic Flickering Stimuli by Wavelet Entropies

PubMed Central

Bhagat, Mayank; Bhushan, Chitresh; Saha, Goutam; Shimjo, Shinsuke; Watanabe, Katsumi; Bhattacharya, Joydeep

2009-01-01

Background Photosensitive epilepsy is a type of reflexive epilepsy triggered by various visual stimuli including colourful ones. Despite the ubiquitous presence of colorful displays, brain responses against different colour combinations are not properly studied. Methodology/Principal Findings Here, we studied the photosensitivity of the human brain against three types of chromatic flickering stimuli by recording neuromagnetic brain responses (magnetoencephalogram, MEG) from nine adult controls, an unmedicated patient, a medicated patient, and two controls age-matched with patients. Dynamical complexities of MEG signals were investigated by a family of wavelet entropies. Wavelet entropy is a newly proposed measure to characterize large scale brain responses, which quantifies the degree of order/disorder associated with a multi-frequency signal response. In particular, we found that as compared to the unmedicated patient, controls showed significantly larger wavelet entropy values. We also found that Renyi entropy is the most powerful feature for the participant classification. Finally, we also demonstrated the effect of combinational chromatic sensitivity on the underlying order/disorder in MEG signals. Conclusions/Significance Our results suggest that when perturbed by potentially epileptic-triggering stimulus, healthy human brain manages to maintain a non-deterministic, possibly nonlinear state, with high degree of disorder, but an epileptic brain represents a highly ordered state which making it prone to hyper-excitation. Further, certain colour combination was found to be more threatening than other combinations. PMID:19779630

Investigating neuromagnetic brain responses against chromatic flickering stimuli by wavelet entropies.

PubMed

Bhagat, Mayank; Bhushan, Chitresh; Saha, Goutam; Shimjo, Shinsuke; Watanabe, Katsumi; Bhattacharya, Joydeep

2009-09-25

Photosensitive epilepsy is a type of reflexive epilepsy triggered by various visual stimuli including colourful ones. Despite the ubiquitous presence of colorful displays, brain responses against different colour combinations are not properly studied. Here, we studied the photosensitivity of the human brain against three types of chromatic flickering stimuli by recording neuromagnetic brain responses (magnetoencephalogram, MEG) from nine adult controls, an unmedicated patient, a medicated patient, and two controls age-matched with patients. Dynamical complexities of MEG signals were investigated by a family of wavelet entropies. Wavelet entropy is a newly proposed measure to characterize large scale brain responses, which quantifies the degree of order/disorder associated with a multi-frequency signal response. In particular, we found that as compared to the unmedicated patient, controls showed significantly larger wavelet entropy values. We also found that Renyi entropy is the most powerful feature for the participant classification. Finally, we also demonstrated the effect of combinational chromatic sensitivity on the underlying order/disorder in MEG signals. Our results suggest that when perturbed by potentially epileptic-triggering stimulus, healthy human brain manages to maintain a non-deterministic, possibly nonlinear state, with high degree of disorder, but an epileptic brain represents a highly ordered state which making it prone to hyper-excitation. Further, certain colour combination was found to be more threatening than other combinations.

Implementing wavelet inverse-transform processor with surface acoustic wave device.

PubMed

Lu, Wenke; Zhu, Changchun; Liu, Qinghong; Zhang, Jingduan

2013-02-01

The objective of this research was to investigate the implementation schemes of the wavelet inverse-transform processor using surface acoustic wave (SAW) device, the length function of defining the electrodes, and the possibility of solving the load resistance and the internal resistance for the wavelet inverse-transform processor using SAW device. In this paper, we investigate the implementation schemes of the wavelet inverse-transform processor using SAW device. In the implementation scheme that the input interdigital transducer (IDT) and output IDT stand in a line, because the electrode-overlap envelope of the input IDT is identical with the one of the output IDT (i.e. the two transducers are identical), the product of the input IDT's frequency response and the output IDT's frequency response can be implemented, so that the wavelet inverse-transform processor can be fabricated. X-112(0)Y LiTaO(3) is used as a substrate material to fabricate the wavelet inverse-transform processor. The size of the wavelet inverse-transform processor using this implementation scheme is small, so its cost is low. First, according to the envelope function of the wavelet function, the length function of the electrodes is defined, then, the lengths of the electrodes can be calculated from the length function of the electrodes, finally, the input IDT and output IDT can be designed according to the lengths and widths for the electrodes. In this paper, we also present the load resistance and the internal resistance as the two problems of the wavelet inverse-transform processor using SAW devices. The solutions to these problems are achieved in this study. When the amplifiers are subjected to the input end and output end for the wavelet inverse-transform processor, they can eliminate the influence of the load resistance and the internal resistance on the output voltage of the wavelet inverse-transform processor using SAW device. Copyright © 2012 Elsevier B.V. All rights reserved.

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital 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.

Islanding detection technique using wavelet energy in grid-connected PV system

NASA Astrophysics Data System (ADS)

Kim, Il Song

2016-08-01

This paper proposes a new islanding detection method using wavelet energy in a grid-connected photovoltaic system. The method detects spectral changes in the higher-frequency components of the point of common coupling voltage and obtains wavelet coefficients by multilevel wavelet analysis. The autocorrelation of the wavelet coefficients can clearly identify islanding detection, even in the variations of the grid voltage harmonics during normal operating conditions. The advantage of the proposed method is that it can detect islanding condition the conventional under voltage/over voltage/under frequency/over frequency methods fail to detect. The theoretical method to obtain wavelet energies is evolved and verified by the experimental result.

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.

Interpretations of gravity and magnetic anomalies in the Songliao Basin with Wavelet Multi-scale Decomposition

NASA Astrophysics Data System (ADS)

Li, Changbo; Wang, Liangshu; Sun, Bin; Feng, Runhai; Wu, Yongjing

2015-09-01

In this paper, we introduce the method of Wavelet Multi-scale Decomposition (WMD) combined with Power Spectrum Analysis (PSA) for the separation of regional gravity and magnetic anomalies. The Songliao Basin is situated between the Siberian Plate and the North China Plate, and its main structural trend of gravity and magnetic anomaly fields is NNE. The study area shows a significant feature of deep collage-type construction. According to the feature of gravity field, the region was divided into five sub-regions. The gravity and magnetic fields of the Songliao Basin were separated using WMD with a 4th order separation. The apparent depth of anomalies in each order was determined by Logarithmic PSA. Then, the shallow high-frequency anomalies were removed and the 2nd-4th order wavelet detail anomalies were used to study the basin's major faults. Twenty-six faults within the basement were recognized. The 4th order wavelet approximate anomalies were used for the inversion of the Moho discontinuity and the Curie isothermal surface.

Scope and applications of translation invariant wavelets to image registration

NASA Technical Reports Server (NTRS)

Chettri, Samir; LeMoigne, Jacqueline; Campbell, William

1997-01-01

The first part of this article introduces the notion of translation invariance in wavelets and discusses several wavelets that have this property. The second part discusses the possible applications of such wavelets to image registration. In the case of registration of affinely transformed images, we would conclude that the notion of translation invariance is not really necessary. What is needed is affine invariance and one way to do this is via the method of moment invariants. Wavelets or, in general, pyramid processing can then be combined with the method of moment invariants to reduce the computational load.

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.

Fast reversible wavelet image compressor

NASA Astrophysics Data System (ADS)

Kim, HyungJun; Li, Ching-Chung

1996-10-01

We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filters can be preformed by using only arithmetic shifting and addition operations. Wavelet coefficients can be encoded with an arithmetic coder which also uses arithmetic shifting and addition operations. Therefore, from the beginning to the end, the while encoding/decoding process can be done within a short period of time. The proposed method naturally extends form the lossless compression to the lossy but high compression range and can be easily adapted to the progressive reconstruction.

Recent advances in wavelet technology

NASA Technical Reports Server (NTRS)

Wells, R. O., Jr.

1994-01-01

Wavelet research has been developing rapidly over the past five years, and in particular in the academic world there has been significant activity at numerous universities. In the industrial world, there has been developments at Aware, Inc., Lockheed, Martin-Marietta, TRW, Kodak, Exxon, and many others. The government agencies supporting wavelet research and development include ARPA, ONR, AFOSR, NASA, and many other agencies. The recent literature in the past five years includes a recent book which is an index of citations in the past decade on this subject, and it contains over 1,000 references and abstracts.

Variable mass pendulum behaviour processed by wavelet analysis

NASA Astrophysics Data System (ADS)

Caccamo, M. T.; Magazù, S.

2017-01-01

The present work highlights how, in order to characterize the motion of a variable mass pendulum, wavelet analysis can be an effective tool in furnishing information on the time evolution of the oscillation spectral content. In particular, the wavelet transform is applied to process the motion of a hung funnel that loses fine sand at an exponential rate; it is shown how, in contrast to the Fourier transform which furnishes only an average frequency value for the motion, the wavelet approach makes it possible to perform a joint time-frequency analysis. The work is addressed at undergraduate and graduate students.

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.

Double Density Dual Tree Discrete Wavelet Transform implementation for Degraded Image Enhancement

NASA Astrophysics Data System (ADS)

Vimala, C.; Aruna Priya, P.

2018-04-01

Wavelet transform is a main tool for image processing applications in modern existence. A Double Density Dual Tree Discrete Wavelet Transform is used and investigated for image denoising. Images are considered for the analysis and the performance is compared with discrete wavelet transform and the Double Density DWT. Peak Signal to Noise Ratio values and Root Means Square error are calculated in all the three wavelet techniques for denoised images and the performance has evaluated. The proposed techniques give the better performance when comparing other two wavelet techniques.

Adaptive Filtering in the Wavelet Transform Domain via Genetic Algorithms

DTIC Science & Technology

2004-08-06

wavelet transforms. Whereas the term “evolved” pertains only to the altered wavelet coefficients used during the inverse transform process. 2...words, the inverse transform produces the original signal x(t) from the wavelet and scaling coefficients. )()( ,, tdtx nk n nk k ψ...reconstruct the original signal as accurately as possible. The inverse transform reconstructs an approximation of the original signal (Burrus

Graph wavelet alignment kernels for drug virtual screening.

PubMed

Smalter, Aaron; Huan, Jun; Lushington, Gerald

2009-06-01

In this paper, we introduce a novel statistical modeling technique for target property prediction, with applications to virtual screening and drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to summarize features capturing graph local topology. We design a novel graph kernel function to utilize the topology features to build predictive models for chemicals via Support Vector Machine classifier. We call the new graph kernel a graph wavelet-alignment kernel. We have evaluated the efficacy of the wavelet-alignment kernel using a set of chemical structure-activity prediction benchmarks. Our results indicate that the use of the kernel function yields performance profiles comparable to, and sometimes exceeding that of the existing state-of-the-art chemical classification approaches. In addition, our results also show that the use of wavelet functions significantly decreases the computational costs for graph kernel computation with more than ten fold speedup.

Characterization and Simulation of Gunfire with Wavelets

DOE PAGES

Smallwood, David O.

1999-01-01

Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The structural response to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The current paper will explore a method to describe the nonstationary random process using a wavelet transform. The gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. A wavelet transform is performed on each of thesemore » records. The gunfire is simulated by generating realizations of records of a single-round firing by computing an inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously analyzed gunfire record. The individual records are assembled into a realization of many rounds firing. A second-order correction of the probability density function is accomplished with a zero memory nonlinear function. The method is straightforward, easy to implement, and produces a simulated record much like the measured gunfire record.« less

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

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.

Image denoising via fundamental anisotropic diffusion and wavelet shrinkage: a comparative study

NASA Astrophysics Data System (ADS)

Bayraktar, Bulent; Analoui, Mostafa

2004-05-01

Noise removal faces a challenge: Keeping the image details. Resolving the dilemma of two purposes (smoothing and keeping image features in tact) working inadvertently of each other was an almost impossible task until anisotropic dif-fusion (AD) was formally introduced by Perona and Malik (PM). AD favors intra-region smoothing over inter-region in piecewise smooth images. Many authors regularized the original PM algorithm to overcome its drawbacks. We compared the performance of denoising using such 'fundamental' AD algorithms and one of the most powerful multiresolution tools available today, namely, wavelet shrinkage. The AD algorithms here are called 'fundamental' in the sense that the regularized versions center around the original PM algorithm with minor changes to the logic. The algorithms are tested with different noise types and levels. On top of the visual inspection, two mathematical metrics are used for performance comparison: Signal-to-noise ratio (SNR) and universal image quality index (UIQI). We conclude that some of the regu-larized versions of PM algorithm (AD) perform comparably with wavelet shrinkage denoising. This saves a lot of compu-tational power. With this conclusion, we applied the better-performing fundamental AD algorithms to a new imaging modality: Optical Coherence Tomography (OCT).

Improvement of electrocardiogram by empirical wavelet transform

NASA Astrophysics Data System (ADS)

Chanchang, Vikanda; Kumchaiseemak, Nakorn; Sutthiopad, Malee; Luengviriya, Chaiya

2017-09-01

Electrocardiogram (ECG) is a crucial tool in the detection of cardiac arrhythmia. It is also often used in a routine physical exam, especially, for elderly people. This graphical representation of electrical activity of heart is obtained by a measurement of voltage at the skin; therefore, the signal is always contaminated by noise from various sources. For a proper interpretation, the quality of the ECG should be improved by a noise reduction. In this article, we present a study of a noise filtration in the ECG by using an empirical wavelet transform (EWT). Unlike the traditional wavelet method, EWT is adaptive since the frequency spectrum of the ECG is taken into account in the construction of the wavelet basis. We show that the signal-to-noise ratio increases after the noise filtration for different noise artefacts.

Time-frequency causality between stock prices and exchange rates: Further evidences from cointegration and wavelet analysis

NASA Astrophysics Data System (ADS)

Afshan, Sahar; Sharif, Arshian; Loganathan, Nanthakumar; Jammazi, Rania

2018-04-01

The current study investigates the relationship between stock prices and exchange rate by using wavelets approach and more focused the continuous, power spectrum, cross and coherence wavelet. The result of Bayer and Hanck (2013) and Gregory and Hansen (1996) confirm the presence of long-run association between stock price and exchange rate in Pakistan. The results of wavelet coherence reveal the dominance of SP during 2005-2006 and 2011-2012 in the period of 8-16 and 16-32 weeks cycle in approximately all the exchange rates against Pakistani rupees. For almost the entire studied period in long scale, the study evidences the strong coherence between both the series. The most interesting part of this coherence is the existence of bidirectional causality in the long timescale. The arrows in this long region are pointing both left up and left down. This suggests that during the time period, our variables are exhibiting out phase relationship with mutually leading and lagging the market. These results are in contrast with many earlier studies of Pakistan.

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

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.

Evidence of Large Fluctuations of Stock Return and Financial Crises from Turkey: Using Wavelet Coherency and Varma Modeling to Forecast Stock Return

NASA Astrophysics Data System (ADS)

Oygur, Tunc; Unal, Gazanfer

Shocks, jumps, booms and busts are typical large fluctuation markers which appear in crisis. Models and leading indicators vary according to crisis type in spite of the fact that there are a lot of different models and leading indicators in literature to determine structure of crisis. In this paper, we investigate structure of dynamic correlation of stock return, interest rate, exchange rate and trade balance differences in crisis periods in Turkey over the period between October 1990 and March 2015 by applying wavelet coherency methodologies to determine nature of crises. The time period includes the Turkeys currency and banking crises; US sub-prime mortgage crisis and the European sovereign debt crisis occurred in 1994, 2001, 2008 and 2009, respectively. Empirical results showed that stock return, interest rate, exchange rate and trade balance differences are significantly linked during the financial crises in Turkey. The cross wavelet power, the wavelet coherency, the multiple wavelet coherency and the quadruple wavelet coherency methodologies have been used to examine structure of dynamic correlation. Moreover, in consequence of quadruple and multiple wavelet coherence, strongly correlated large scales indicate linear behavior and, hence VARMA (vector autoregressive moving average) gives better fitting and forecasting performance. In addition, increasing the dimensions of the model for strongly correlated scales leads to more accurate results compared to scalar counterparts.

Rendering of 3D-wavelet-compressed concentric mosaic scenery with progressive inverse wavelet synthesis (PIWS)

NASA Astrophysics Data System (ADS)

Wu, Yunnan; Luo, Lin; Li, Jin; Zhang, Ya-Qin

2000-05-01

The concentric mosaics offer a quick solution to the construction and navigation of a virtual environment. To reduce the vast data amount of the concentric mosaics, a compression scheme based on 3D wavelet transform has been proposed in a previous paper. In this work, we investigate the efficient implementation of the renderer. It is preferable not to expand the compressed bitstream as a whole, so that the memory consumption of the renderer can be reduced. Instead, only the data necessary to render the current view are accessed and decoded. The progressive inverse wavelet synthesis (PIWS) algorithm is proposed to provide the random data access and to reduce the calculation for the data access requests to a minimum. A mixed cache is used in PIWS, where the entropy decoded wavelet coefficient, intermediate result of lifting and fully synthesized pixel are all stored at the same memory unit because of the in- place calculation property of the lifting implementation. PIWS operates with a finite state machine, where each memory unit is attached with a state to indicate what type of content is currently stored. The computational saving achieved by PIWS is demonstrated with extensive experiment results.

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.

Wavelet entropy of BOLD time series: An application to Rolandic epilepsy.

PubMed

Gupta, Lalit; Jansen, Jacobus F A; Hofman, Paul A M; Besseling, René M H; de Louw, Anton J A; Aldenkamp, Albert P; Backes, Walter H

2017-12-01

To assess the wavelet entropy for the characterization of intrinsic aberrant temporal irregularities in the time series of resting-state blood-oxygen-level-dependent (BOLD) signal fluctuations. Further, to evaluate the temporal irregularities (disorder/order) on a voxel-by-voxel basis in the brains of children with Rolandic epilepsy. The BOLD time series was decomposed using the discrete wavelet transform and the wavelet entropy was calculated. Using a model time series consisting of multiple harmonics and nonstationary components, the wavelet entropy was compared with Shannon and spectral (Fourier-based) entropy. As an application, the wavelet entropy in 22 children with Rolandic epilepsy was compared to 22 age-matched healthy controls. The images were obtained by performing resting-state functional magnetic resonance imaging (fMRI) using a 3T system, an 8-element receive-only head coil, and an echo planar imaging pulse sequence ( T2*-weighted). The wavelet entropy was also compared to spectral entropy, regional homogeneity, and Shannon entropy. Wavelet entropy was found to identify the nonstationary components of the model time series. In Rolandic epilepsy patients, a significantly elevated wavelet entropy was observed relative to controls for the whole cerebrum (P = 0.03). Spectral entropy (P = 0.41), regional homogeneity (P = 0.52), and Shannon entropy (P = 0.32) did not reveal significant differences. The wavelet entropy measure appeared more sensitive to detect abnormalities in cerebral fluctuations represented by nonstationary effects in the BOLD time series than more conventional measures. This effect was observed in the model time series as well as in Rolandic epilepsy. These observations suggest that the brains of children with Rolandic epilepsy exhibit stronger nonstationary temporal signal fluctuations than controls. 2 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2017;46:1728-1737. © 2017 International Society for Magnetic

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.

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.

Application of time-resolved glucose concentration photoacoustic signals based on an improved wavelet denoising

NASA Astrophysics Data System (ADS)

Ren, Zhong; Liu, Guodong; Huang, Zhen

2014-10-01

Real-time monitoring of blood glucose concentration (BGC) is a great important procedure in controlling diabetes mellitus and preventing the complication for diabetic patients. Noninvasive measurement of BGC has already become a research hotspot because it can overcome the physical and psychological harm. Photoacoustic spectroscopy is a well-established, hybrid and alternative technique used to determine the BGC. According to the theory of photoacoustic technique, the blood is irradiated by plused laser with nano-second repeation time and micro-joule power, the photoacoustic singals contained the information of BGC are generated due to the thermal-elastic mechanism, then the BGC level can be interpreted from photoacoustic signal via the data analysis. But in practice, the time-resolved photoacoustic signals of BGC are polluted by the varities of noises, e.g., the interference of background sounds and multi-component of blood. The quality of photoacoustic signal of BGC directly impacts the precision of BGC measurement. So, an improved wavelet denoising method was proposed to eliminate the noises contained in BGC photoacoustic signals. To overcome the shortcoming of traditional wavelet threshold denoising, an improved dual-threshold wavelet function was proposed in this paper. Simulation experimental results illustrated that the denoising result of this improved wavelet method was better than that of traditional soft and hard threshold function. To varify the feasibility of this improved function, the actual photoacoustic BGC signals were test, the test reslut demonstrated that the signal-to-noises ratio(SNR) of the improved function increases about 40-80%, and its root-mean-square error (RMSE) decreases about 38.7-52.8%.

Optical asymmetric image encryption using gyrator wavelet transform

NASA Astrophysics Data System (ADS)

Mehra, Isha; Nishchal, Naveen K.

2015-11-01

In this paper, we propose a new optical information processing tool termed as gyrator wavelet transform to secure a fully phase image, based on amplitude- and phase-truncation approach. The gyrator wavelet transform constitutes four basic parameters; gyrator transform order, type and level of mother wavelet, and position of different frequency bands. These parameters are used as encryption keys in addition to the random phase codes to the optical cryptosystem. This tool has also been applied for simultaneous compression and encryption of an image. The system's performance and its sensitivity to the encryption parameters, such as, gyrator transform order, and robustness has also been analyzed. It is expected that this tool will not only update current optical security systems, but may also shed some light on future developments. The computer simulation results demonstrate the abilities of the gyrator wavelet transform as an effective tool, which can be used in various optical information processing applications, including image encryption, and image compression. Also this tool can be applied for securing the color image, multispectral, and three-dimensional images.

Wavelet Analysis of SAR Images for Coastal Monitoring

NASA Technical Reports Server (NTRS)

Liu, Antony K.; Wu, Sunny Y.; Tseng, William Y.; Pichel, William G.

1998-01-01

The mapping of mesoscale ocean features in the coastal zone is a major potential application for satellite data. The evolution of mesoscale features such as oil slicks, fronts, eddies, and ice edge can be tracked by the wavelet analysis using satellite data from repeating paths. The wavelet transform has been applied to satellite images, such as those from Synthetic Aperture Radar (SAR), Advanced Very High-Resolution Radiometer (AVHRR), and ocean color sensor for feature extraction. In this paper, algorithms and techniques for automated detection and tracking of mesoscale features from satellite SAR imagery employing wavelet analysis have been developed. Case studies on two major coastal oil spills have been investigated using wavelet analysis for tracking along the coast of Uruguay (February 1997), and near Point Barrow, Alaska (November 1997). Comparison of SAR images with SeaWiFS (Sea-viewing Wide Field-of-view Sensor) data for coccolithophore bloom in the East Bering Sea during the fall of 1997 shows a good match on bloom boundary. This paper demonstrates that this technique is a useful and promising tool for monitoring of coastal waters.

Wavelet packets for multi- and hyper-spectral imagery

NASA Astrophysics Data System (ADS)

Benedetto, J. J.; Czaja, W.; Ehler, M.; Flake, C.; Hirn, M.

2010-01-01

State of the art dimension reduction and classification schemes in multi- and hyper-spectral imaging rely primarily on the information contained in the spectral component. To better capture the joint spatial and spectral data distribution we combine the Wavelet Packet Transform with the linear dimension reduction method of Principal Component Analysis. Each spectral band is decomposed by means of the Wavelet Packet Transform and we consider a joint entropy across all the spectral bands as a tool to exploit the spatial information. Dimension reduction is then applied to the Wavelet Packets coefficients. We present examples of this technique for hyper-spectral satellite imaging. We also investigate the role of various shrinkage techniques to model non-linearity in our approach.

Comparisons between real and complex Gauss wavelet transform methods of three-dimensional shape reconstruction

NASA Astrophysics Data System (ADS)

Xu, Luopeng; Dan, Youquan; Wang, Qingyuan

2015-10-01

The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.

Wavelets on the Group SO(3) and the Sphere S3

NASA Astrophysics Data System (ADS)

Bernstein, Swanhild

2007-09-01

The construction of wavelets relies on translations and dilations which are perfectly given in R. On the sphere translations can be considered as rotations but it difficult to say what are dilations. For the 2-dimensional sphere there exist two different approaches to obtain wavelets which are worth to be considered. The first concept goes back to Freeden and collaborators [2] which defines wavelets by means of kernels of spherical singular integrals. The other concept developed by Antoine and Vandergheynst and coworkers [3] is a purely group theoretical approach and defines dilations as dilations in the tangent plane. Surprisingly both concepts coincides for zonal functions. We will define wavelets on the 3-dimensional sphere by means of kernels of singular integrals and demonstrate that wavelets constructed by Antoine and Vandergheynst for zonal functions meet our definition.

Analysis and Synthesis of Pseudo-Periodic[InlineEquation not available: see fulltext.]-Like Noise by Means of Wavelets with Applications to Digital Audio

NASA Astrophysics Data System (ADS)

Polotti, Pietro; Evangelista, Gianpaolo

2001-12-01

Voiced musical sounds have nonzero energy in sidebands of the frequency partials. Our work is based on the assumption, often experimentally verified, that the energy distribution of the sidebands is shaped as powers of the inverse of the distance from the closest partial. The power spectrum of these pseudo-periodic processes is modeled by means of a superposition of modulated[InlineEquation not available: see fulltext.] components, that is, by a pseudo-periodic[InlineEquation not available: see fulltext.]-like process. Due to the fundamental selfsimilar character of the wavelet transform,[InlineEquation not available: see fulltext.] processes can be fruitfully analyzed and synthesized by means of wavelets. We obtain a set of very loosely correlated coefficients at each scale level that can be well approximated by white noise in the synthesis process. Our computational scheme is based on an orthogonal[InlineEquation not available: see fulltext.]-band filter bank and a dyadic wavelet transform per channel. The[InlineEquation not available: see fulltext.] channels are tuned to the left and right sidebands of the harmonics so that sidebands are mutually independent. The structure computes the expansion coefficients of a new orthogonal and complete set of harmonic-band wavelets. The main point of our scheme is that we need only two parameters per harmonic in order to model the stochastic fluctuations of sounds from a pure periodic behavior.

ON THE BASIS PROPERTY OF THE HAAR SYSTEM IN THE SPACE \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack) AND THE PRINCIPLE OF LOCALIZATION IN THE MEAN

NASA Astrophysics Data System (ADS)

Sharapudinov, I. I.

1987-02-01

Let p=p(t) be a measurable function defined on \\lbrack0,\\,1\\rbrack. If p(t) is essentially bounded on \\lbrack0,\\,1\\rbrack, denote by \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack) the set of measurable functions f defined on \\lbrack0,\\,1\\rbrack for which \\int_0^1\\vert f(t)\\vert^{p(t)}dt<\\infty. The space \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack) with p(t)\\geqslant 1 is a normed space with norm \\displaystyle \\vert\\vert f\\vert\\vert _p=\\inf\\bigg\\{\\alpha>0:\\,\\int_0^1\\bigg\\vert\\frac{f(t)}{\\alpha}\\bigg\\vert^{p(t)}dt\\leqslant1\\bigg\\}.This paper examines the question of whether the Haar system is a basis in \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack). Conditions that are in a certain sense definitive on the function p(t) in order that the Haar system be a basis of \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack) are obtained. The concept of a localization principle in the mean is introduced, and its connection with the space \\mathscr{L}^{p(t)}(\\lbrack0,\\,1\\rbrack) is exhibited.Bibliography: 2 titles.

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.

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

Determination of phase from the ridge of CWT using generalized Morse wavelet

NASA Astrophysics Data System (ADS)

Kocahan, Ozlem; Tiryaki, Erhan; Coskun, Emre; Ozder, Serhat

2018-03-01

The selection of wavelet is an important step in order to determine the phase from the fringe patterns. In the present work, a new wavelet for phase retrieval from the ridge of continuous wavelet transform (CWT) is presented. The phase distributions have been extracted from the optical fringe pattern by choosing the zero order generalized morse wavelet (GMW) as a mother wavelet. The aim of the study is to reveal the ways in which the two varying parameters of GMW affect the phase calculation. To show the validity of this method, an experimental study has been conducted by using the diffraction phase microscopy (DPM) setup; consequently, the profiles of red blood cells have been retrieved. The results for the CWT ridge technique with GMW have been compared with the results for the Morlet wavelet and the Paul wavelet; the results are almost identical for Paul and zero order GMW because of their degree of freedom. Also, for further discussion, the Fourier transform and the Stockwell transform have been applied comparatively. The outcome of the comparison reveals that GMWs are highly applicable to the research in various areas, predominantly biomedicine.

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.

Fringe pattern information retrieval using wavelets

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.; Patimo, Caterina; Manicone, Pasquale D.; Lamberti, Luciano

2005-08-01

Two-dimensional phase modulation is currently the basic model used in the interpretation of fringe patterns that contain displacement information, moire, holographic interferometry, speckle techniques. Another way to look to these two-dimensional signals is to consider them as frequency modulated signals. This alternative interpretation has practical implications similar to those that exist in radio engineering for handling frequency modulated signals. Utilizing this model it is possible to obtain frequency information by using the energy approach introduced by Ville in 1944. A natural complementary tool of this process is the wavelet methodology. The use of wavelet makes it possible to obtain the local values of the frequency in a one or two dimensional domain without the need of previous phase retrieval and differentiation. Furthermore from the properties of wavelets it is also possible to obtain at the same time the phase of the signal with the advantage of a better noise removal capabilities and the possibility of developing simpler algorithms for phase unwrapping due to the availability of the derivative of the phase.

Pattern recognition of concrete surface cracks and defects using integrated image processing algorithms

NASA Astrophysics Data System (ADS)

Balbin, Jessie R.; Hortinela, Carlos C.; Garcia, Ramon G.; Baylon, Sunnycille; Ignacio, Alexander Joshua; Rivera, Marco Antonio; Sebastian, Jaimie

2017-06-01

Pattern recognition of concrete surface crack defects is very important in determining stability of structure like building, roads or bridges. Surface crack is one of the subjects in inspection, diagnosis, and maintenance as well as life prediction for the safety of the structures. Traditionally determining defects and cracks on concrete surfaces are done manually by inspection. Moreover, any internal defects on the concrete would require destructive testing for detection. The researchers created an automated surface crack detection for concrete using image processing techniques including Hough transform, LoG weighted, Dilation, Grayscale, Canny Edge Detection and Haar Wavelet Transform. An automatic surface crack detection robot is designed to capture the concrete surface by sectoring method. Surface crack classification was done with the use of Haar trained cascade object detector that uses both positive samples and negative samples which proved that it is possible to effectively identify the surface crack defects.

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.

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.

Necessary and sufficient condition for the realization of the complex wavelet

NASA Astrophysics Data System (ADS)

Keita, Alpha; Qing, Qianqin; Wang, Nengchao

1997-04-01

Wavelet theory is a whole new signal analysis theory in recent years, and the appearance of which is attracting lots of experts in many different fields giving it a deepen study. Wavelet transformation is a new kind of time. Frequency domain analysis method of localization in can-be- realized time domain or frequency domain. It has many perfect characteristics that many other kinds of time frequency domain analysis, such as Gabor transformation or Viginier. For example, it has orthogonality, direction selectivity, variable time-frequency domain resolution ratio, adjustable local support, parsing data in little amount, and so on. All those above make wavelet transformation a very important new tool and method in signal analysis field. Because the calculation of complex wavelet is very difficult, in application, real wavelet function is used. In this paper, we present a necessary and sufficient condition that the real wavelet function can be obtained by the complex wavelet function. This theorem has some significant values in theory. The paper prepares its technique from Hartley transformation, then, it gives the complex wavelet was a signal engineering expert. His Hartley transformation, which also mentioned by Hartley, had been overlooked for about 40 years, for the social production conditions at that time cannot help to show its superiority. Only when it came to the end of 70s and the early 80s, after the development of the fast algorithm of Fourier transformation and the hardware implement to some degree, the completely some positive-negative transforming method was coming to take seriously. W transformation, which mentioned by Zhongde Wang, pushed the studying work of Hartley transformation and its fast algorithm forward. The kernel function of Hartley transformation.

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.

Necessary and sufficient conditions for discrete wavelet frames in CN

NASA Astrophysics Data System (ADS)

Deepshikha; Vashisht, Lalit K.

2017-07-01

We present necessary and sufficient conditions with explicit frame bounds for a discrete wavelet system of the form {DaTk ϕ } a ∈ U(N) , k ∈IN to be a frame for the unitary space CN. It is shown that the canonical dual of a discrete wavelet frame for CN has the same structure. This is not true (well known) for canonical dual of a wavelet frame for L2(R) . Several numerical examples are given to illustrate the results.

Multiscale peak detection in wavelet space.

PubMed

Zhang, Zhi-Min; Tong, Xia; Peng, Ying; Ma, Pan; Zhang, Ming-Jin; Lu, Hong-Mei; Chen, Xiao-Qing; Liang, Yi-Zeng

2015-12-07

Accurate peak detection is essential for analyzing high-throughput datasets generated by analytical instruments. Derivatives with noise reduction and matched filtration are frequently used, but they are sensitive to baseline variations, random noise and deviations in the peak shape. A continuous wavelet transform (CWT)-based method is more practical and popular in this situation, which can increase the accuracy and reliability by identifying peaks across scales in wavelet space and implicitly removing noise as well as the baseline. However, its computational load is relatively high and the estimated features of peaks may not be accurate in the case of peaks that are overlapping, dense or weak. In this study, we present multi-scale peak detection (MSPD) by taking full advantage of additional information in wavelet space including ridges, valleys, and zero-crossings. It can achieve a high accuracy by thresholding each detected peak with the maximum of its ridge. It has been comprehensively evaluated with MALDI-TOF spectra in proteomics, the CAMDA 2006 SELDI dataset as well as the Romanian database of Raman spectra, which is particularly suitable for detecting peaks in high-throughput analytical signals. Receiver operating characteristic (ROC) curves show that MSPD can detect more true peaks while keeping the false discovery rate lower than MassSpecWavelet and MALDIquant methods. Superior results in Raman spectra suggest that MSPD seems to be a more universal method for peak detection. MSPD has been designed and implemented efficiently in Python and Cython. It is available as an open source package at .

Wavelet Representation of the Corneal Pulse for Detecting Ocular Dicrotism

PubMed Central

Melcer, Tomasz; Danielewska, Monika E.; Iskander, D. Robert

2015-01-01

Purpose To develop a reliable and powerful method for detecting the ocular dicrotism from non-invasively acquired signals of corneal pulse without the knowledge of the underlying cardiopulmonary information present in signals of ocular blood pulse and the electrical heart activity. Methods Retrospective data from a study on glaucomatous and age-related changes in corneal pulsation [PLOS ONE 9(7),(2014):e102814] involving 261 subjects was used. Continuous wavelet representation of the signal derivative of the corneal pulse was considered with a complex Gaussian derivative function chosen as mother wavelet. Gray-level Co-occurrence Matrix has been applied to the image (heat-maps) of CWT to yield a set of parameters that can be used to devise the ocular dicrotic pulse detection schemes based on the Conditional Inference Tree and the Random Forest models. The detection scheme was first tested on synthetic signals resembling those of a dicrotic and a non-dicrotic ocular pulse before being used on all 261 real recordings. Results A detection scheme based on a single feature of the Continuous Wavelet Transform of the corneal pulse signal resulted in a low detection rate. Conglomeration of a set of features based on measures of texture (homogeneity, correlation, energy, and contrast) resulted in a high detection rate reaching 93%. Conclusion It is possible to reliably detect a dicrotic ocular pulse from the signals of corneal pulsation without the need of acquiring additional signals related to heart activity, which was the previous state-of-the-art. The proposed scheme can be applied to other non-stationary biomedical signals related to ocular dynamics. PMID:25906236

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.

Doppler radar fall activity detection using the wavelet transform.

PubMed

Su, Bo Yu; Ho, K C; Rantz, Marilyn J; Skubic, Marjorie

2015-03-01

We propose in this paper the use of Wavelet transform (WT) to detect human falls using a ceiling mounted Doppler range control radar. The radar senses any motions from falls as well as nonfalls due to the Doppler effect. The WT is very effective in distinguishing the falls from other activities, making it a promising technique for radar fall detection in nonobtrusive inhome elder care applications. The proposed radar fall detector consists of two stages. The prescreen stage uses the coefficients of wavelet decomposition at a given scale to identify the time locations in which fall activities may have occurred. The classification stage extracts the time-frequency content from the wavelet coefficients at many scales to form a feature vector for fall versus nonfall classification. The selection of different wavelet functions is examined to achieve better performance. Experimental results using the data from the laboratory and real inhome environments validate the promising and robust performance of the proposed detector.

Wavelet-domain de-noising technique for THz pulsed spectroscopy

NASA Astrophysics Data System (ADS)

Chernomyrdin, Nikita V.; Zaytsev, Kirill I.; Gavdush, Arsenii A.; Fokina, Irina N.; Karasik, Valeriy E.; Reshetov, Igor V.; Kudrin, Konstantin G.; Nosov, Pavel A.; Yurchenko, Stanislav O.

2014-09-01

De-noising of terahertz (THz) pulsed spectroscopy (TPS) data is an essential problem, since a noise in the TPS system data prevents correct reconstruction of the sample spectral dielectric properties and to perform the sample internal structure studying. There are certain regions in TPS signal Fourier spectrum, where Fourier-domain signal-to-noise ratio is relatively small. Effective de-noising might potentially expand the range of spectrometer spectral sensitivity and reduce the time of waveform registration, which is an essential problem for biomedical applications of TPS. In this work, it is shown how the recent progress in signal processing in wavelet-domain could be used for TPS waveforms de-noising. It demonstrates the ability to perform effective de-noising of TPS data using the algorithm of the Fast Wavelet Transform (FWT). The results of the optimal wavelet basis selection and wavelet-domain thresholding technique selection are reported. Developed technique is implemented for reconstruction of in vivo healthy and deseased skin samplesspectral characteristics at THz frequency range.

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.

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.

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.

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.

Evaluation of the Use of Second Generation Wavelets in the Coherent Vortex Simulation Approach

NASA Technical Reports Server (NTRS)

Goldstein, D. E.; Vasilyev, O. V.; Wray, A. A.; Rogallo, R. S.

2000-01-01

The objective of this study is to investigate the use of the second generation bi-orthogonal wavelet transform for the field decomposition in the Coherent Vortex Simulation of turbulent flows. The performances of the bi-orthogonal second generation wavelet transform and the orthogonal wavelet transform using Daubechies wavelets with the same number of vanishing moments are compared in a priori tests using a spectral direct numerical simulation (DNS) database of isotropic turbulence fields: 256(exp 3) and 512(exp 3) DNS of forced homogeneous turbulence (Re(sub lambda) = 168) and 256(exp 3) and 512(exp 3) DNS of decaying homogeneous turbulence (Re(sub lambda) = 55). It is found that bi-orthogonal second generation wavelets can be used for coherent vortex extraction. The results of a priori tests indicate that second generation wavelets have better compression and the residual field is closer to Gaussian. However, it was found that the use of second generation wavelets results in an integral length scale for the incoherent part that is larger than that derived from orthogonal wavelets. A way of dealing with this difficulty is suggested.

A wavelet approach to binary blackholes with asynchronous multitasking

NASA Astrophysics Data System (ADS)

Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo

2016-03-01

Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.

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.

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.

ECG denoising with adaptive bionic wavelet transform.

PubMed

Sayadi, Omid; Shamsollahi, Mohammad Bagher

2006-01-01

In this paper a new ECG denoising scheme is proposed using a novel adaptive wavelet transform, named bionic wavelet transform (BWT), which had been first developed based on a model of the active auditory system. There has been some outstanding features with the BWT such as nonlinearity, high sensitivity and frequency selectivity, concentrated energy distribution and its ability to reconstruct signal via inverse transform but the most distinguishing characteristic of BWT is that its resolution in the time-frequency domain can be adaptively adjusted not only by the signal frequency but also by the signal instantaneous amplitude and its first-order differential. Besides by optimizing the BWT parameters parallel to modifying a new threshold value, one can handle ECG denoising with results comparing to those of wavelet transform (WT). Preliminary tests of BWT application to ECG denoising were constructed on the signals of MIT-BIH database which showed high performance of noise reduction.

Identification of particle-laden flow features from wavelet decomposition

NASA Astrophysics Data System (ADS)

Jackson, A.; Turnbull, B.

2017-12-01

A wavelet decomposition based technique is applied to air pressure data obtained from laboratory-scale powder snow avalanches. This technique is shown to be a powerful tool for identifying both repeatable and chaotic features at any frequency within the signal. Additionally, this technique is demonstrated to be a robust method for the removal of noise from the signal as well as being capable of removing other contaminants from the signal. Whilst powder snow avalanches are the focus of the experiments analysed here, the features identified can provide insight to other particle-laden gravity currents and the technique described is applicable to a wide variety of experimental signals.

Properties of wavelet discretization of Black-Scholes equation

NASA Astrophysics Data System (ADS)

Finěk, Václav

2017-07-01

Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.

Stationary wavelet transform for under-sampled MRI reconstruction.

PubMed

Kayvanrad, Mohammad H; McLeod, A Jonathan; Baxter, John S H; McKenzie, Charles A; Peters, Terry M

2014-12-01

In addition to coil sensitivity data (parallel imaging), sparsity constraints are often used as an additional lp-penalty for under-sampled MRI reconstruction (compressed sensing). Penalizing the traditional decimated wavelet transform (DWT) coefficients, however, results in visual pseudo-Gibbs artifacts, some of which are attributed to the lack of translation invariance of the wavelet basis. We show that these artifacts can be greatly reduced by penalizing the translation-invariant stationary wavelet transform (SWT) coefficients. This holds with various additional reconstruction constraints, including coil sensitivity profiles and total variation. Additionally, SWT reconstructions result in lower error values and faster convergence compared to DWT. These concepts are illustrated with extensive experiments on in vivo MRI data with particular emphasis on multiple-channel acquisitions. Copyright © 2014 Elsevier Inc. All rights reserved.

[A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

PubMed

Zhonggang, Liang; Hong, Yan

2006-10-01

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

Wavelet Compression of Satellite-Transmitted Digital Mammograms

NASA Technical Reports Server (NTRS)

Zheng, Yuan F.

2001-01-01

Breast cancer is one of the major causes of cancer death in women in the United States. The most effective way to treat breast cancer is to detect it at an early stage by screening patients periodically. Conventional film-screening mammography uses X-ray films which are effective in detecting early abnormalities of the breast. Direct digital mammography has the potential to improve the image quality and to take advantages of convenient storage, efficient transmission, and powerful computer-aided diagnosis, etc. One effective alternative to direct digital imaging is secondary digitization of X-ray films. This technique may not provide as high an image quality as the direct digital approach, but definitely have other advantages inherent to digital images. One of them is the usage of satellite-transmission technique for transferring digital mammograms between a remote image-acquisition site and a central image-reading site. This technique can benefit a large population of women who reside in remote areas where major screening and diagnosing facilities are not available. The NASA-Lewis Research Center (LeRC), in collaboration with the Cleveland Clinic Foundation (CCF), has begun a pilot study to investigate the application of the Advanced Communications Technology Satellite (ACTS) network to telemammography. The bandwidth of the T1 transmission is limited (1.544 Mbps) while the size of a mammographic image is huge. It takes a long time to transmit a single mammogram. For example, a mammogram of 4k by 4k pixels with 16 bits per pixel needs more than 4 minutes to transmit. Four images for a typical screening exam would take more than 16 minutes. This is too long a time period for a convenient screening. Consequently, compression is necessary for making satellite-transmission of mammographic images practically possible. The Wavelet Research Group of the Department of Electrical Engineering at The Ohio State University (OSU) participated in the LeRC-CCF collaboration by

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.

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.

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.

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.

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.

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

An improved peak frequency shift method for Q estimation based on generalized seismic wavelet function

NASA Astrophysics Data System (ADS)

Wang, Qian; Gao, Jinghuai

2018-02-01

As a powerful tool for hydrocarbon detection and reservoir characterization, the quality factor, Q, provides useful information in seismic data processing and interpretation. In this paper, we propose a novel method for Q estimation. The generalized seismic wavelet (GSW) function was introduced to fit the amplitude spectrum of seismic waveforms with two parameters: fractional value and reference frequency. Then we derive an analytical relation between the GSW function and the Q factor of the medium. When a seismic wave propagates through a viscoelastic medium, the GSW function can be employed to fit the amplitude spectrum of the source and attenuated wavelets, then the fractional values and reference frequencies can be evaluated numerically from the discrete Fourier spectrum. After calculating the peak frequency based on the obtained fractional value and reference frequency, the relationship between the GSW function and the Q factor can be built by the conventional peak frequency shift method. Synthetic tests indicate that our method can achieve higher accuracy and be more robust to random noise compared with existing methods. Furthermore, the proposed method is applicable to different types of source wavelet. Field data application also demonstrates the effectiveness of our method in seismic attenuation and the potential in the reservoir characteristic.

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.

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.

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.

Multiscale computations with a wavelet-adaptive algorithm

NASA Astrophysics Data System (ADS)

Rastigejev, Yevgenii Anatolyevich

A wavelet-based adaptive multiresolution algorithm for the numerical solution of multiscale problems governed by partial differential equations is introduced. The main features of the method include fast algorithms for the calculation of wavelet coefficients and approximation of derivatives on nonuniform stencils. The connection between the wavelet order and the size of the stencil is established. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution which are used in conjunction with an appropriate threshold criteria to adapt the collocation grid. The efficient data structures for grid representation as well as related computational algorithms to support grid rearrangement procedure are developed. The algorithm is applied to the simulation of phenomena described by Navier-Stokes equations. First, we undertake the study of the ignition and subsequent viscous detonation of a H2 : O2 : Ar mixture in a one-dimensional shock tube. Subsequently, we apply the algorithm to solve the two- and three-dimensional benchmark problem of incompressible flow in a lid-driven cavity at large Reynolds numbers. For these cases we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees of freedom. The simulations show the striking ability of the algorithm to adapt to a solution having different scales at different spatial locations so as to produce accurate results at a relatively low computational cost.

Wavelet packet-based insufficiency murmurs analysis method

NASA Astrophysics Data System (ADS)

Choi, Samjin; Jiang, Zhongwei

2007-12-01

In this paper, the aortic and mitral insufficiency murmurs analysis method using the wavelet packet technique is proposed for classifying the valvular heart defects. Considering the different frequency distributions between the normal sound and insufficiency murmurs in frequency domain, we used two properties such as the relative wavelet energy and the Shannon wavelet entropy which described the energy information and the entropy information at the selected frequency band, respectively. Then, the signal to murmur ratio (SMR) measures which could mean the ratio between the frequency bands for normal heart sounds and for aortic and mitral insufficiency murmurs allocated to 15.62-187.50 Hz and 187.50-703.12 Hz respectively, were employed as a classification manner to identify insufficiency murmurs. The proposed measures were validated by some case studies. The 194 heart sound signals with 48 normal and 146 abnormal sound cases acquired from 6 healthy volunteers and 30 patients were tested. The normal sound signals recorded by applying a self-produced wireless electric stethoscope system to subjects with no history of other heart complications were used. Insufficiency murmurs were grouped into two valvular heart defects such as aortic insufficiency and mitral insufficiency. These murmur subjects included no other coexistent valvular defects. As a result, the proposed insufficiency murmurs detection method showed relatively very high classification efficiency. Therefore, the proposed heart sound classification method based on the wavelet packet was validated for the classification of valvular heart defects, especially insufficiency murmurs.

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.

Wavelet analysis of epileptic spikes

NASA Astrophysics Data System (ADS)

Latka, Miroslaw; Was, Ziemowit; Kozik, Andrzej; West, Bruce J.

2003-05-01

Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.

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.

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.

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.

Analysis of wavelet technology for NASA applications

NASA Technical Reports Server (NTRS)

Wells, R. O., Jr.

1994-01-01

The purpose of this grant was to introduce a broad group of NASA researchers and administrators to wavelet technology and to determine its future role in research and development at NASA JSC. The activities of several briefings held between NASA JSC scientists and Rice University researchers are discussed. An attached paper, 'Recent Advances in Wavelet Technology', summarizes some aspects of these briefings. Two proposals submitted to NASA reflect the primary areas of common interest. They are image analysis and numerical solutions of partial differential equations arising in computational fluid dynamics and structural mechanics.

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.

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.

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.

Multimode waveguide speckle patterns for compressive sensing.

PubMed

Valley, George C; Sefler, George A; Justin Shaw, T

2016-06-01

Compressive sensing (CS) of sparse gigahertz-band RF signals using microwave photonics may achieve better performances with smaller size, weight, and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a sub-Gaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with a performance similar to that of the multimode fiber. The CS simulations show that all measured and calculated speckle MMs exhibit a robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse gigahertz-band RF signals using CS.

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.

Steerable dyadic wavelet transform and interval wavelets for enhancement of digital mammography

NASA Astrophysics Data System (ADS)

Laine, Andrew F.; Koren, Iztok; Yang, Wuhai; Taylor, Fred J.

1995-04-01

This paper describes two approaches for accomplishing interactive feature analysis by overcomplete multiresolution representations. We show quantitatively that transform coefficients, modified by an adaptive non-linear operator, can make more obvious unseen or barely seen features of mammography without requiring additional radiation. Our results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features. We design a filter bank representing a steerable dyadic wavelet transform that can be used for multiresolution analysis along arbitrary orientations. Digital mammograms are enhanced by orientation analysis performed by a steerable dyadic wavelet transform. Arbitrary regions of interest (ROI) are enhanced by Deslauriers-Dubuc interpolation representations on an interval. We demonstrate that our methods can provide radiologists with an interactive capability to support localized processing of selected (suspicion) areas (lesions). Features extracted from multiscale representations can provide an adaptive mechanism for accomplishing local contrast enhancement. By improving the visualization of breast pathology can improve changes of early detection while requiring less time to evaluate mammograms for most patients.

Wavelet decomposition based principal component analysis for face recognition using MATLAB

NASA Astrophysics Data System (ADS)

Sharma, Mahesh Kumar; Sharma, Shashikant; Leeprechanon, Nopbhorn; Ranjan, Aashish

2016-03-01

For the realization of face recognition systems in the static as well as in the real time frame, algorithms such as principal component analysis, independent component analysis, linear discriminate analysis, neural networks and genetic algorithms are used for decades. This paper discusses an approach which is a wavelet decomposition based principal component analysis for face recognition. Principal component analysis is chosen over other algorithms due to its relative simplicity, efficiency, and robustness features. The term face recognition stands for identifying a person from his facial gestures and having resemblance with factor analysis in some sense, i.e. extraction of the principal component of an image. Principal component analysis is subjected to some drawbacks, mainly the poor discriminatory power and the large computational load in finding eigenvectors, in particular. These drawbacks can be greatly reduced by combining both wavelet transform decomposition for feature extraction and principal component analysis for pattern representation and classification together, by analyzing the facial gestures into space and time domain, where, frequency and time are used interchangeably. From the experimental results, it is envisaged that this face recognition method has made a significant percentage improvement in recognition rate as well as having a better computational efficiency.

Wavelet-based unsupervised learning method for electrocardiogram suppression in surface electromyograms.

PubMed

Niegowski, Maciej; Zivanovic, Miroslav

2016-03-01

We present a novel approach aimed at removing electrocardiogram (ECG) perturbation from single-channel surface electromyogram (EMG) recordings by means of unsupervised learning of wavelet-based intensity images. The general idea is to combine the suitability of certain wavelet decomposition bases which provide sparse electrocardiogram time-frequency representations, with the capacity of non-negative matrix factorization (NMF) for extracting patterns from images. In order to overcome convergence problems which often arise in NMF-related applications, we design a novel robust initialization strategy which ensures proper signal decomposition in a wide range of ECG contamination levels. Moreover, the method can be readily used because no a priori knowledge or parameter adjustment is needed. The proposed method was evaluated on real surface EMG signals against two state-of-the-art unsupervised learning algorithms and a singular spectrum analysis based method. The results, expressed in terms of high-to-low energy ratio, normalized median frequency, spectral power difference and normalized average rectified value, suggest that the proposed method enables better ECG-EMG separation quality than the reference methods. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.

Parameters effective on estimating a nonstationary mixed-phase wavelet using cumulant matching approach

NASA Astrophysics Data System (ADS)

Vosoughi, Ehsan; Javaherian, Abdolrahim

2018-01-01

Seismic inversion is a process performed to remove the effects of propagated wavelets in order to recover the acoustic impedance. To obtain valid velocity and density values related to subsurface layers through the inversion process, it is highly essential to perform reliable wavelet estimation such as cumulant matching approach. For this purpose, the seismic data were windowed in this work in such a way that two consecutive windows were only one sample apart. Also, we did not consider any fixed wavelet for any window and let the phase of each wavelet rotate in each sample in the window. Comparing the fourth order cumulant of the whitened trace and fourth-order moment of the all-pass operator in each window generated a cost function that should be minimized with a non-linear optimization method. In this regard, parameters effective on the estimation of the nonstationary mixed-phase wavelets were tested over the created nonstationary seismic trace at 0.82 s and 1.6 s. Besides, we compared the consequences of each parameter on estimated wavelets at two mentioned times. The parameters studied in this work are window length, taper type, the number of iteration, signal-to-noise ratio, bandwidth to central frequency ratio, and Q factor. The results show that applying the optimum values of the effective parameters, the average correlation of the estimated mixed-phase wavelets with the original ones is about 87%. Moreover, the effectiveness of the proposed approach was examined on a synthetic nonstationary seismic section with variable Q factor values alongside the time and offset axis. Eventually, the cumulant matching method was applied on a cross line of the migrated data from a 3D data set of an oilfield in the Persian Gulf. Also, the effect of the wrong Q estimation on the estimated mixed-phase wavelet was considered on the real data set. It is concluded that the accuracy of the estimated wavelet relied on the estimated Q and more than 10% error in the estimated value

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.

Study of spectro-temporal variation in paleo-climatic marine proxy records using wavelet transformations

NASA Astrophysics Data System (ADS)

Pandey, Chhavi P.

2017-10-01

Wavelet analysis is a powerful mathematical and computational tool to study periodic phenomena in time series particu-larly in the presence of potential frequency changes in time. Continuous wavelet transformation (CWT) provides localised spectral information of the analysed dataset and in particular useful to study multiscale, nonstationary processes occurring over finite spatial and temporal domains. In the present work, oxygen-isotope ratio from the plantonic foraminifera species (viz. Globigerina bul-loides and Globigerinoides ruber) acquired from the broad central plateau of the Maldives ridge situated in south-eastern Arabian sea have been used as climate proxy. CWT of the time series generated using both the biofacies indicate spectro-temporal varia-tion of the natural climatic cycles. The dominant period resembles to the period of Milankovitch glacial-interglacial cycle. Apart from that, various other cycles are present in the time series. The results are in good agreement with the astronomical theory of paleoclimates and can provide better visualisation of Indian summer monsoon in the context of climate change.

An adaptive morphological gradient lifting wavelet for detecting bearing defects

NASA Astrophysics Data System (ADS)

Li, Bing; Zhang, Pei-lin; Mi, Shuang-shan; Hu, Ren-xi; Liu, Dong-sheng

2012-05-01

This paper presents a novel wavelet decomposition scheme, named adaptive morphological gradient lifting wavelet (AMGLW), for detecting bearing defects. The adaptability of the AMGLW consists in that the scheme can select between two filters, mean the average filter and morphological gradient filter, to update the approximation signal based on the local gradient of the analyzed signal. Both a simulated signal and vibration signals acquired from bearing are employed to evaluate and compare the proposed AMGLW scheme with the traditional linear wavelet transform (LWT) and another adaptive lifting wavelet (ALW) developed in literature. Experimental results reveal that the AMGLW outperforms the LW and ALW obviously for detecting bearing defects. The impulsive components can be enhanced and the noise can be depressed simultaneously by the presented AMGLW scheme. Thus the fault characteristic frequencies of bearing can be clearly identified. Furthermore, the AMGLW gets an advantage over LW in computation efficiency. It is quite suitable for online condition monitoring of bearings and other rotating machineries.

Experimental study on the crack detection with optimized spatial wavelet analysis and windowing

NASA Astrophysics Data System (ADS)

Ghanbari Mardasi, Amir; Wu, Nan; Wu, Christine

2018-05-01

In this paper, a high sensitive crack detection is experimentally realized and presented on a beam under certain deflection by optimizing spatial wavelet analysis. Due to the crack existence in the beam structure, a perturbation/slop singularity is induced in the deflection profile. Spatial wavelet transformation works as a magnifier to amplify the small perturbation signal at the crack location to detect and localize the damage. The profile of a deflected aluminum cantilever beam is obtained for both intact and cracked beams by a high resolution laser profile sensor. Gabor wavelet transformation is applied on the subtraction of intact and cracked data sets. To improve detection sensitivity, scale factor in spatial wavelet transformation and the transformation repeat times are optimized. Furthermore, to detect the possible crack close to the measurement boundaries, wavelet transformation edge effect, which induces large values of wavelet coefficient around the measurement boundaries, is efficiently reduced by introducing different windowing functions. The result shows that a small crack with depth of less than 10% of the beam height can be localized with a clear perturbation. Moreover, the perturbation caused by a crack at 0.85 mm away from one end of the measurement range, which is covered by wavelet transform edge effect, emerges by applying proper window functions.

Electrocardiogram signal denoising based on a new improved wavelet thresholding

NASA Astrophysics Data System (ADS)

Han, Guoqiang; Xu, Zhijun

2016-08-01

Good quality electrocardiogram (ECG) is utilized by physicians for the interpretation and identification of physiological and pathological phenomena. In general, ECG signals may mix various noises such as baseline wander, power line interference, and electromagnetic interference in gathering and recording process. As ECG signals are non-stationary physiological signals, wavelet transform is investigated to be an effective tool to discard noises from corrupted signals. A new compromising threshold function called sigmoid function-based thresholding scheme is adopted in processing ECG signals. Compared with other methods such as hard/soft thresholding or other existing thresholding functions, the new algorithm has many advantages in the noise reduction of ECG signals. It perfectly overcomes the discontinuity at ±T of hard thresholding and reduces the fixed deviation of soft thresholding. The improved wavelet thresholding denoising can be proved to be more efficient than existing algorithms in ECG signal denoising. The signal to noise ratio, mean square error, and percent root mean square difference are calculated to verify the denoising performance as quantitative tools. The experimental results reveal that the waves including P, Q, R, and S waves of ECG signals after denoising coincide with the original ECG signals by employing the new proposed method.

Wavelet analysis of MR functional data from the cerebellum

NASA Astrophysics Data System (ADS)

Romero Sánchez, Karen; Vásquez Reyes, Marcos A.; González Gómez, Dulce I.; Hidalgo Tobón, Silvia; Hernández López, Javier M.; Dies Suarez, Pilar; Barragán Pérez, Eduardo; De Celis Alonso, Benito

2014-11-01

The main goal of this project was to create a computer algorithm based on wavelet analysis of BOLD signals, which automatically diagnosed ADHD using information from resting state MR experiments. Male right handed volunteers (infants with ages between 7 and 11 years old) were studied and compared with age matched controls. Wavelet analysis, which is a mathematical tool used to decompose time series into elementary constituents and detect hidden information, was applied here to the BOLD signal obtained from the cerebellum 8 region of all our volunteers. Statistical differences between the values of the a parameters of wavelet analysis was found and showed significant differences (p<0.02) between groups. This difference might help in the future to distinguish healthy from ADHD patients and therefore diagnose ADHD.

Evolutionary Wavelet Neural Network ensembles for breast cancer and Parkinson's disease prediction.

PubMed

Khan, Maryam Mahsal; Mendes, Alexandre; Chalup, Stephan K

2018-01-01

Wavelet Neural Networks are a combination of neural networks and wavelets and have been mostly used in the area of time-series prediction and control. Recently, Evolutionary Wavelet Neural Networks have been employed to develop cancer prediction models. The present study proposes to use ensembles of Evolutionary Wavelet Neural Networks. The search for a high quality ensemble is directed by a fitness function that incorporates the accuracy of the classifiers both independently and as part of the ensemble itself. The ensemble approach is tested on three publicly available biomedical benchmark datasets, one on Breast Cancer and two on Parkinson's disease, using a 10-fold cross-validation strategy. Our experimental results show that, for the first dataset, the performance was similar to previous studies reported in literature. On the second dataset, the Evolutionary Wavelet Neural Network ensembles performed better than all previous methods. The third dataset is relatively new and this study is the first to report benchmark results.

Wavelet Transform Analysis of the Power Spectrum of Centre of Pressure Signals to Detect the Critical Point Interval of Postural Control

NASA Astrophysics Data System (ADS)

Singh, Neeraj Kumar; Snoussi, Hichem; Hewson, David; Duchêne, Jacques

The aim of this study was to develop a method to detecting the critical point interval (CPI) when sensory feedback is used as part of a closed-loop postural control strategy. Postural balance was evaluated using centre of pressure (COP) displacements from a force plate for 17 control and 10 elderly subjects under eyes open, eyes closed, and vibration conditions. A modified local-maximum-modulus wavelet transform analysis using the power spectrum of COP signals was used to calculate CPI. Lower CPI values indicate increased closed-loop postural control with a quicker response to sensory input. Such a strategy requires greater energy expenditure due to the repeated muscular interventions to remain stable. The CPI for elderly occurred significantly quicker than for controls, indicating tighter control of posture. Similar results were observed for eyes closed and vibration conditions. The CPI parameter can be used to detect differences in postural control due to ageing.

Controlled wavelet domain sparsity for x-ray tomography

NASA Astrophysics Data System (ADS)

Purisha, Zenith; Rimpeläinen, Juho; Bubba, Tatiana; Siltanen, Samuli

2018-01-01

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter \

Construction of Orthonormal Wavelets Using Symbolic Algebraic Methods

NASA Astrophysics Data System (ADS)

Černá, Dana; Finěk, Václav

2009-09-01

Our contribution is concerned with the solution of nonlinear algebraic equations systems arising from the computation of scaling coefficients of orthonormal wavelets with compact support. Specifically Daubechies wavelets, symmlets, coiflets, and generalized coiflets. These wavelets are defined as a solution of equation systems which are partly linear and partly nonlinear. The idea of presented methods consists in replacing those equations for scaling coefficients by equations for scaling moments. It enables us to eliminate some quadratic conditions in the original system and then simplify it. The simplified system is solved with the aid of the Gröbner basis method. The advantage of our approach is that in some cases, it provides all possible solutions and these solutions can be computed to arbitrary precision. For small systems, we are even able to find explicit solutions. The computation was carried out by symbolic algebra software Maple.

Wavelet regression model in forecasting crude oil price

NASA Astrophysics Data System (ADS)

Hamid, Mohd Helmie; Shabri, Ani

2017-05-01

This study presents the performance of wavelet multiple linear regression (WMLR) technique in daily crude oil forecasting. WMLR model was developed by integrating the discrete wavelet transform (DWT) and multiple linear regression (MLR) model. The original time series was decomposed to sub-time series with different scales by wavelet theory. Correlation analysis was conducted to assist in the selection of optimal decomposed components as inputs for the WMLR model. The daily WTI crude oil price series has been used in this study to test the prediction capability of the proposed model. The forecasting performance of WMLR model were also compared with regular multiple linear regression (MLR), Autoregressive Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) using root mean square errors (RMSE) and mean absolute errors (MAE). Based on the experimental results, it appears that the WMLR model performs better than the other forecasting technique tested in this study.

The cross wavelet and wavelet coherence analysis of spatio-temporal rainfall-groundwater system in Pingtung plain, Taiwan

NASA Astrophysics Data System (ADS)

Lin, Yuan-Chien; Yu, Hwa-Lung

2013-04-01

The increasing frequency and intensity of extreme rainfall events has been observed recently in Taiwan. Particularly, Typhoon Morakot, Typhoon Fanapi, and Typhoon Megi consecutively brought record-breaking intensity and magnitude of rainfalls to different locations of Taiwan in these two years. However, records show the extreme rainfall events did not elevate the amount of annual rainfall accordingly. Conversely, the increasing frequency of droughts has also been occurring in Taiwan. The challenges have been confronted by governmental agencies and scientific communities to come up with effective adaptation strategies for natural disaster reduction and sustainable environment establishment. Groundwater has long been a reliable water source for a variety of domestic, agricultural, and industrial uses because of its stable quantity and quality. In Taiwan, groundwater accounts for the largest proportion of all water resources for about 40%. This study plans to identify and quantify the nonlinear relationship between precipitation and groundwater recharge, find the non-stationary time-frequency relations between the variations of rainfall and groundwater levels to understand the phase difference of time series. Groundwater level data and over-50-years hourly rainfall records obtained from 20 weather stations in Pingtung Plain, Taiwan has been collected. Extract the space-time pattern by EOF method, which is a decomposition of a signal or data set in terms of orthogonal basis functions determined from the data for both time series and spatial patterns, to identify the important spatial pattern of groundwater recharge and using cross wavelet and wavelet coherence method to identify the relationship between rainfall and groundwater levels. Results show that EOF method can specify the spatial-temporal patterns which represents certain geological characteristics and other mechanisms of groundwater, and the wavelet coherence method can identify general correlation between

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.

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.

Wavelet-based reversible watermarking for authentication

NASA Astrophysics Data System (ADS)

Tian, Jun

2002-04-01

In the digital information age, digital content (audio, image, and video) can be easily copied, manipulated, and distributed. Copyright protection and content authentication of digital content has become an urgent problem to content owners and distributors. Digital watermarking has provided a valuable solution to this problem. Based on its application scenario, most digital watermarking methods can be divided into two categories: robust watermarking and fragile watermarking. As a special subset of fragile watermark, reversible watermark (which is also called lossless watermark, invertible watermark, erasable watermark) enables the recovery of the original, unwatermarked content after the watermarked content has been detected to be authentic. Such reversibility to get back unwatermarked content is highly desired in sensitive imagery, such as military data and medical data. In this paper we present a reversible watermarking method based on an integer wavelet transform. We look into the binary representation of each wavelet coefficient and embed an extra bit to expandable wavelet coefficient. The location map of all expanded coefficients will be coded by JBIG2 compression and these coefficient values will be losslessly compressed by arithmetic coding. Besides these two compressed bit streams, an SHA-256 hash of the original image will also be embedded for authentication purpose.

Spectral Data Reduction via Wavelet Decomposition

NASA Technical Reports Server (NTRS)

Kaewpijit, S.; LeMoigne, J.; El-Ghazawi, T.; Rood, Richard (Technical Monitor)

2002-01-01

The greatest advantage gained from hyperspectral imagery is that narrow spectral features can be used to give more information about materials than was previously possible with broad-band multispectral imagery. For many applications, the new larger data volumes from such hyperspectral sensors, however, present a challenge for traditional processing techniques. For example, the actual identification of each ground surface pixel by its corresponding reflecting spectral signature is still one of the most difficult challenges in the exploitation of this advanced technology, because of the immense volume of data collected. Therefore, conventional classification methods require a preprocessing step of dimension reduction to conquer the so-called "curse of dimensionality." Spectral data reduction using wavelet decomposition could be useful, as it does not only reduce the data volume, but also preserves the distinctions between spectral signatures. This characteristic is related to the intrinsic property of wavelet transforms that preserves high- and low-frequency features during the signal decomposition, therefore preserving peaks and valleys found in typical spectra. When comparing to the most widespread dimension reduction technique, the Principal Component Analysis (PCA), and looking at the same level of compression rate, we show that Wavelet Reduction yields better classification accuracy, for hyperspectral data processed with a conventional supervised classification such as a maximum likelihood method.

Use of the wavelet transform to investigate differences in brain PET images between patient groups

NASA Astrophysics Data System (ADS)

Ruttimann, Urs E.; Unser, Michael A.; Rio, Daniel E.; Rawlings, Robert R.

1993-06-01

Suitability of the wavelet transform was studied for the analysis of glucose utilization differences between subject groups as displayed in PET images. To strengthen statistical inference, it was of particular interest investigating the tradeoff between signal localization and image decomposition into uncorrelated components. This tradeoff is shown to be controlled by wavelet regularity, with the optimal compromise attained by third-order orthogonal spline wavelets. Testing of the ensuing wavelet coefficients identified only about 1.5% as statistically different (p < .05) from noise, which then served to resynthesize the difference images by the inverse wavelet transform. The resulting images displayed relatively uniform, noise-free regions of significant differences with, due to the good localization maintained by the wavelets, very little reconstruction artifacts.

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

Design of compactly supported wavelet to match singularities in medical images

NASA Astrophysics Data System (ADS)

Fung, Carrson C.; Shi, Pengcheng

2002-11-01

Analysis and understanding of medical images has important clinical values for patient diagnosis and treatment, as well as technical implications for computer vision and pattern recognition. One of the most fundamental issues is the detection of object boundaries or singularities, which is often the basis for further processes such as organ/tissue recognition, image registration, motion analysis, measurement of anatomical and physiological parameters, etc. The focus of this work involved taking a correlation based approach toward edge detection, by exploiting some of desirable properties of wavelet analysis. This leads to the possibility of constructing a bank of detectors, consisting of multiple wavelet basis functions of different scales which are optimal for specific types of edges, in order to optimally detect all the edges in an image. Our work involved developing a set of wavelet functions which matches the shape of the ramp and pulse edges. The matching algorithm used focuses on matching the edges in the frequency domain. It was proven that this technique could create matching wavelets applicable at all scales. Results have shown that matching wavelets can be obtained for the pulse edge while the ramp edge requires another matching algorithm.

Features in the primordial spectrum from WMAP: A wavelet analysis

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

Shafieloo, Arman; Souradeep, Tarun; Manimaran, P.

2007-06-15

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [A. Shafieloo and T. Souradeep, Phys. Rev. D 70, 043523 (2004).], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, 'best fit' scale free spectra ({delta}lnL{approx_equal}25 withmore » respect to the Harrison-Zeldovich spectrum, and, {delta}lnL{approx_equal}11 with respect to the power law spectrum with n{sub s}=0.95). In this paper we use the discrete wavelet transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infrared cutoff at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.« less

Analysis of wheezes using wavelet higher order spectral features.

PubMed

Taplidou, Styliani A; Hadjileontiadis, Leontios J

2010-07-01

Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively

Discrete wavelet transform: a tool in smoothing kinematic data.

PubMed

Ismail, A R; Asfour, S S

1999-03-01

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Discrete Wavelet Transform for Fault Locations in Underground Distribution System

NASA Astrophysics Data System (ADS)

Apisit, C.; Ngaopitakkul, A.

2010-10-01

In this paper, a technique for detecting faults in underground distribution system is presented. Discrete Wavelet Transform (DWT) based on traveling wave is employed in order to detect the high frequency components and to identify fault locations in the underground distribution system. The first peak time obtained from the faulty bus is employed for calculating the distance of fault from sending end. The validity of the proposed technique is tested with various fault inception angles, fault locations and faulty phases. The result is found that the proposed technique provides satisfactory result and will be very useful in the development of power systems protection scheme.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

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.

Multifractal Cross Wavelet Analysis

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Gao, Xing-Lu; Zhou, Wei-Xing; Stanley, H. Eugene

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.

Time Domain Propagation of Quantum and Classical Systems using a Wavelet Basis Set Method

NASA Astrophysics Data System (ADS)

Lombardini, Richard; Nowara, Ewa; Johnson, Bruce

2015-03-01

The use of an orthogonal wavelet basis set (Optimized Maximum-N Generalized Coiflets) to effectively model physical systems in the time domain, in particular the electromagnetic (EM) pulse and quantum mechanical (QM) wavefunction, is examined in this work. Although past research has demonstrated the benefits of wavelet basis sets to handle computationally expensive problems due to their multiresolution properties, the overlapping supports of neighboring wavelet basis functions poses problems when dealing with boundary conditions, especially with material interfaces in the EM case. Specifically, this talk addresses this issue using the idea of derivative matching creating fictitious grid points (T.A. Driscoll and B. Fornberg), but replaces the latter element with fictitious wavelet projections in conjunction with wavelet reconstruction filters. Two-dimensional (2D) systems are analyzed, EM pulse incident on silver cylinders and the QM electron wave packet circling the proton in a hydrogen atom system (reduced to 2D), and the new wavelet method is compared to the popular finite-difference time-domain technique.

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis.

PubMed

Li, Sikun; Wang, Xiangzhao; Su, Xianyu; Tang, Feng

2012-04-20

This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.

Applications of wavelets in interferometry and artificial vision

NASA Astrophysics Data System (ADS)

Escalona Z., Rafael A.

2001-08-01

In this paper we present a different point of view of phase measurements performed in interferometry, image processing and intelligent vision using Wavelet Transform. In standard and white-light interferometry, the phase function is retrieved by using phase-shifting, Fourier-Transform, cosinus-inversion and other known algorithms. Our novel technique presented here is faster, robust and shows excellent accuracy in phase determinations. Finally, in our second application, fringes are no more generate by some light interaction but result from the observation of adapted strip set patterns directly printed on the target of interest. The moving target is simply observed by a conventional vision system and usual phase computation algorithms are adapted to an image processing by wavelet transform, in order to sense target position and displacements with a high accuracy. In general, we have determined that wavelet transform presents properties of robustness, relative speed of calculus and very high accuracy in phase computations.

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

Appearance and characterization of fruit image textures for quality sorting using wavelet transform and genetic algorithms.

PubMed

Khoje, Suchitra

2018-02-01

Images of four qualities of mangoes and guavas are evaluated for color and textural features to characterize and classify them, and to model the fruit appearance grading. The paper discusses three approaches to identify most discriminating texture features of both the fruits. In the first approach, fruit's color and texture features are selected using Mahalanobis distance. A total of 20 color features and 40 textural features are extracted for analysis. Using Mahalanobis distance and feature intercorrelation analyses, one best color feature (mean of a* [L*a*b* color space]) and two textural features (energy a*, contrast of H*) are selected as features for Guava while two best color features (R std, H std) and one textural features (energy b*) are selected as features for mangoes with the highest discriminate power. The second approach studies some common wavelet families for searching the best classification model for fruit quality grading. The wavelet features extracted from five basic mother wavelets (db, bior, rbior, Coif, Sym) are explored to characterize fruits texture appearance. In third approach, genetic algorithm is used to select only those color and wavelet texture features that are relevant to the separation of the class, from a large universe of features. The study shows that image color and texture features which were identified using a genetic algorithm can distinguish between various qualities classes of fruits. The experimental results showed that support vector machine classifier is elected for Guava grading with an accuracy of 97.61% and artificial neural network is elected from Mango grading with an accuracy of 95.65%. The proposed method is nondestructive fruit quality assessment method. The experimental results has proven that Genetic algorithm along with wavelet textures feature has potential to discriminate fruit quality. Finally, it can be concluded that discussed method is an accurate, reliable, and objective tool to determine fruit

Damage Identification in Beam Structure using Spatial Continuous Wavelet Transform

NASA Astrophysics Data System (ADS)

Janeliukstis, R.; Rucevskis, S.; Wesolowski, M.; Kovalovs, A.; Chate, A.

2015-11-01

In this paper the applicability of spatial continuous wavelet transform (CWT) technique for damage identification in the beam structure is analyzed by application of different types of wavelet functions and scaling factors. The proposed method uses exclusively mode shape data from the damaged structure. To examine limitations of the method and to ascertain its sensitivity to noisy experimental data, several sets of simulated data are analyzed. Simulated test cases include numerical mode shapes corrupted by different levels of random noise as well as mode shapes with different number of measurement points used for wavelet transform. A broad comparison of ability of different wavelet functions to detect and locate damage in beam structure is given. Effectiveness and robustness of the proposed algorithms are demonstrated experimentally on two aluminum beams containing single mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer with PZT actuator as vibration excitation source for the experimental study.

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.

S2LET: A code to perform fast wavelet analysis on the sphere

NASA Astrophysics Data System (ADS)

Leistedt, B.; McEwen, J. D.; Vandergheynst, P.; Wiaux, Y.

2013-10-01

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-dependent features of signals on the sphere. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.

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.

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.

Wavelet methodology to improve single unit isolation in primary motor cortex cells.

PubMed

Ortiz-Rosario, Alexis; Adeli, Hojjat; Buford, John A

2015-05-15

The proper isolation of action potentials recorded extracellularly from neural tissue is an active area of research in the fields of neuroscience and biomedical signal processing. This paper presents an isolation methodology for neural recordings using the wavelet transform (WT), a statistical thresholding scheme, and the principal component analysis (PCA) algorithm. The effectiveness of five different mother wavelets was investigated: biorthogonal, Daubachies, discrete Meyer, symmetric, and Coifman; along with three different wavelet coefficient thresholding schemes: fixed form threshold, Stein's unbiased estimate of risk, and minimax; and two different thresholding rules: soft and hard thresholding. The signal quality was evaluated using three different statistical measures: mean-squared error, root-mean squared, and signal to noise ratio. The clustering quality was evaluated using two different statistical measures: isolation distance, and L-ratio. This research shows that the selection of the mother wavelet has a strong influence on the clustering and isolation of single unit neural activity, with the Daubachies 4 wavelet and minimax thresholding scheme performing the best. Copyright © 2015. Published by Elsevier B.V.

Wavelet methodology to improve single unit isolation in primary motor cortex cells

PubMed Central

Ortiz-Rosario, Alexis; Adeli, Hojjat; Buford, John A.

2016-01-01

The proper isolation of action potentials recorded extracellularly from neural tissue is an active area of research in the fields of neuroscience and biomedical signal processing. This paper presents an isolation methodology for neural recordings using the wavelet transform (WT), a statistical thresholding scheme, and the principal component analysis (PCA) algorithm. The effectiveness of five different mother wavelets was investigated: biorthogonal, Daubachies, discrete Meyer, symmetric, and Coifman; along with three different wavelet coefficient thresholding schemes: fixed form threshold, Stein’s unbiased estimate of risk, and minimax; and two different thresholding rules: soft and hard thresholding. The signal quality was evaluated using three different statistical measures: mean-squared error, root-mean squared, and signal to noise ratio. The clustering quality was evaluated using two different statistical measures: isolation distance, and L-ratio. This research shows that the selection of the mother wavelet has a strong influence on the clustering and isolation of single unit neural activity, with the Daubachies 4 wavelet and minimax thresholding scheme performing the best. PMID:25794461

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.

Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins

NASA Technical Reports Server (NTRS)

Brenner, Marty; Lind, Rick

1998-01-01

Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.

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

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.

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.

The Brera Multiscale Wavelet ROSAT HRI Source Catalog. I. The Algorithm

NASA Astrophysics Data System (ADS)

Lazzati, Davide; Campana, Sergio; Rosati, Piero; Panzera, Maria Rosa; Tagliaferri, Gianpiero

1999-10-01

We present a new detection algorithm based on the wavelet transform for the analysis of high-energy astronomical images. The wavelet transform, because of its multiscale structure, is suited to the optimal detection of pointlike as well as extended sources, regardless of any loss of resolution with the off-axis angle. Sources are detected as significant enhancements in the wavelet space, after the subtraction of the nonflat components of the background. Detection thresholds are computed through Monte Carlo simulations in order to establish the expected number of spurious sources per field. The source characterization is performed through a multisource fitting in the wavelet space. The procedure is designed to correctly deal with very crowded fields, allowing for the simultaneous characterization of nearby sources. To obtain a fast and reliable estimate of the source parameters and related errors, we apply a novel decimation technique that, taking into account the correlation properties of the wavelet transform, extracts a subset of almost independent coefficients. We test the performance of this algorithm on synthetic fields, analyzing with particular care the characterization of sources in poor background situations, where the assumption of Gaussian statistics does not hold. In these cases, for which standard wavelet algorithms generally provide underestimated errors, we infer errors through a procedure that relies on robust basic statistics. Our algorithm is well suited to the analysis of images taken with the new generation of X-ray instruments equipped with CCD technology, which will produce images with very low background and/or high source density.

Reversible wavelet filter banks with side informationless spatially adaptive low-pass filters

NASA Astrophysics Data System (ADS)

Abhayaratne, Charith

2011-07-01

Wavelet transforms that have an adaptive low-pass filter are useful in applications that require the signal singularities, sharp transitions, and image edges to be left intact in the low-pass signal. In scalable image coding, the spatial resolution scalability is achieved by reconstructing the low-pass signal subband, which corresponds to the desired resolution level, and discarding other high-frequency wavelet subbands. In such applications, it is vital to have low-pass subbands that are not affected by smoothing artifacts associated with low-pass filtering. We present the mathematical framework for achieving 1-D wavelet transforms that have a spatially adaptive low-pass filter (SALP) using the prediction-first lifting scheme. The adaptivity decisions are computed using the wavelet coefficients, and no bookkeeping is required for the perfect reconstruction. Then, 2-D wavelet transforms that have a spatially adaptive low-pass filter are designed by extending the 1-D SALP framework. Because the 2-D polyphase decompositions are used in this case, the 2-D adaptivity decisions are made nonseparable as opposed to the separable 2-D realization using 1-D transforms. We present examples using the 2-D 5/3 wavelet transform and their lossless image coding and scalable decoding performances in terms of quality and resolution scalability. The proposed 2-D-SALP scheme results in better performance compared to the existing adaptive update lifting schemes.

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.

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.

Non-parametric transient classification using adaptive wavelets

NASA Astrophysics Data System (ADS)

Varughese, Melvin M.; von Sachs, Rainer; Stephanou, Michael; Bassett, Bruce A.

2015-11-01

Classifying transients based on multiband light curves is a challenging but crucial problem in the era of GAIA and Large Synoptic Sky Telescope since the sheer volume of transients will make spectroscopic classification unfeasible. We present a non-parametric classifier that predicts the transient's class given training data. It implements two novel components: the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients - as well as the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The classifier is simple to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant. Hence, BAGIDIS does not need the light curves to be aligned to extract features. Further, BAGIDIS is non-parametric so it can be used effectively in blind searches for new objects. We demonstrate the effectiveness of our classifier against the Supernova Photometric Classification Challenge to correctly classify supernova light curves as Type Ia or non-Ia. We train our classifier on the spectroscopically confirmed subsample (which is not representative) and show that it works well for supernova with observed light-curve time spans greater than 100 d (roughly 55 per cent of the data set). For such data, we obtain a Ia efficiency of 80.5 per cent and a purity of 82.4 per cent, yielding a highly competitive challenge score of 0.49. This indicates that our `model-blind' approach may be particularly suitable for the general classification of astronomical transients in the era of large synoptic sky surveys.

Hardware Design and Implementation of a Wavelet De-Noising Procedure for Medical Signal Preprocessing

PubMed Central

Chen, Szi-Wen; Chen, Yuan-Ho

2015-01-01

In this paper, a discrete wavelet transform (DWT) based de-noising with its applications into the noise reduction for medical signal preprocessing is introduced. This work focuses on the hardware realization of a real-time wavelet de-noising procedure. The proposed de-noising circuit mainly consists of three modules: a DWT, a thresholding, and an inverse DWT (IDWT) modular circuits. We also proposed a novel adaptive thresholding scheme and incorporated it into our wavelet de-noising procedure. Performance was then evaluated on both the architectural designs of the software and. In addition, the de-noising circuit was also implemented by downloading the Verilog codes to a field programmable gate array (FPGA) based platform so that its ability in noise reduction may be further validated in actual practice. Simulation experiment results produced by applying a set of simulated noise-contaminated electrocardiogram (ECG) signals into the de-noising circuit showed that the circuit could not only desirably meet the requirement of real-time processing, but also achieve satisfactory performance for noise reduction, while the sharp features of the ECG signals can be well preserved. The proposed de-noising circuit was further synthesized using the Synopsys Design Compiler with an Artisan Taiwan Semiconductor Manufacturing Company (TSMC, Hsinchu, Taiwan) 40 nm standard cell library. The integrated circuit (IC) synthesis simulation results showed that the proposed design can achieve a clock frequency of 200 MHz and the power consumption was only 17.4 mW, when operated at 200 MHz. PMID:26501290

Edge detection based on adaptive threshold b-spline wavelet for optical sub-aperture measuring

NASA Astrophysics Data System (ADS)

Zhang, Shiqi; Hui, Mei; Liu, Ming; Zhao, Zhu; Dong, Liquan; Liu, Xiaohua; Zhao, Yuejin

2015-08-01

In the research of optical synthetic aperture imaging system, phase congruency is the main problem and it is necessary to detect sub-aperture phase. The edge of the sub-aperture system is more complex than that in the traditional optical imaging system. And with the existence of steep slope for large-aperture optical component, interference fringe may be quite dense when interference imaging. Deep phase gradient may cause a loss of phase information. Therefore, it's urgent to search for an efficient edge detection method. Wavelet analysis as a powerful tool is widely used in the fields of image processing. Based on its properties of multi-scale transform, edge region is detected with high precision in small scale. Longing with the increase of scale, noise is reduced in contrary. So it has a certain suppression effect on noise. Otherwise, adaptive threshold method which sets different thresholds in various regions can detect edge points from noise. Firstly, fringe pattern is obtained and cubic b-spline wavelet is adopted as the smoothing function. After the multi-scale wavelet decomposition of the whole image, we figure out the local modulus maxima in gradient directions. However, it also contains noise, and thus adaptive threshold method is used to select the modulus maxima. The point which greater than threshold value is boundary point. Finally, we use corrosion and expansion deal with the resulting image to get the consecutive boundary of image.

Hardware design and implementation of a wavelet de-noising procedure for medical signal preprocessing.

PubMed

Chen, Szi-Wen; Chen, Yuan-Ho

2015-10-16

In this paper, a discrete wavelet transform (DWT) based de-noising with its applications into the noise reduction for medical signal preprocessing is introduced. This work focuses on the hardware realization of a real-time wavelet de-noising procedure. The proposed de-noising circuit mainly consists of three modules: a DWT, a thresholding, and an inverse DWT (IDWT) modular circuits. We also proposed a novel adaptive thresholding scheme and incorporated it into our wavelet de-noising procedure. Performance was then evaluated on both the architectural designs of the software and. In addition, the de-noising circuit was also implemented by downloading the Verilog codes to a field programmable gate array (FPGA) based platform so that its ability in noise reduction may be further validated in actual practice. Simulation experiment results produced by applying a set of simulated noise-contaminated electrocardiogram (ECG) signals into the de-noising circuit showed that the circuit could not only desirably meet the requirement of real-time processing, but also achieve satisfactory performance for noise reduction, while the sharp features of the ECG signals can be well preserved. The proposed de-noising circuit was further synthesized using the Synopsys Design Compiler with an Artisan Taiwan Semiconductor Manufacturing Company (TSMC, Hsinchu, Taiwan) 40 nm standard cell library. The integrated circuit (IC) synthesis simulation results showed that the proposed design can achieve a clock frequency of 200 MHz and the power consumption was only 17.4 mW, when operated at 200 MHz.

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

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

Denoising solar radiation data using coiflet wavelets

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

Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my; Janier, Josefina B., E-mail: josefinajanier@petronas.com.my; Muthuvalu, Mohana Sundaram, E-mail: mohana.muthuvalu@petronas.com.my

Signal denoising and smoothing plays an important role in processing the given signal either from experiment or data collection through observations. Data collection usually was mixed between true data and some error or noise. This noise might be coming from the apparatus to measure or collect the data or human error in handling the data. Normally before the data is use for further processing purposes, the unwanted noise need to be filtered out. One of the efficient methods that can be used to filter the data is wavelet transform. Due to the fact that the received solar radiation data fluctuatesmore » according to time, there exist few unwanted oscillation namely noise and it must be filtered out before the data is used for developing mathematical model. In order to apply denoising using wavelet transform (WT), the thresholding values need to be calculated. In this paper the new thresholding approach is proposed. The coiflet2 wavelet with variation diminishing 4 is utilized for our purpose. From numerical results it can be seen clearly that, the new thresholding approach give better results as compare with existing approach namely global thresholding value.« less

JPEG and wavelet compression of ophthalmic images

NASA Astrophysics Data System (ADS)

Eikelboom, Robert H.; Yogesan, Kanagasingam; Constable, Ian J.; Barry, Christopher J.

1999-05-01

This study was designed to determine the degree and methods of digital image compression to produce ophthalmic imags of sufficient quality for transmission and diagnosis. The photographs of 15 subjects, which inclined eyes with normal, subtle and distinct pathologies, were digitized to produce 1.54MB images and compressed to five different methods: (i) objectively by calculating the RMS error between the uncompressed and compressed images, (ii) semi-subjectively by assessing the visibility of blood vessels, and (iii) subjectively by asking a number of experienced observers to assess the images for quality and clinical interpretation. Results showed that as a function of compressed image size, wavelet compressed images produced less RMS error than JPEG compressed images. Blood vessel branching could be observed to a greater extent after Wavelet compression compared to JPEG compression produced better images then a JPEG compression for a given image size. Overall, it was shown that images had to be compressed to below 2.5 percent for JPEG and 1.7 percent for Wavelet compression before fine detail was lost, or when image quality was too poor to make a reliable diagnosis.

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.

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.

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.

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.

Tool Condition Monitoring in Micro-End Milling using wavelets

NASA Astrophysics Data System (ADS)

Dubey, N. K.; Roushan, A.; Rao, U. S.; Sandeep, K.; Patra, K.

2018-04-01

In this work, Tool Condition Monitoring (TCM) strategy is developed for micro-end milling of titanium alloy and mild steel work-pieces. Full immersion slot milling experiments are conducted using a solid tungsten carbide end mill for more than 1900 s to have reasonable amount of tool wear. During the micro-end milling process, cutting force and vibration signals are acquired using Kistler piezo-electric 3-component force dynamometer (9256C2) and accelerometer (NI cDAQ-9188) respectively. The force components and the vibration signals are processed using Discrete Wavelet Transformation (DWT) in both time and frequency window. 5-level wavelet packet decomposition using Db-8 wavelet is carried out and the detailed coefficients D1 to D5 for each of the signals are obtained. The results of the wavelet transformation are correlated with the tool wear. In case of vibration signals, de-noising is done for higher frequency components (D1) and force signals were de-noised for lower frequency components (D5). Increasing value of MAD (Mean Absolute Deviation) of the detail coefficients for successive channels depicted tool wear. The predictions of the tool wear are confirmed from the actual wear observed in the SEM of the worn tool.

Wavelet-based multiscale analysis of bioimpedance data measured by electric cell-substrate impedance sensing for classification of cancerous and normal cells.

PubMed

Das, Debanjan; Shiladitya, Kumar; Biswas, Karabi; Dutta, Pranab Kumar; Parekh, Aditya; Mandal, Mahitosh; Das, Soumen

2015-12-01

The paper presents a study to differentiate normal and cancerous cells using label-free bioimpedance signal measured by electric cell-substrate impedance sensing. The real-time-measured bioimpedance data of human breast cancer cells and human epithelial normal cells employs fluctuations of impedance value due to cellular micromotions resulting from dynamic structural rearrangement of membrane protrusions under nonagitated condition. Here, a wavelet-based multiscale quantitative analysis technique has been applied to analyze the fluctuations in bioimpedance. The study demonstrates a method to classify cancerous and normal cells from the signature of their impedance fluctuations. The fluctuations associated with cellular micromotion are quantified in terms of cellular energy, cellular power dissipation, and cellular moments. The cellular energy and power dissipation are found higher for cancerous cells associated with higher micromotions in cancer cells. The initial study suggests that proposed wavelet-based quantitative technique promises to be an effective method to analyze real-time bioimpedance signal for distinguishing cancer and normal cells.

Wavelet analysis applied to the IRAS cirrus

NASA Technical Reports Server (NTRS)

Langer, William D.; Wilson, Robert W.; Anderson, Charles H.

1994-01-01

The structure of infrared cirrus clouds is analyzed with Laplacian pyramid transforms, a form of non-orthogonal wavelets. Pyramid and wavelet transforms provide a means to decompose images into their spatial frequency components such that all spatial scales are treated in an equivalent manner. The multiscale transform analysis is applied to IRAS 100 micrometer maps of cirrus emission in the north Galactic pole region to extract features on different scales. In the maps we identify filaments, fragments and clumps by separating all connected regions. These structures are analyzed with respect to their Hausdorff dimension for evidence of the scaling relationships in the cirrus clouds.

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.

Automated transformation-invariant shape recognition through wavelet multiresolution

NASA Astrophysics Data System (ADS)

Brault, Patrice; Mounier, Hugues

2001-12-01

We present here new results in Wavelet Multi-Resolution Analysis (W-MRA) applied to shape recognition in automatic vehicle driving applications. Different types of shapes have to be recognized in this framework. They pertain to most of the objects entering the sensors field of a car. These objects can be road signs, lane separation lines, moving or static obstacles, other automotive vehicles, or visual beacons. The recognition process must be invariant to global, affine or not, transformations which are : rotation, translation and scaling. It also has to be invariant to more local, elastic, deformations like the perspective (in particular with wide angle camera lenses), and also like deformations due to environmental conditions (weather : rain, mist, light reverberation) or optical and electrical signal noises. To demonstrate our method, an initial shape, with a known contour, is compared to the same contour altered by rotation, translation, scaling and perspective. The curvature computed for each contour point is used as a main criterion in the shape matching process. The original part of this work is to use wavelet descriptors, generated with a fast orthonormal W-MRA, rather than Fourier descriptors, in order to provide a multi-resolution description of the contour to be analyzed. In such way, the intrinsic spatial localization property of wavelet descriptors can be used and the recognition process can be speeded up. The most important part of this work is to demonstrate the potential performance of Wavelet-MRA in this application of shape recognition.

Dual tree fractional quaternion wavelet transform for disparity estimation.

PubMed

Kumar, Sanoj; Kumar, Sanjeev; Sukavanam, Nagarajan; Raman, Balasubramanian

2014-03-01

This paper proposes a novel phase based approach for computing disparity as the optical flow from the given pair of consecutive images. A new dual tree fractional quaternion wavelet transform (FrQWT) is proposed by defining the 2D Fourier spectrum upto a single quadrant. In the proposed FrQWT, each quaternion wavelet consists of a real part (a real DWT wavelet) and three imaginary parts that are organized according to the quaternion algebra. First two FrQWT phases encode the shifts of image features in the absolute horizontal and vertical coordinate system, while the third phase has the texture information. The FrQWT allowed a multi-scale framework for calculating and adjusting local disparities and executing phase unwrapping from coarse to fine scales with linear computational efficiency. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Analysis of longer period variation of the Kuroshio Current intrusion into the Luzon Strait using rectified wavelet power spectra

NASA Astrophysics Data System (ADS)

Yuan, Yaochu; Yang, Chenghao; Tseng, Yu-heng; Zhu, Xiao-Hua; Wang, Huiqun; Chen, Hong

2017-08-01

Longer period variation of the Kuroshio into the Luzon Strait (LS) was identified using acoustic Doppler current profiler (ADCP) observations as well as pressure and temperature time series data recorded by two TDs (manufactured by the RBR Ltd.) at mooring station N2 (20°40.441‧N, 120°38.324‧E). The ADCP was deployed at depths of 50-300 m between July 7, 2009 and April 10, 2011, and the TDs at around 340 and 365 m between July 9, 2009 and July 9, 2011. Observations provide strong evidence of longer period variation of the Kuroshio into the LS using the Vector rotary spectra (VRS) and Rectified wavelet power spectra analysis (RWPSA). RWPSA of the observations allowed the identification of two types of dominant periods. The first type, with the strongest power spectral density (PSD), had a dominant period of 112 d and was found throughout the upper 300 m. For example, the maximum PSD for western and northern velocity components time series were 3800 and 3550 at 50 m, respectively. The maximum power spectral density decrease with deeper depths, i.e., the depth dependence of maximum PSD. The 112 d period was also identified in the pressure and temperature time series data, at 340 m and 365 m. Combined RWPSA with VRS and mechanism analysis, it is clear that the occurrence of the most dominant period of 112 d in the upper 300 m is related to the clockwise meandering of the Kuroshio into the LS, which is caused by westward propagating stronger anticyclonic eddies from the interior ocean due to the interaction of Rossby eddies with the Kuroshio. The second type of dominant period, for example a 40 d period, is related to the anticlockwise meandering of the Kuroshio. The final dominant period of 14 d coincides with the fortnightly spring-neap tidal period.

3D Texture Analysis in Renal Cell Carcinoma Tissue Image Grading

PubMed Central

Cho, Nam-Hoon; Choi, Heung-Kook

2014-01-01

One of the most significant processes in cancer cell and tissue image analysis is the efficient extraction of features for grading purposes. This research applied two types of three-dimensional texture analysis methods to the extraction of feature values from renal cell carcinoma tissue images, and then evaluated the validity of the methods statistically through grade classification. First, we used a confocal laser scanning microscope to obtain image slices of four grades of renal cell carcinoma, which were then reconstructed into 3D volumes. Next, we extracted quantitative values using a 3D gray level cooccurrence matrix (GLCM) and a 3D wavelet based on two types of basis functions. To evaluate their validity, we predefined 6 different statistical classifiers and applied these to the extracted feature sets. In the grade classification results, 3D Haar wavelet texture features combined with principal component analysis showed the best discrimination results. Classification using 3D wavelet texture features was significantly better than 3D GLCM, suggesting that the former has potential for use in a computer-based grading system. PMID:25371701

Wavelet-enhanced convolutional neural network: a new idea in a deep learning paradigm.

PubMed

Savareh, Behrouz Alizadeh; Emami, Hassan; Hajiabadi, Mohamadreza; Azimi, Seyed Majid; Ghafoori, Mahyar

2018-05-29

Manual brain tumor segmentation is a challenging task that requires the use of machine learning techniques. One of the machine learning techniques that has been given much attention is the convolutional neural network (CNN). The performance of the CNN can be enhanced by combining other data analysis tools such as wavelet transform. In this study, one of the famous implementations of CNN, a fully convolutional network (FCN), was used in brain tumor segmentation and its architecture was enhanced by wavelet transform. In this combination, a wavelet transform was used as a complementary and enhancing tool for CNN in brain tumor segmentation. Comparing the performance of basic FCN architecture against the wavelet-enhanced form revealed a remarkable superiority of enhanced architecture in brain tumor segmentation tasks. Using mathematical functions and enhancing tools such as wavelet transform and other mathematical functions can improve the performance of CNN in any image processing task such as segmentation and classification.

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.

Evolutionary Wavelet Neural Network ensembles for breast cancer and Parkinson’s disease prediction

PubMed Central

Mendes, Alexandre; Chalup, Stephan K.

2018-01-01

Wavelet Neural Networks are a combination of neural networks and wavelets and have been mostly used in the area of time-series prediction and control. Recently, Evolutionary Wavelet Neural Networks have been employed to develop cancer prediction models. The present study proposes to use ensembles of Evolutionary Wavelet Neural Networks. The search for a high quality ensemble is directed by a fitness function that incorporates the accuracy of the classifiers both independently and as part of the ensemble itself. The ensemble approach is tested on three publicly available biomedical benchmark datasets, one on Breast Cancer and two on Parkinson’s disease, using a 10-fold cross-validation strategy. Our experimental results show that, for the first dataset, the performance was similar to previous studies reported in literature. On the second dataset, the Evolutionary Wavelet Neural Network ensembles performed better than all previous methods. The third dataset is relatively new and this study is the first to report benchmark results. PMID:29420578

Nonstationary Dynamics Data Analysis with Wavelet-SVD Filtering

NASA Technical Reports Server (NTRS)

Brenner, Marty; Groutage, Dale; Bessette, Denis (Technical Monitor)

2001-01-01

Nonstationary time-frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time-frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied.

Wigner functions from the two-dimensional wavelet group.

PubMed

Ali, S T; Krasowska, A E; Murenzi, R

2000-12-01

Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.

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 transformation to determine impedance spectra of lithium-ion rechargeable battery

NASA Astrophysics Data System (ADS)

Hoshi, Yoshinao; Yakabe, Natsuki; Isobe, Koichiro; Saito, Toshiki; Shitanda, Isao; Itagaki, Masayuki

2016-05-01

A new analytical method is proposed to determine the electrochemical impedance of lithium-ion rechargeable batteries (LIRB) from time domain data by wavelet transformation (WT). The WT is a waveform analysis method that can transform data in the time domain to the frequency domain while retaining time information. In this transformation, the frequency domain data are obtained by the convolution integral of a mother wavelet and original time domain data. A complex Morlet mother wavelet (CMMW) is used to obtain the complex number data in the frequency domain. The CMMW is expressed by combining a Gaussian function and sinusoidal term. The theory to select a set of suitable conditions for variables and constants related to the CMMW, i.e., band, scale, and time parameters, is established by determining impedance spectra from wavelet coefficients using input voltage to the equivalent circuit and the output current. The impedance spectrum of LIRB determined by WT agrees well with that measured using a frequency response analyzer.

Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images.

PubMed

Boix, Macarena; Cantó, Begoña

2013-04-01

Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.

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

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

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

Wavelet-based group and phase velocity measurements: Method

NASA Astrophysics Data System (ADS)

Yang, H. Y.; Wang, W. W.; Hung, S. H.

2016-12-01

Measurements of group and phase velocities of surface waves are often carried out by applying a series of narrow bandpass or stationary Gaussian filters localized at specific frequencies to wave packets and estimating the corresponding arrival times at the peak envelopes and phases of the Fourier spectra. However, it's known that seismic waves are inherently nonstationary and not well represented by a sum of sinusoids. Alternatively, a continuous wavelet transform (CWT) which decomposes a time series into a family of wavelets, translated and scaled copies of a generally fast oscillating and decaying function known as the mother wavelet, is capable of retaining localization in both the time and frequency domain and well-suited for the time-frequency analysis of nonstationary signals. Here we develop a wavelet-based method to measure frequency-dependent group and phase velocities, an essential dataset used in crust and mantle tomography. For a given time series, we employ the complex morlet wavelet to obtain the scalogram of amplitude modulus |Wg| and phase φ on the time-frequency plane. The instantaneous frequency (IF) is then calculated by taking the derivative of phase with respect to time, i.e., (1/2π)dφ(f, t)/dt. Time windows comprising strong energy arrivals to be measured can be identified by those IFs close to the frequencies with the maximum modulus and varying smoothly and monotonically with time. The respective IFs in each selected time window are further interpolated to yield a smooth branch of ridge points or representative IFs at which the arrival time, tridge(f), and phase, φridge(f), after unwrapping and correcting cycle skipping based on a priori knowledge of the possible velocity range, are determined for group and phase velocity estimation. We will demonstrate our measurement method using both ambient noise cross correlation functions and multi-mode surface waves from earthquakes. The obtained dispersion curves will be compared with those by a

A Lossless hybrid wavelet-fractal compression for welding radiographic images.

PubMed

Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud

2016-01-01

In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.

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 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.

Identification of speech transients using variable frame rate analysis and wavelet packets.

PubMed

Rasetshwane, Daniel M; Boston, J Robert; Li, Ching-Chung

2006-01-01

Speech transients are important cues for identifying and discriminating speech sounds. Yoo et al. and Tantibundhit et al. were successful in identifying speech transients and, emphasizing them, improving the intelligibility of speech in noise. However, their methods are computationally intensive and unsuitable for real-time applications. This paper presents a method to identify and emphasize speech transients that combines subband decomposition by the wavelet packet transform with variable frame rate (VFR) analysis and unvoiced consonant detection. The VFR analysis is applied to each wavelet packet to define a transitivity function that describes the extent to which the wavelet coefficients of that packet are changing. Unvoiced consonant detection is used to identify unvoiced consonant intervals and the transitivity function is amplified during these intervals. The wavelet coefficients are multiplied by the transitivity function for that packet, amplifying the coefficients localized at times when they are changing and attenuating coefficients at times when they are steady. Inverse transform of the modified wavelet packet coefficients produces a signal corresponding to speech transients similar to the transients identified by Yoo et al. and Tantibundhit et al. A preliminary implementation of the algorithm runs more efficiently.

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

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.

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.

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.

Exploiting the wavelet structure in compressed sensing MRI.

PubMed

Chen, Chen; Huang, Junzhou

2014-12-01

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms. Copyright © 2014 Elsevier Inc. All rights reserved.

MATLAB for laser speckle contrast analysis (LASCA): a practice-based approach

NASA Astrophysics Data System (ADS)

Postnikov, Eugene B.; Tsoy, Maria O.; Postnov, Dmitry E.

2018-04-01

Laser Speckle Contrast Analysis (LASCA) is one of the most powerful modern methods for revealing blood dynamics. The experimental design and theory for this method are well established, and the computational recipie is often regarded to be trivial. However, the achieved performance and spatial resolution may considerable differ for different implementations. We comprise a minireview of known approaches to the spatial laser speckle contrast data processing and their realization in MATLAB code providing an explicit correspondence to the mathematical representation, a discussion of available implementations. We also present the algorithm based on the 2D Haar wavelet transform, also supplied with the program code. This new method provides an opportunity to introduce horizontal, vertical and diagonal speckle contrasts; it may be used for processing highly anisotropic images of vascular trees. We provide the comparative analysis of the accuracy of vascular pattern detection and the processing times with a special attention to details of the used MATLAB procedures.

Understanding north-western Mediterranean climate variability: a multi-proxy and multi-sequence approach based on wavelet analysis.

NASA Astrophysics Data System (ADS)

Azuara, Julien; Lebreton, Vincent; Jalali, Bassem; Sicre, Marie-Alexandrine; Sabatier, Pierre; Dezileau, Laurent; Peyron, Odile; Frigola, Jaime; Combourieu-Nebout, Nathalie

2017-04-01

Forcings and physical mechanisms underlying Holocene climate variability still remain poorly understood. Comparison of different paleoclimatic reconstructions using spectral analysis allows to investigate their common periodicities and helps to understand the causes of past climate changes. Wavelet analysis applied on several proxy time series from the Atlantic domain already revealed the first key-issues on the origin of Holocene climate variability. However the differences in duration, resolution and variance between the time-series are important issues for comparing paleoclimatic sequences in the frequency domain. This work compiles 7 paleoclimatic proxy records from 4 time-series from the north-western Mediterranean all ranging from 7000 to 1000 yrs cal BP: -pollen and clay mineral contents from the lagoonal sediment core PB06 recovered in southern France, -Sea Surface Temperatures (SST) derived from alkenones, concentration of terrestrial alkanes and their average chain length (ACL) from core KSGC-31_GolHo-1B recovered in the Gulf of Lion inner-shelf, - δ18O record from speleothems recovered in the Asiul Cave in north-western Spain, -grain size record from the deep basin sediment drift core MD99-2343 north of Minorca island. A comparison of their frequency content is proposed using wavelet analysis and cluster analysis of wavelet power spectra. Common cyclicities are assessed using cross-wavelet analysis. In addition, a new algorithm is used in order to propagate the age model errors within wavelet power spectra. Results are consistents with a non-stationnary Holocene climate variability. The Halstatt cycles (2000-2500 years) depicted in many proxies (ACL, errestrial alkanes and SSTs) demonstrate solar activity influence in the north-western Mediterranean climate. Cluster analysis shows that pollen and ACL proxies, both indicating changes in aridity, are clearly distinct from other proxies and share significant common periodicities around 1000 and 600 years

Wavelet-linear genetic programming: A new approach for modeling monthly streamflow

NASA Astrophysics Data System (ADS)

Ravansalar, Masoud; Rajaee, Taher; Kisi, Ozgur

2017-06-01

The streamflows are important and effective factors in stream ecosystems and its accurate prediction is an essential and important issue in water resources and environmental engineering systems. A hybrid wavelet-linear genetic programming (WLGP) model, which includes a discrete wavelet transform (DWT) and a linear genetic programming (LGP) to predict the monthly streamflow (Q) in two gauging stations, Pataveh and Shahmokhtar, on the Beshar River at the Yasuj, Iran were used in this study. In the proposed WLGP model, the wavelet analysis was linked to the LGP model where the original time series of streamflow were decomposed into the sub-time series comprising wavelet coefficients. The results were compared with the single LGP, artificial neural network (ANN), a hybrid wavelet-ANN (WANN) and Multi Linear Regression (MLR) models. The comparisons were done by some of the commonly utilized relevant physical statistics. The Nash coefficients (E) were found as 0.877 and 0.817 for the WLGP model, for the Pataveh and Shahmokhtar stations, respectively. The comparison of the results showed that the WLGP model could significantly increase the streamflow prediction accuracy in both stations. Since, the results demonstrate a closer approximation of the peak streamflow values by the WLGP model, this model could be utilized for the simulation of cumulative streamflow data prediction in one month ahead.

A data-driven wavelet-based approach for generating jumping loads

NASA Astrophysics Data System (ADS)

Chen, Jun; Li, Guo; Racic, Vitomir

2018-06-01

This paper suggests an approach to generate human jumping loads using wavelet transform and a database of individual jumping force records. A total of 970 individual jumping force records of various frequencies were first collected by three experiments from 147 test subjects. For each record, every jumping pulse was extracted and decomposed into seven levels by wavelet transform. All the decomposition coefficients were stored in an information database. Probability distributions of jumping cycle period, contact ratio and energy of the jumping pulse were statistically analyzed. Inspired by the theory of DNA recombination, an approach was developed by interchanging the wavelet coefficients between different jumping pulses. To generate a jumping force time history with N pulses, wavelet coefficients were first selected randomly from the database at each level. They were then used to reconstruct N pulses by the inverse wavelet transform. Jumping cycle periods and contract ratios were then generated randomly based on their probabilistic functions. These parameters were assigned to each of the N pulses which were in turn scaled by the amplitude factors βi to account for energy relationship between successive pulses. The final jumping force time history was obtained by linking all the N cycles end to end. This simulation approach can preserve the non-stationary features of the jumping load force in time-frequency domain. Application indicates that this approach can be used to generate jumping force time history due to single people jumping and also can be extended further to stochastic jumping loads due to groups and crowds.

The Wavelet Element Method. Part 2; Realization and Additional Features in 2D and 3D

NASA Technical Reports Server (NTRS)

Canuto, Claudio; Tabacco, Anita; Urban, Karsten

1998-01-01

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.

Forced Ignition Study Based On Wavelet Method

NASA Astrophysics Data System (ADS)

Martelli, E.; Valorani, M.; Paolucci, S.; Zikoski, Z.

2011-05-01

The control of ignition in a rocket engine is a critical problem for combustion chamber design. Therefore it is essential to fully understand the mechanism of ignition during its earliest stages. In this paper the characteristics of flame kernel formation and initial propagation in a hydrogen-argon-oxygen mixing layer are studied using 2D direct numerical simulations with detailed chemistry and transport properties. The flame kernel is initiated by adding an energy deposition source term in the energy equation. The effect of unsteady strain rate is studied by imposing a 2D turbulence velocity field, which is initialized by means of a synthetic field. An adaptive wavelet method, based on interpolating wavelets is used in this study to solve the compressible reactive Navier- Stokes equations. This method provides an alternative means to refine the computational grid points according to local demands of the physical solution. The present simulations show that in the very early instants the kernel perturbed by the turbulent field is characterized by an increased burning area and a slightly increased rad- ical formation. In addition, the calculations show that the wavelet technique yields a significant reduction in the number of degrees of freedom necessary to achieve a pre- scribed solution accuracy.

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.

Neural network face recognition using wavelets

NASA Astrophysics Data System (ADS)

Karunaratne, Passant V.; Jouny, Ismail I.

1997-04-01

The recognition of human faces is a phenomenon that has been mastered by the human visual system and that has been researched extensively in the domain of computer neural networks and image processing. This research is involved in the study of neural networks and wavelet image processing techniques in the application of human face recognition. The objective of the system is to acquire a digitized still image of a human face, carry out pre-processing on the image as required, an then, given a prior database of images of possible individuals, be able to recognize the individual in the image. The pre-processing segment of the system includes several procedures, namely image compression, denoising, and feature extraction. The image processing is carried out using Daubechies wavelets. Once the images have been passed through the wavelet-based image processor they can be efficiently analyzed by means of a neural network. A back- propagation neural network is used for the recognition segment of the system. The main constraints of the system is with regard to the characteristics of the images being processed. The system should be able to carry out effective recognition of the human faces irrespective of the individual's facial-expression, presence of extraneous objects such as head-gear or spectacles, and face/head orientation. A potential application of this face recognition system would be as a secondary verification method in an automated teller machine.

Long memory analysis by using maximal overlapping discrete wavelet transform

NASA Astrophysics Data System (ADS)

Shafie, Nur Amalina binti; Ismail, Mohd Tahir; Isa, Zaidi

2015-05-01

Long memory process is the asymptotic decay of the autocorrelation or spectral density around zero. The main objective of this paper is to do a long memory analysis by using the Maximal Overlapping Discrete Wavelet Transform (MODWT) based on wavelet variance. In doing so, stock market of Malaysia, China, Singapore, Japan and United States of America are used. The risk of long term and short term investment are also being looked into. MODWT can be analyzed with time domain and frequency domain simultaneously and decomposing wavelet variance to different scales without loss any information. All countries under studied show that they have long memory. Subprime mortgage crisis in 2007 is occurred in the United States of America are possible affect to the major trading countries. Short term investment is more risky than long term investment.

An adaptive demodulation approach for bearing fault detection based on adaptive wavelet filtering and spectral subtraction

NASA Astrophysics Data System (ADS)

Zhang, Yan; Tang, Baoping; Liu, Ziran; Chen, Rengxiang

2016-02-01

Fault diagnosis of rolling element bearings is important for improving mechanical system reliability and performance. Vibration signals contain a wealth of complex information useful for state monitoring and fault diagnosis. However, any fault-related impulses in the original signal are often severely tainted by various noises and the interfering vibrations caused by other machine elements. Narrow-band amplitude demodulation has been an effective technique to detect bearing faults by identifying bearing fault characteristic frequencies. To achieve this, the key step is to remove the corrupting noise and interference, and to enhance the weak signatures of the bearing fault. In this paper, a new method based on adaptive wavelet filtering and spectral subtraction is proposed for fault diagnosis in bearings. First, to eliminate the frequency associated with interfering vibrations, the vibration signal is bandpass filtered with a Morlet wavelet filter whose parameters (i.e. center frequency and bandwidth) are selected in separate steps. An alternative and efficient method of determining the center frequency is proposed that utilizes the statistical information contained in the production functions (PFs). The bandwidth parameter is optimized using a local ‘greedy’ scheme along with Shannon wavelet entropy criterion. Then, to further reduce the residual in-band noise in the filtered signal, a spectral subtraction procedure is elaborated after wavelet filtering. Instead of resorting to a reference signal as in the majority of papers in the literature, the new method estimates the power spectral density of the in-band noise from the associated PF. The effectiveness of the proposed method is validated using simulated data, test rig data, and vibration data recorded from the transmission system of a helicopter. The experimental results and comparisons with other methods indicate that the proposed method is an effective approach to detecting the fault-related impulses

Analysis of the Emitted Wavelet of High-Resolution Bowtie GPR Antennas

PubMed Central

Rial, Fernando I.; Lorenzo, Henrique; Pereira, Manuel; Armesto, Julia

2009-01-01

Most Ground Penetrating Radars (GPR) cover a wide frequency range by emitting very short time wavelets. In this work, we study in detail the wavelet emitted by two bowtie GPR antennas with nominal frequencies of 800 MHz and 1 GHz. Knowledge of this emitted wavelet allows us to extract as much information as possible from recorded signals, using advanced processing techniques and computer simulations. Following previously published methodology used by Rial et al. [1], which ensures system stability and reliability in data acquisition, a thorough analysis of the wavelet in both time and frequency domain is performed. Most of tests were carried out with air as propagation medium, allowing a proper analysis of the geometrical attenuation factor. Furthermore, we attempt to determine, for each antenna, a time zero in the records to allow us to correctly assign a position to the reflectors detected by the radar. Obtained results indicate that the time zero is not a constant value for the evaluated antennas, but instead depends on the characteristics of the material in contact with the antenna. PMID:22408523

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

Wavelet transform approach for fitting financial time series data

NASA Astrophysics Data System (ADS)

Ahmed, Amel Abdoullah; Ismail, Mohd Tahir

2015-10-01

This study investigates a newly developed technique; a combined wavelet filtering and VEC model, to study the dynamic relationship among financial time series. Wavelet filter has been used to annihilate noise data in daily data set of NASDAQ stock market of US, and three stock markets of Middle East and North Africa (MENA) region, namely, Egypt, Jordan, and Istanbul. The data covered is from 6/29/2001 to 5/5/2009. After that, the returns of generated series by wavelet filter and original series are analyzed by cointegration test and VEC model. The results show that the cointegration test affirms the existence of cointegration between the studied series, and there is a long-term relationship between the US, stock markets and MENA stock markets. A comparison between the proposed model and traditional model demonstrates that, the proposed model (DWT with VEC model) outperforms traditional model (VEC model) to fit the financial stock markets series well, and shows real information about these relationships among the stock markets.

On-Line Robust Modal Stability Prediction using Wavelet Processing

NASA Technical Reports Server (NTRS)

Brenner, Martin J.; Lind, Rick

1998-01-01

Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.

Improving 3D Wavelet-Based Compression of Hyperspectral Images

NASA Technical Reports Server (NTRS)

Klimesh, Matthew; Kiely, Aaron; Xie, Hua; Aranki, Nazeeh

2009-01-01

Two methods of increasing the effectiveness of three-dimensional (3D) wavelet-based compression of hyperspectral images have been developed. (As used here, images signifies both images and digital data representing images.) The methods are oriented toward reducing or eliminating detrimental effects of a phenomenon, referred to as spectral ringing, that is described below. In 3D wavelet-based compression, an image is represented by a multiresolution wavelet decomposition consisting of several subbands obtained by applying wavelet transforms in the two spatial dimensions corresponding to the two spatial coordinate axes of the image plane, and by applying wavelet transforms in the spectral dimension. Spectral ringing is named after the more familiar spatial ringing (spurious spatial oscillations) that can be seen parallel to and near edges in ordinary images reconstructed from compressed data. These ringing phenomena are attributable to effects of quantization. In hyperspectral data, the individual spectral bands play the role of edges, causing spurious oscillations to occur in the spectral dimension. In the absence of such corrective measures as the present two methods, spectral ringing can manifest itself as systematic biases in some reconstructed spectral bands and can reduce the effectiveness of compression of spatially-low-pass subbands. One of the two methods is denoted mean subtraction. The basic idea of this method is to subtract mean values from spatial planes of spatially low-pass subbands prior to encoding, because (a) such spatial planes often have mean values that are far from zero and (b) zero-mean data are better suited for compression by methods that are effective for subbands of two-dimensional (2D) images. In this method, after the 3D wavelet decomposition is performed, mean values are computed for and subtracted from each spatial plane of each spatially-low-pass subband. The resulting data are converted to sign-magnitude form and compressed in a

Application of Wavelet Analysis on Variability, Teleconnectivity, and Predictability November-January Taiwan rainfall

NASA Astrophysics Data System (ADS)

T.; Gan, Y.

2009-04-01

First the wavelet analysis was used to analyze the variability of winter (November-January) rainfall (1974-2006) of Taiwan and seasonal sea surface temperature (SST) in selected domains of the Pacific Ocean. From the scale average wavelet power (SAWP) computed for the seasonal rainfall and seasonal SST, it seems that these data exhibit interannual oscillations at 2-4-year period. Correlations between rainfall and SST SAWP were further estimated. Next the SST in selected sectors of the western Pacific Ocean (around 5°N-30°N, 120°E-150°E) was used as predictors to predict the winter rainfall of Taiwan at one season lead time using an Artificial Neural Network calibrated by Genetic Algorithm (ANN-GA). The ANN-GA was first calibrated using the 1974-1998 data and independently validated using 1999-2005 data. In terms of summary statistics such as the correlation coefficient, root-mean-square errors (RMSE), and Hansen-Kuipers (HK) scores, the seasonal prediction for northern and western Taiwan are generally good for both calibration and validation stages, but not so in some stations located in southeast Taiwan and Central Mountain.

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.

Lattice functions, wavelet aliasing, and SO(3) mappings of orthonormal filters

NASA Astrophysics Data System (ADS)

John, Sarah

1998-01-01

A formulation of multiresolution in terms of a family of dyadic lattices {Sj;j∈Z} and filter matrices Mj⊂U(2)⊂GL(2,C) illuminates the role of aliasing in wavelets and provides exact relations between scaling and wavelet filters. By showing the {DN;N∈Z+} collection of compactly supported, orthonormal wavelet filters to be strictly SU(2)⊂U(2), its representation in the Euler angles of the rotation group SO(3) establishes several new results: a 1:1 mapping of the {DN} filters onto a set of orbits on the SO(3) manifold; an equivalence of D∞ to the Shannon filter; and a simple new proof for a criterion ruling out pathologically scaled nonorthonormal filters.

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.

Adaptive Filtering in the Wavelet Transform Domain Via Genetic Algorithms

DTIC Science & Technology