2-D Continuous Wavelet Transform for ESPI phase-maps denoising
NASA Astrophysics Data System (ADS)
Escalante, Nivia; Villa, Jesús; de la Rosa, Ismael; de la Rosa, Enrique; González-Ramírez, Efrén; Gutiérrez, Osvaldo; Olvera, Carlos; Araiza, María
2013-09-01
In this work we introduce a 2-D Continuous Wavelet Transform (2-D CWT) method for denoising ESPI phase-maps. Multiresolution analysis with 2-D wavelets can provide high directional sensitivity and high anisotropy which are proper characteristics for this task. In particular, the 2-D CWT method using Gabor atoms (Gabor mother wavelets) which can naturally model phase fringes, has a good performance against noise and can preserve phase fringes. We describe the theoretical basis of the proposed technique and show some experimental results with real and simulated ESPI phase-maps. As can be verified the proposal is robust and effective.
Interpretation of gravity data using 2-D continuous wavelet transformation and 3-D inverse modeling
NASA Astrophysics Data System (ADS)
Roshandel Kahoo, Amin; Nejati Kalateh, Ali; Salajegheh, Farshad
2015-10-01
Recently the continuous wavelet transform has been proposed for interpretation of potential field anomalies. In this paper, we introduced a 2D wavelet based method that uses a new mother wavelet for determination of the location and the depth to the top and base of gravity anomaly. The new wavelet is the first horizontal derivatives of gravity anomaly of a buried cube with unit dimensions. The effectiveness of the proposed method is compared with Li and Oldenburg inversion algorithm and is demonstrated with synthetics and real gravity data. The real gravity data is taken over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The obtained results of the 2D wavelet based algorithm and Li and Oldenburg inversion on the Mobrun ore body had desired similarities to the drill-hole depth information. In all of the inversion algorithms the model non-uniqueness is the challenging problem. Proposed method is based on a simple theory and there is no model non-uniqueness on it.
2-D wavelet with position controlled resolution
NASA Astrophysics Data System (ADS)
Walczak, Andrzej; Puzio, Leszek
2005-09-01
Wavelet transformation localizes all irregularities in the scene. It is most effective in the case when intensities in the scene have no sharp details. It is the case often present in a medical imaging. To identify the shape one has to extract it from the scene as typical irregularity. When the scene does not contain sharp changes then common differential filters are not efficient tool for a shape extraction. The new 2-D wavelet for such task has been proposed. Described wavelet transform is axially symmetric and has varied scale in dependence on the distance from the centre of the wavelet symmetry. The analytical form of the wavelet has been presented as well as its application for details extraction in the scene. Most important feature of the wavelet transform is that it gives a multi-scale transformation, and if zoom is on the wavelet selectivity varies proportionally to the zoom step. As a result, the extracted shape does not change during zoom operation. What is more the wavelet selectivity can be fit to the local intensity gradient properly to obtain best extraction of the irregularities.
The 2D large deformation analysis using Daubechies wavelet
NASA Astrophysics Data System (ADS)
Liu, Yanan; Qin, Fei; Liu, Yinghua; Cen, Zhangzhi
2010-01-01
In this paper, Daubechies (DB) wavelet is used for solution of 2D large deformation problems. Because the DB wavelet scaling functions are directly used as basis function, no meshes are needed in function approximation. Using the DB wavelet, the solution formulations based on total Lagrangian approach for two-dimensional large deformation problems are established. Due to the lack of Kroneker delta properties in wavelet scaling functions, Lagrange multipliers are used for imposition of boundary condition. Numerical examples of 2D large deformation problems illustrate that this method is effective and stable.
Applications of a fast, continuous wavelet transform
Dress, W.B.
1997-02-01
A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.
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.
Applications of a fast continuous wavelet transform
NASA Astrophysics Data System (ADS)
Dress, William B.
1997-04-01
A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice
NASA Astrophysics Data System (ADS)
Liu, Hong; Mo, Yu L.
1998-08-01
There are many textures such as woven fabrics having repeating Textron. In order to handle the textural characteristics of images with defects, this paper proposes a new method based on 2D wavelet transform. In the method, a new concept of different adaptive wavelet bases is used to match the texture pattern. The 2D wavelet transform has two different adaptive orthonormal wavelet bases for rows and columns which differ from Daubechies wavelet bases. The orthonormal wavelet bases for rows and columns are generated by genetic algorithm. The experiment result demonstrate the ability of the different adaptive wavelet bases to characterize the texture and locate the defects in the texture.
A parallel splitting wavelet method for 2D conservation laws
NASA Astrophysics Data System (ADS)
Schmidt, Alex A.; Kozakevicius, Alice J.; Jakobsson, Stefan
2016-06-01
The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.
The Continuous wavelet in airborne gravimetry
NASA Astrophysics Data System (ADS)
Liang, X.; Liu, L.
2013-12-01
Airborne gravimetry is an efficient method to recover medium and high frequency band of earth gravity over any region, especially inaccessible areas, which can measure gravity data with high accuracy,high resolution and broad range in a rapidly and economical way, and It will play an important role for geoid and geophysical exploration. Filtering methods for reducing high-frequency errors is critical to the success of airborne gravimetry due to Aircraft acceleration determination based on GPS.Tradiontal filters used in airborne gravimetry are FIR,IIR filer and so on. This study recommends an improved continuous wavelet to process airborne gravity data. Here we focus on how to construct the continuous wavelet filters and show their working principle. Particularly the technical parameters (window width parameter and scale parameter) of the filters are tested. Then the raw airborne gravity data from the first Chinese airborne gravimetry campaign are filtered using FIR-low pass filter and continuous wavelet filters to remove the noise. The comparison to reference data is performed to determinate external accuracy, which shows that continuous wavelet filters applied to airborne gravity in this thesis have good performances. The advantages of the continuous wavelet filters over digital filters are also introduced. The effectiveness of the continuous wavelet filters for airborne gravimetry is demonstrated through real data computation.
Image denoising with 2D scale-mixing complex wavelet transforms.
Remenyi, Norbert; Nicolis, Orietta; Nason, Guy; Vidakovic, Brani
2014-12-01
This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images. PMID:25312931
Wavelet diagnostics of the flow control of unsteady separation on a 2D Wind Turbine Airfoil
NASA Astrophysics Data System (ADS)
Bai, Zhe; Lewalle, Jacques; Wang, Guannan; Glauser, Mark
2013-11-01
We investigated the aerodynamic characteristics of a 2D wind turbine airfoil. Unsteadiness was associated with the wake of a cylinder upstream of the airfoil. The experiments were conducted in both the baseline case, and with active closed-loop control on the suction surface of the airfoil. The data consisted of surface pressure time series. Continuous wavelet analysis gave the phase, band-pass filtered signals and envelope of harmonics of the fundamental shedding frequency. Coherence of pairs of signals was also used to map the flow characteristics. For the baseline and controlled case, we will report on the relation between phase of the leading edge fluctuations, unsteady flow separation and lift and drag coefficients. Our goal is to develop a more effective controller. The experiment was funded by DoE through University of Minnesota Wind Energy Consortium. Thanks for the support from the MAE department of Syracuse University.
Wavelet regularization of the 2D incompressible Euler equations
NASA Astrophysics Data System (ADS)
Nguyen van Yen, Romain; Farge, Marie; Schneider, Kai
2009-11-01
We examine the viscosity dependence of the solutions of two-dimensional Navier-Stokes equations in periodic and wall-bounded domains, for Reynolds numbers varying from 10^3 to 10^7. We compare the Navier-Stokes solutions to those of the regularized two-dimensional Euler equations. The regularization is performed by applying at each time step the wavelet-based CVS filter (Farge et al., Phys. Fluids, 11, 1999), which splits turbulent fluctuations into coherent and incoherent contributions. We find that for Reynolds 10^5 the dissipation of coherent enstrophy tends to become independent of Reynolds, while the dissipation of total enstrophy decays to zero logarithmically with Reynolds. In the wall-bounded case, we observe an additional production of enstrophy at the wall. As a result, coherent enstrophy diverges when Reynolds tends to infinity, but its time derivative seems to remain bounded independently of Reynolds. This indicates that a balance may have been established between coherent enstrophy dissipation and coherent enstrophy production at the wall. The Reynolds number for which the dissipation of coherent enstrophy becomes independent on the Reynolds number is proposed to define the onset of the fully-turbulent regime.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Wavelet characterization of 2D turbulence and intermittency in magnetized electron plasmas
NASA Astrophysics Data System (ADS)
Romé, M.; Chen, S.; Maero, G.
2016-06-01
A study of the free relaxation of turbulence in a two-dimensional (2D) flow is presented, with a focus on the role of the initial vorticity conditions. Exploiting a well-known analogy with 2D inviscid incompressible fluids, the system investigated here is a magnetized pure electron plasma. The dynamics of this system are simulated by means of a 2D particle-in-cell code, starting from different spiral density (vorticity) distributions. A wavelet multiresolution analysis is adopted, which allows the coherent and incoherent parts of the flow to be separated. Comparison of the turbulent evolution in the different cases is based on the investigation of the time evolution of statistical properties, including the probability distribution functions and structure functions of the vorticity increments. It is also based on an analysis of the enstrophy evolution and its spectrum for the two components. In particular, while the statistical features assess the degree of flow intermittency, spectral analysis allows us not only to estimate the time required to reach a state of fully developed turbulence, but also estimate its dependence on the thickness of the initial spiral density distribution, accurately tracking the dynamics of both the coherent structures and the turbulent background. The results are compared with those relevant to annular initial vorticity distributions (Chen et al 2015 J. Plasma Phys. 81 495810511).
An Automatic 3D Facial Landmarking Algorithm Using 2D Gabor Wavelets.
de Jong, Markus A; Wollstein, Andreas; Ruff, Clifford; Dunaway, David; Hysi, Pirro; Spector, Tim; Fan Liu; Niessen, Wiro; Koudstaal, Maarten J; Kayser, Manfred; Wolvius, Eppo B; Bohringer, Stefan
2016-02-01
In this paper, we present a novel approach to automatic 3D facial landmarking using 2D Gabor wavelets. Our algorithm considers the face to be a surface and uses map projections to derive 2D features from raw data. Extracted features include texture, relief map, and transformations thereof. We extend an established 2D landmarking method for simultaneous evaluation of these data. The method is validated by performing landmarking experiments on two data sets using 21 landmarks and compared with an active shape model implementation. On average, landmarking error for our method was 1.9 mm, whereas the active shape model resulted in an average landmarking error of 2.3 mm. A second study investigating facial shape heritability in related individuals concludes that automatic landmarking is on par with manual landmarking for some landmarks. Our algorithm can be trained in 30 min to automatically landmark 3D facial data sets of any size, and allows for fast and robust landmarking of 3D faces. PMID:26540684
A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform
Tang, Hui; Tong, Dan; Dong Bao, Xu; Dillenseger, Jean-Louis
2015-04-15
Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time.
Spike detection using the continuous wavelet transform.
Nenadic, Zoran; Burdick, Joel W
2005-01-01
This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution. PMID:15651566
NASA Astrophysics Data System (ADS)
Hu, Li-Yun; Fan, Hong-Yi
2010-07-01
In a preceding letter (2007 Opt. Lett. 32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.
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.
Elastic Wave Propagation in Concrete and Continuous Wavelet Transform
Chiang, C.-H.; Gi, Y.-F.; Pan, C.-L.; Cheng, C.-C.
2005-04-09
Elastic wave methods, such as the ultrasonic pulse velocity and the impact echo, are often subject to multiple reflections at the boundaries of various constituents of concrete. Current study aims to improve the feature identification of elastic wave propagation due to buried objects in concrete slabs and cylinders. Embedded steel reinforcement, steel and PVC tubes, wooden disks, and rubber spheres are tested. The received signals are analyzed using continuous wavelet transform. As a result, signals are decomposed into distinctive frequency bands with transient information preserved. The interpretation of multiple reflections at different boundary conditions thus becomes more straightforward. Features related to reflections from steel bar, PVC tube, and steel tube can be readily identified in the magnitude plot of wavelet coefficients. Vibration modes of the concrete slab corresponding to different buried objects can also be separated based on corresponding time duration.
Elastic Wave Propagation in Concrete and Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Chiang, Chih-Hung; Gi, Yu-Fung; Pan, Chi-Ling; Cheng, Chia-Chi
2005-04-01
Elastic wave methods, such as the ultrasonic pulse velocity and the impact echo, are often subject to multiple reflections at the boundaries of various constituents of concrete. Current study aims to improve the feature identification of elastic wave propagation due to buried objects in concrete slabs and cylinders. Embedded steel reinforcement, steel and PVC tubes, wooden disks, and rubber spheres are tested. The received signals are analyzed using continuous wavelet transform. As a result, signals are decomposed into distinctive frequency bands with transient information preserved. The interpretation of multiple reflections at different boundary conditions thus becomes more straightforward. Features related to reflections from steel bar, PVC tube, and steel tube can be readily identified in the magnitude plot of wavelet coefficients. Vibration modes of the concrete slab corresponding to different buried objects can also be separated based on corresponding time duration.
NASA Astrophysics Data System (ADS)
Wang, Chun-Hsiung; Hsu, Kuan-Yu; Lee, Chih-Kung
2016-03-01
A real-time three-dimensional surface profile metrology system was implemented by integrating Fourier Transform (FT) based algorithms to convert interference intensity fringes to wrapped frequency phase maps and then to unwrapped phase maps. The revival of this field can find its roots in recognizing the development of high-resolution high-speed CCD/CMOS over the years. Two-dimensional Continuous Wavelet Transform (2D-CWT), which possesses the ability to construct daughter wavelets of good time and frequency localization according to different fringes conditions from a characteristic mother wavelet, was implemented with an attempt to reduce redundant fitting process of ordinary Short Time Fourier Transform (STFT), also known as Windowed Fourier Transform (WFT), and therefore to accelerate the FT-related algorithms needed. Implemented with the efficient wavelet construction process by using 2D-CWT, Electronic Speckle Pattern Interferometer (ESPI) was adopted to take advantage of this new process. Different from using several phase shifting steps before to solve the direction ambiguity, which takes time to capture multiple intensity maps during measurement, the phase maps needed were retrieved from a single frame interference fringes. It is to be noted that this one-image interference fringe was captured by having a pre-introduced spatial carrier frequency embedded within the experimental setup so as to remove the directional ambiguity. 2D-CWT dealing with different signal-to-noise ratios was also designed by selecting wavelet parameters properly, which is expected to achieve higher accuracy and faster processing speed. For phase unwrapping, Poisson's equation with Neumann boundary condition was solved by using FFT. The benefit of using 2D-CWTs with different wavelets as compared to WFT was demonstrated experimentally.
NASA Astrophysics Data System (ADS)
Tang, Xiangyang; Ning, Ruola; Yu, Rongfeng; Conover, David L.
1999-05-01
The application of the newly developed flat panel x-ray imaging detector in cone beam volume CT has attracted increasing interest recently. Due to an imperfect solid state array manufacturing process, however, defective elements, gain non-uniformity and offset image unavoidably exist in all kinds of flat panel x-ray imaging detectors, which will cause severe streak and ring artifacts in a cone beam reconstruction image and severely degrade image quality. A calibration technique, in which the artifacts resulting from the defective elements, gain non-uniformity and offset image can be reduced significantly, is presented in this paper. The detection of defective elements is distinctively based upon two-dimensional (2D) wavelet analysis. Because of its inherent localizability in recognizing singularities or discontinuities, wavelet analysis possesses the capability of detecting defective elements over a rather large x-ray exposure range, e.g., 20% to approximately 60% of the dynamic range of the detector used. Three-dimensional (3D) images of a low-contrast CT phantom have been reconstructed from projection images acquired by a flat panel x-ray imaging detector with and without calibration process applied. The artifacts caused individually by defective elements, gain non-uniformity and offset image have been separated and investigated in detail, and the correlation with each other have also been exposed explicitly. The investigation is enforced by quantitative analysis of the signal to noise ratio (SNR) and the image uniformity of the cone beam reconstruction image. It has been demonstrated that the ring and streak artifacts resulting from the imperfect performance of a flat panel x-ray imaging detector can be reduced dramatically, and then the image qualities of a cone beam reconstruction image, such as contrast resolution and image uniformity are improved significantly. Furthermore, with little modification, the calibration technique presented here is also applicable
Continuous wavelet analysis of stent-induced perturbations in a bent pipe model for curved arteries
NASA Astrophysics Data System (ADS)
Bulusu, Kartik V.; Glenn, Autumn L.; Shu, Fangjun; Hussain, Shadman; Plesniak, Michael W.
2011-11-01
Secondary flow vortical structures were observed in a 180 degree circular bend under physiological flow conditions with a stent model installed upstream of the bend. Phase-locked 2-D PIV measurements were made at various cross-sectional planes along the bend. Stent-induced perturbations led to a transient flow regime with a multiplicity of vortical patterns initiated during the deceleration phase of the systolic peak (starting at t/T=0.21). An exploratory investigation of vortical scale-count metrics from continuous wavelet transforms, was performed using a Ricker wavelet. The metrics highlight the evolution of a pair of ordered, coherent, high-circulation, counter-rotating vortical structures (at t/T=0.21) into multiple, disordered, low-circulation, coherent vortical structures (by t/T=0.30). The overarching goal of this study is to create a regime map of secondary flow morphologies based on the driving physiological waveform. An approach to develop a regime map using vortical scale-count metrics is outlined. Supported by the National Science Foundation under Grant No. CBET-0828903.
Cell classification by moments and continuous wavelet transform methods
Chen, Qian; Fan, Yuan; Udpa, Lalita; Ayres, Virginia M
2007-01-01
Image processing techniques are bringing new insights to biomedical research. The automatic recognition and classification of biomedical objects can enhance work efficiency while identifying new inter-relationships among biological features. In this work, a simple rule-based decision tree classifier is developed to classify typical features of mixed cell types investigated by atomic force microscopy (AFM). A combination of continuous wavelet transform (CWT) and moment-based features are extracted from the AFM data to represent that shape information of different cellular objects at multiple resolution levels. The features are shown to be invariant under operations of translation, rotation, and scaling. The features are then used in a simple rule-based classifier to discriminate between anucleate versus nucleate cell types or to distinguish cells from a fibrous environment such as a tissue scaffold or stint. Since each feature has clear physical meaning, the decision rule of this tree classifier is simple, which makes it very suitable for online processing. Experimental results on AFM data confirm that the performance of this classifier is robust and reliable. PMID:17722546
NASA Astrophysics Data System (ADS)
Nenna, V.; Pidlisecky, A.
2012-12-01
scales: 1:4 km, 4:9 km, 9:15 km, and 15:30 km. The average normalized power within a scale bin for each sounding and time-channel are combined into four 2D maps. The maps show similar results over several time-channels, which allows us to average results in three time bins: early- (channels 6-12), mid- (channels 13-16), and late-time (channels 17-20). The B-field and dB/dt power maps contain highly linear and angular features that manifest differently in the two data sets and do not correlate with subsurface structure. Comparison of power maps from the two data types suggests that cultural noise is most prevalent at short spatial scales, which is consistent with the finite spatial continuity of infrastructure, and at late-time, when geologic signals are weakest and the signal to noise ratio is smallest. We conclude from these results that a CWT approach can be used to identify areas in which cultural noise impacts collected data. Future work is required to assess the magnitude of this impact and to filter the signals from cultural noise from the data.
NASA Astrophysics Data System (ADS)
Kulesh, M.; Holschneider, M.
2007-12-01
Surface wave propagation in heterogeneous media can provide a valuable source of information about the subsurface structure and its elastic properties. The processing of experimental seismic data sets related to the surface waves is computationally expensive and requires sophisticated techniques in order to infer the physical properties and structure of the subsurface from the bulk of available information. Most of the previous studies related to these problems are based on Fourier analysis. However, the frequency- dependent measurements, or time-frequency analysis offer additional insight and performance in any applications where Fourier techniques have been used. This analysis consists of examining the variation of the frequency content of a signal with time and is particularly suitable in geophysical applications. The continuous wavelet transform gives a suitable general framework for solving these types of problems; this approach is powerful and elegant, but is not the only available for the practical applications. Other methods such as the Gabor transform, the S-transform or bilinear transforms can be used as well. The relative performance of time-frequency analysis from different approaches is primarily controlled by the frequency resolution capability. To perform the time-frequency analysis of digital seismic data, we propose in this contribution a new free software package developed by the authors and based on the continuous wavelet transform. This package allows to perform the direct and inverse continuous wavelet transform, 2C and 3C polarization analysis and filtering, modeling the dispersed and attenuated wave propagation in the time-frequency domain and optimization in signal and wavelet domains. The aim of these operations is to extract polarization properties, velocities and attenuation parameters from a seismogram. The novelty of this package is that we incorporate the continuous wavelet transform into the library where the kernel is the time
Sequential damage detection based on the continuous wavelet transform
NASA Astrophysics Data System (ADS)
Liao, Yizheng; Balafas, Konstantinos; Rajagopal, Ram; Kiremidjian, Anne S.
2015-03-01
This paper presents a sequential structural damage detection algorithm that is based on a statistical model for the wavelet transform of the structural responses. The detector uses the coefficients of the wavelet model and does not require prior knowledge of the structural properties. Principal Component Analysis is applied to select and extract the most sensitive features from the wavelet coefficients as the damage sensitive features. The damage detection algorithm is validated using the simulation data collected from a four-story steel moment frame. Various features have been explored and the detection algorithm was able to identify damage. Additionally, we show that for a desired probability of false alarm, the proposed detector is asymptotically optimal on the expected delay.
Continuous Wavelet Transform Analysis of Acceleration Signals Measured from a Wave Buoy
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
Continuous wavelet transform analysis of acceleration signals measured from a wave buoy.
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
Identification of diesel front sound source based on continuous wavelet transform.
Hao, Zhi-yong; Han, Jun
2004-09-01
Acoustic signals from diesel engines contain useful information but also include considerable noise components. To extract information for condition monitoring purposes, continuous wavelet transform (CWT) is used for the characterization of engine acoustics. This paper first reviews CWT characteristics represented by short duration transient signals. Wavelet selection and CWT are then implemented and wavelet transform is used to analyze the major sources of the engine front's exterior radiation sound. The research provides a reliable basis for engineering practice to reduce vehicle sound level. Comparison of the identification results of the measured acoustic signals with the identification results of the measured surface vibration showed good agreement. PMID:15323001
NASA Astrophysics Data System (ADS)
Gdeisat, Munther; Burton, David; Lilley, Francis; Lalor, Michael; Moore, Chris
2010-04-01
This paper proposes the use of the two-dimensional continuous Paul wavelet transform to extract the phase of spatial carrier fringe patterns. The proposed algorithm has been tested using computer-generated and real fringe patterns, and these tests have demonstrated the suitability of the proposed technique for the phase demodulation of fringe patterns. Additionally, this algorithm is compared to three two-dimensional continuous wavelet algorithms that have figured prominently in the literature, specifically the Morlet, advanced Morlet and fan mother wavelets. This comparison has revealed that the proposed algorithm outperforms the other three mother wavelets in terms of its suitability for extracting the phase of fringe patterns that exhibit large phase variations.
Addison, Paul S
2016-06-01
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
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
Analysis of Mold Friction in a Continuous Casting Using Wavelet Entropy
NASA Astrophysics Data System (ADS)
Yong, Ma; Fangyin, Wang; Cheng, Peng; Wei, Gui; Bohan, Fang
2016-06-01
By studying mold friction (MDF), we observed that monitoring and controlling of the friction between the strand and the mold is very important for continuous casting to improve lubrication and prevent breakout. However, existing analysis technologies of MDF do not support the continuous casting very well. In addition, we found that the wavelet entropy has multiscale and statistical properties. Informed by these observations, in this article, we use wavelet entropy to judge the lubrication state between the strand and the mold. First, we demonstrate the implementation and superiority of wavelet entropy and how it helps in efficient evaluation of the lubrication state in mold. A study of wavelet entropy of MDF, which is obtained from the abnormal continuous casting production, such as level fluctuation, submerged entry nozzle broken, and breakout, has been performed to achieve relevant conclusions. The results indicate that the information of MDF in time and frequency domains could be obtained simultaneously by the application of wavelet entropy and that the wavelet entropy has a good sensibility for the study of disorder of MDF, which could further reveal the nature of MDF.
Zhang, Chang-jiang; Li, Dan-ting; Liang, Jiu-zhen; Cheng, Cun-gui
2007-01-01
Infrared spectra of semen celosiae and semen celosiae cristatae were obtained directly, quickly and accurately by Fourier transform infrared spectroscopy (FTIR) with OMNI sampler. Continuous wavelet transform was used to extrude local region of infrared spectra of semen celosiae and its confusable varieties. The difference of infrared spectra between semen celosiae and semen celosiae cristatae was extruded greatly. Accurate identification rate was improved greatly. Morlet wavelet, which can detect singular values of signal effectively, was selected as the mother wavelet. One-dimensional continuous wavelet transform was implemented for the infrared spectra of semen celosiae and its confusable varieties. The difference between semen celosiae and semen celosiae cristatae was observed at all scales in the wavelet domain. An optimal scale, at which the difference between semen celosiae and semen celosiae cristatae was the most obvious, was selected to identify semen celosiae and semen celosiae cristatae. The results show that it is effective to apply continuous wavelet transform on the basis of FTIR to identify the traditional Chinese medicinal materials, which are the same genus but different species. PMID:17390647
A self-calibrated angularly continuous 2D GRAPPA kernel for propeller trajectories
Skare, Stefan; Newbould, Rexford D; Nordell, Anders; Holdsworth, Samantha J; Bammer, Roland
2008-01-01
The k-space readout of propeller-type sequences may be accelerated by the use of parallel imaging (PI). For PROPELLER, the main benefits are reduced blurring due to T2 decay and SAR reduction, while for EPI-based propeller acquisitions such as Turbo-PROP and SAP-EPI, the faster k-space traversal alleviates geometric distortions. In this work, the feasibility of calculating a 2D GRAPPA kernel on only the undersampled propeller blades themselves is explored, using the matching orthogonal undersampled blade. It is shown that the GRAPPA kernel varies slowly across blades, therefore an angularly continuous 2D GRAPPA kernel is proposed, in which the angular variation of the weights is parameterized. This new angularly continuous kernel formulation greatly increases the numerical stability of the GRAPPA weight estimation, allowing the generation of fully sampled diagnostic quality images using only the undersampled propeller data. PMID:19025911
Delay-dependent stability and stabilisation of continuous 2D delayed systems with saturating control
NASA Astrophysics Data System (ADS)
Hmamed, Abdelaziz; Kririm, Said; Benzaouia, Abdellah; Tadeo, Fernando
2016-09-01
This paper deals with the stabilisation problem of continuous two-dimensional (2D) delayed systems, in the presence of saturations on the control signals. For this, a new delay decomposition approach is proposed to deal with the stability and stabilisation issues. The idea is that the range of variation of each delay is divided into segments, and a specific Lyapunov- Krasovskii functional is used that contains different weight matrices in each segment. Then, based on this approach, new delay-dependent stability and stabilisation criteria for continuous 2D delayed systems are derived. These criteria are less conservative and include some existing results as special cases. Some numerical examples are provided to show that a significant improvement is achieved using the proposed approach.
Exploration of EEG features of Alzheimer's disease using continuous wavelet transform.
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. PMID:25863694
A new methodology to map double-cropping croplands based on continuous wavelet transform
NASA Astrophysics Data System (ADS)
Qiu, Bingwen; Zhong, Ming; Tang, Zhenghong; Wang, Chongyang
2014-02-01
Cropping intensity is one of the major factors in crop production and agricultural intensification. A new double-cropping croplands mapping methodology using Moderate Resolution Imaging Spectroradiometer (MODIS) time series datasets through continuous wavelet transform was proposed in this study. This methodology involved four steps. First, daily continuous MODIS Enhanced Vegetation Index (EVI) time series datasets were developed for the study year. Next, the EVI time series datasets were transformed into a two dimensional (time-frequency) wavelet scalogram based on continuous wavelet transform. Third, a feature extraction process was conducted on the wavelet scalogram, where the characteristic spectra were calculated from the wavelet scalogram and the feature peak within two skeleton lines was obtained. Finally, a threshold was determined for feature peak values to discriminate double-cropping croplands within each pixel. The application of the proposed procedure to China's Henan Province in 2010 produced an objective and accurate spatial distribution map, which correlated well with in situ observation data (over 90% agreement). The proposed new methodology efficiently handled complex variability that might be caused by regional variation in climate, management practices, growth peaks by winter weed or winter wheat, and data noise. Therefore, the methodology shows promise for future studies at regional and global scales.
Clifford Continuous Wavelet Transforms in Ll{sub 0,2} and Ll{sub 0,3}
Bernstein, S.
2008-09-01
We consider Clifford-valued functions defined on R{sup n}. From the viewpoint of square integrable group representations a continuous wavelet transform is an irreducible continuous unitary representation of the affin group on the real line but also on R{sup n}. We will demonstrate that different Clifford continuous wavelet transforms can be obtained inside the calculus with similar properties than the real valued transform. Nevertheless, the Clifford wavelet transform is neither just a special vector transform nor just a wavelet transform applied to each component of the Clifford-valued function.
NASA Astrophysics Data System (ADS)
Galiana-Merino, J. J.; Rosa-Herranz, J. L.; Rosa-Cintas, S.; Martinez-Espla, J. J.
2013-01-01
A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of multichannel seismic data. The considered time-frequency transforms include the continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform. The developed approaches provide a fast and precise time-frequency examination of the seismograms at different frequency bands. Moreover, filtering methods for noise, transients or even baseline removal, are implemented. The primary motivation is to support seismologists with a user-friendly and fast program for the wavelet analysis, providing practical and understandable results. Program summaryProgram title: SeismicWaveTool Catalogue identifier: AENG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 611072 No. of bytes in distributed program, including test data, etc.: 14688355 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.8.0.347 (R2009a) or higher. Wavelet Toolbox is required. Computer: Developed on a MacBook Pro. Tested on Mac and PC. No computer-specific optimization was performed. Operating system: Any supporting MATLAB (MathWorks Inc.) v7.8.0.347 (R2009a) or higher. Tested on Mac OS X 10.6.8, Windows XP and Vista. Classification: 13. Nature of problem: Numerous research works have developed a great number of free or commercial wavelet based software, which provide specific solutions for the analysis of seismic data. On the other hand, standard toolboxes, packages or libraries, such as the MathWorks' Wavelet Toolbox for MATLAB, offer command line functions and interfaces for the wavelet analysis of one-component signals. Thus, software usually is focused on very specific problems
NASA Astrophysics Data System (ADS)
Fayadh, Rashid A.; Malek, F.; Fadhil, Hilal A.; Dawood, Sameer A.; Abdullah, Farah Salwani
2015-05-01
In this paper, three levels of analysis and synthesis filter banks were used to create coefficients for a continuous wavelet transform (CWT) and discrete wavelet transform (DWT). The main property of these wavelet transform schemes is their ability to construct the transmitted signal across a log-normal fading channel over additive white Gaussian noise (AWGN). Wireless rake-receiver structure was chosen as a major application to reduce the inter-symbol interference (ISI) and to minimize the noise. In this work, a new scheme of rake receiver is proposed to receive indoor, multi-path components (MPCs) for ultra-wideband (UWB) wireless communication systems. Rake receivers consist of a continuous wavelet rake (CW-rake) and a discrete wavelet rake (DW-rake), and they use huge bandwidth (7.5 GHz), as reported by the Federal Communications Commission (FCC). The indoor channel models chose for analysis in this research were the non line-of-sight (LOS) channel model (CM4 from 4 to 10 meters) to show the behavior of bit error rate (BER) with respect to signal-to noise ratio (SNR). Two types of rake receiver were used in the simulation, i.e., partial-rake and selective-rake receivers with the maximal ratio combining (MRC) technique to capture the energy of the signal from the output of the rake's fingers.
NASA Astrophysics Data System (ADS)
Sandirasegaram, Nicholas; English, Ryan
2005-05-01
The performance of several combinations of feature extraction and target classification algorithms is analyzed for Synthetic Aperture Radar (SAR) imagery using the standard Moving and Stationary Target Acquisition and Recognition (MSTAR) evaluation method. For feature extraction, 2D Fast Fourier Transform (FFT) is used to extract Fourier coefficients (frequency information) while 2D wavelet decomposition is used to extract wavelet coefficients (time-frequency information), from which subsets of characteristic in-class "invariant" coefficients are developed. Confusion matrices and Receiver Operating Characteristic (ROC) curves are used to evaluate and compare combinations of these characteristic coefficients with several classification methods, including Lp metric distances, a Multi Layer Perceptron (MLP) Neural Network (NN) and AND Corporation's Holographic Neural Technology (HNeT) classifier. The evaluation method examines the trade-off between correct detection rate and false alarm rate for each combination of feature-classifier systems. It also measures correct classification, misclassification and rejection rates for a 90% detection rate. Our analysis demonstrates the importance of feature and classifier selection in accurately classifying new target images.
On the equivalence of moment quantization and continuous wavelet transform analysis
NASA Astrophysics Data System (ADS)
Handy, Carlos R.; Murenzi, Romain
1998-12-01
The space of polynomials maps onto itself under affine transformations, 0305-4470/31/49/012/img1. This suggests that a moment reformulation of continuous wavelet transform (CWT) theory (the affine convolution, 0305-4470/31/49/012/img2, of a signal, or wavefunction, 0305-4470/31/49/012/img3) should lead to significant simplifications in its implementation. We present a comprehensive formalism, with numerical examples, that inextricably links moment quantization (MQ) and CWT theory. For rational fraction potential problems and mother wavelets of the form 0305-4470/31/49/012/img4 (Q(x) an appropriate polynomial), MQ permits a more efficient and accurate (in a pointwise convergent sense) CWT implementation; whereas, CWT broadens the scope of applicability for MQ methods, and is its natural extension when a more global approximation is desired. Our formalism also gives one justification for the empirical superiority manifested by previous MQ studies, as compared with dyadic wavelet reconstruction methods. We implement our formalism in the context of the quartic, sextic and octic anharmonic oscillator potentials, and demonstrate the flexibility of the method by treating both the Mexican hat wavelet transform, as well as that based on the mother wavelet 0305-4470/31/49/012/img5.
Chen, Hui; Lin, Zan; Mo, Lin; Wu, Hegang; Wu, Tong; Tan, Chao
2015-12-01
Spectrum is inherently local in nature since it can be thought of as a signal being composed of various frequency components. Wavelet transform (WT) is a powerful tool that partitions a signal into components with different frequency. The property of multi-resolution enables WT a very effective and natural tool for analyzing spectrum-like signal. In this study, a continuous wavelet transform (CWT)-based variable selection procedure was proposed to search for a set of informative wavelet coefficients for constructing a near-infrared (NIR) spectral diagnosis model of cancer. The CWT provided a fine multi-resolution feature space for selecting best predictors. A measure of discriminating power (DP) was defined to evaluate the coefficients. Partial least squares-discriminant analysis (PLS-DA) was used as the classification algorithm. A NIR spectral dataset associated to cancer diagnosis was used for experiment. The optimal results obtained correspond to the wavelet of db2. It revealed that on condition of having better performance on the training set, the optimal PLS-DA model using only 40 wavelet coefficients in 10 scales achieved the same performance as the one using all the variables in the original space on the test set: an overall accuracy of 93.8%, sensitivity of 92.5% and specificity of 96.3%. It confirms that the CWT-based feature selection coupled with PLS-DA is feasible and effective for constructing models of diagnostic cancer by NIR spectroscopy. PMID:26143320
Wavelet Processing of Continuous Scanning Laser Doppler Vibrometry data in Non-Destructive Testing
NASA Astrophysics Data System (ADS)
Chiariotti, P.; Revel, G. M.; Martarelli, M.
2015-11-01
The present paper proposes a novel non-destructive testing procedure based on the exploitation of the simultaneous time and spatial sampling provided by Continuous Scanning Laser Doppler Vibrometry (CSLDV) and the feature extraction capabilities of wavelet-based processing. Two criteria for selecting in an objective way the mother-wavelet to be used in the decomposition procedure, the Relative Wavelet Energy and Energy to Shannon Entropy Ratio, are compared in terms of capability of best locating the damage. The paper demonstrates the applicability of the procedure for the identification of superficial and in-depth defects in simulated and real test cases when an area scan is performed over the test sample. The method shows promising results, since defects are identified in different severity conditions.
Application Of Continuous Wavelet Transform On Aeromagnetic Data To Identify Volcanic Rocks
NASA Astrophysics Data System (ADS)
Yang, Y.; Li, Y.; Liu, T.
2008-12-01
This paper focuses on the application of continuous wavelet transform on aeromagnetic data, to locate and characterize volcanic rocks. The studied structure is sited in the north centre of the Huanghua depression in the Bohaiwan basin of east China. As channels of magmatism activities, the faults have caused multi-stage magma outpouring and intrusion, forming igneous rocks of different series of strata. As a traditional frequency decomposition method, the discrete wavelet transform is unable to localize frequency variations over time. To handle this problem, the short time Fourier transform method is widely used for the decomposition of non-stationary signals. One problem with this approach is that the fixed width `window function' results in limited resolution. Therefore, the continuous wavelet transform decomposition was used as an alternative approach to overcome this resolution problem. In the continuous wavelet transform, the signal is multiplied with a function similar to a `window function' but the width of the window is not fixed. The time window width is allowed to vary depending upon the frequency that is being considered. As for the magnetic anomalies of igneous rocks, they have different frequencies due to their depths; by analyzing the complex wavelet-based time-frequency characteristics of certain frequencies, we can identify the residual anomalies caused by volcanic rocks in different depths. The theoretical results show that local high frequency spectrum anomalies are the reflection of magnetic sources, and different scales (or different center frequencies) reflect different source depths, with larger scales for deeper sources. Therefore, by analyzing the complex wavelet-based frequency spectrum under different centre frequencies, we can analyze the distribution of magnetic field sources. Then the continuous wavelet transform was applied on the RTP aeromagnetic data of our study area. The data processing results present a detailed description of the
Mouse EEG spike detection based on the adapted continuous wavelet transform
NASA Astrophysics Data System (ADS)
Tieng, Quang M.; Kharatishvili, Irina; Chen, Min; Reutens, David C.
2016-04-01
Objective. Electroencephalography (EEG) is an important tool in the diagnosis of epilepsy. Interictal spikes on EEG are used to monitor the development of epilepsy and the effects of drug therapy. EEG recordings are generally long and the data voluminous. Thus developing a sensitive and reliable automated algorithm for analyzing EEG data is necessary. Approach. A new algorithm for detecting and classifying interictal spikes in mouse EEG recordings is proposed, based on the adapted continuous wavelet transform (CWT). The construction of the adapted mother wavelet is founded on a template obtained from a sample comprising the first few minutes of an EEG data set. Main Result. The algorithm was tested with EEG data from a mouse model of epilepsy and experimental results showed that the algorithm could distinguish EEG spikes from other transient waveforms with a high degree of sensitivity and specificity. Significance. Differing from existing approaches, the proposed approach combines wavelet denoising, to isolate transient signals, with adapted CWT-based template matching, to detect true interictal spikes. Using the adapted wavelet constructed from a predefined template, the adapted CWT is calculated on small EEG segments to fit dynamical changes in the EEG recording.
NASA Astrophysics Data System (ADS)
Huang, Yan; Tian, Qingjiu; Wang, Lei; Geng, Jun; Lyu, Chunguang
2014-01-01
The existing hyperspectral vegetation indices used for estimating the canopy leaf area index (LAI) of winter wheat (Triticum aestivum L.) performed well, but the use of such indices at late growth stages can lead to inaccurate results. To improve the performance of LAI models for wheat in late growth stages, the continuous wavelet transform (CWT) method was applied in this study and used to decompose the canopy reflectance and its first derivative into wavelet coefficients. The correlation scalograms of wavelet coefficients and the LAI were then constructed and used to extract the top 1% correlated region as the wavelet feature. The canopy LAI estimation model for late growth wheat was established at last and compared with models based on 12 different types of hyperspectral vegetation indices. The results showed that, compared with the estimation models using the hyperspectral vegetation indices (for which the R2 values were all less than 0.15 and the root-mean-square errors (RMSEs) were greater than 1), the CWT-based canopy LAI estimation model for late growth wheat had obvious improvements in accuracy (maximum R2 of 0.53 and minimum of RMSE of 0.78). Hence, this new method shows promise for use in agricultural and ecological applications.
NASA Astrophysics Data System (ADS)
Ok, Jong G.; Panday, Ashwin; Lee, Taehwa; Jay Guo, L.
2014-11-01
We present a versatile and simple methodology for continuous and scalable 2D micro/nano-structure fabrication via sequential 1D patterning strokes enabled by dynamic nano-inscribing (DNI) and vibrational indentation patterning (VIP) as well as a `single-stroke' 2D patterning using a DNI tool in VIP.
Ok, Jong G; Panday, Ashwin; Lee, Taehwa; Jay Guo, L
2014-12-21
We present a versatile and simple methodology for continuous and scalable 2D micro/nano-structure fabrication via sequential 1D patterning strokes enabled by dynamic nano-inscribing (DNI) and vibrational indentation patterning (VIP) as well as a 'single-stroke' 2D patterning using a DNI tool in VIP. PMID:25363145
Time-Frequency-Wavenumber Analysis of Surface Waves Using the Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Poggi, V.; Fäh, D.; Giardini, D.
2013-03-01
A modified approach to surface wave dispersion analysis using active sources is proposed. The method is based on continuous recordings, and uses the continuous wavelet transform to analyze the phase velocity dispersion of surface waves. This gives the possibility to accurately localize the phase information in time, and to isolate the most significant contribution of the surface waves. To extract the dispersion information, then, a hybrid technique is applied to the narrowband filtered seismic recordings. The technique combines the flexibility of the slant stack method in identifying waves that propagate in space and time, with the resolution of f- k approaches. This is particularly beneficial for higher mode identification in cases of high noise levels. To process the continuous wavelet transform, a new mother wavelet is presented and compared to the classical and widely used Morlet type. The proposed wavelet is obtained from a raised-cosine envelope function (Hanning type). The proposed approach is particularly suitable when using continuous recordings (e.g., from seismological-like equipment) since it does not require any hardware-based source triggering. This can be subsequently done with the proposed method. Estimation of the surface wave phase delay is performed in the frequency domain by means of a covariance matrix averaging procedure over successive wave field excitations. Thus, no record stacking is necessary in the time domain and a large number of consecutive shots can be used. This leads to a certain simplification of the field procedures. To demonstrate the effectiveness of the method, we tested it on synthetics as well on real field data. For the real case we also combine dispersion curves from ambient vibrations and active measurements.
Determination of human EEG alpha entrainment ERD/ERS using the continuous complex wavelet transform
NASA Astrophysics Data System (ADS)
Chorlian, David B.; Porjesz, Bernice; Begleiter, Henri
2003-04-01
Alpha entrainment caused by exposure to a background stimulus continuously flickering at a rate of 8 1/3 Hz was affected by the appearance of a foreground target stimulus to which the subjects were requested to press a button. With the use of bipolar derivations (to reduce volume conduction effects), scalp recorded EEG potentials were subjected to a continuous wavelet transform using complex Morlet wavelets at a range of scales. Complex Morlet wavelets were used to calculate efficiently instantaneous amplitudes and phases on a per-trial basis, rather than using the Hilbert transform on band-pass filtered data. Multiple scales were employed to contrast the pattern of alpha activity with those in other bands, and to determine whether the harmonics observed in the spectral analysis of the data were simply a result of the non-sinusoidal response to the entraining signal or a distinct neural phenomenon. We were thus able to calculate desynchronization/resynchronization for both the entrained and non-entrained alpha activity. The occurance of the target stimulus caused a sharp increase in amplitude in both the entrained and non-entrained alpha activity, followed by a sharp decrease, and then a return to baseline, over a period of 2.5 seconds. However, the entrained alpha activity showed a much more rapid recovery than non-entrained activity.
Gu Junhua; Xu Haiguang; Wang Jingying; Chen Wen; An Tao
2013-08-10
We propose a continuous wavelet transform based non-parametric foreground subtraction method for the detection of redshifted 21 cm signal from the epoch of reionization. This method works based on the assumption that the foreground spectra are smooth in frequency domain, while the 21 cm signal spectrum is full of saw-tooth-like structures, thus their characteristic scales are significantly different. We can distinguish them in the wavelet coefficient space easily and perform the foreground subtraction. Compared with the traditional spectral fitting based method, our method is more tolerant to complex foregrounds. Furthermore, we also find that when the instrument has uncorrected response error, our method can also work significantly better than the spectral fitting based method. Our method can obtain similar results with the Wp smoothing method, which is also a non-parametric method, but our method consumes much less computing time.
Heterogeneities Analysis Using the Generalized Fractal Dimension and Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Ouadfeul, S.; Aliouane, L.; Boudella, A.
2012-04-01
The main goal of this work is analyze heterogeneities from well-logs data using the wavelet transform modulus maxima lines (WTMM). Firstly, the continuous wavelet transform (CWT) with sliding window is calculated. The next step consists to calculate the maxima of the modulus of the CWT and estimate the spectrum of exponents. The three generalized fractal dimensions D0, D1 and D2 are then estimated. Application of the proposed idea at the synthetic and real well-logs data of a borehole located in the Algerian Sahara shows that the fractal dimensions are very sensitive to lithological variations. The generalized fractal dimensions are a very robust tool than can be used for petroleum reservoir characterization. Keywrods: reservoir, Heterogeneities, WTMM, fractal dimension.
NASA Astrophysics Data System (ADS)
Gu, Junhua; Xu, Haiguang; Wang, Jingying; An, Tao; Chen, Wen
2013-08-01
We propose a continuous wavelet transform based non-parametric foreground subtraction method for the detection of redshifted 21 cm signal from the epoch of reionization. This method works based on the assumption that the foreground spectra are smooth in frequency domain, while the 21 cm signal spectrum is full of saw-tooth-like structures, thus their characteristic scales are significantly different. We can distinguish them in the wavelet coefficient space easily and perform the foreground subtraction. Compared with the traditional spectral fitting based method, our method is more tolerant to complex foregrounds. Furthermore, we also find that when the instrument has uncorrected response error, our method can also work significantly better than the spectral fitting based method. Our method can obtain similar results with the Wp smoothing method, which is also a non-parametric method, but our method consumes much less computing time.
A method for the analysis of respiratory sinus arrhythmia using continuous wavelet transforms.
Cnockaert, Laurence; Migeotte, Pierre-François; Daubigny, Lise; Prisk, G Kim; Grenez, Francis; Sá, Rui Carlos
2008-05-01
A continuous wavelet transform-based method is presented to study the nonstationary strength and phase delay of the respiratory sinus arrhythmia (RSA). The RSA is the cyclic variation of instantaneous heart rate at the breathing frequency. In studies of cardio-respiratory interaction during sleep, paced breathing or postural changes, low respiratory frequencies, and fast changes can occur. Comparison on synthetic data presented here shows that the proposed method outperforms traditional short-time Fourier-transform analysis in these conditions. On the one hand, wavelet analysis presents a sufficient frequency-resolution to handle low respiratory frequencies, for which time frames should be long in Fourier-based analysis. On the other hand, it is able to track fast variations of the signals in both amplitude and phase for which time frames should be short in Fourier-based analysis. PMID:18440911
2D CFD Analysis of an Airfoil with Active Continuous Trailing Edge Flap
NASA Astrophysics Data System (ADS)
Jaksich, Dylan; Shen, Jinwei
2014-11-01
Efficient and quieter helicopter rotors can be achieved through on-blade control devices, such as active Continuous Trailing-Edge Flaps driven by embedded piezoelectric material. This project aims to develop a CFD simulation tool to predict the aerodynamic characteristics of an airfoil with CTEF using open source code: OpenFOAM. Airfoil meshes used by OpenFOAM are obtained with MATLAB scripts. Once created it is possible to rotate the airfoil to various angles of attack. When the airfoil is properly set up various OpenFOAM properties, such as kinematic viscosity and flow velocity, are altered to achieve the desired testing conditions. Upon completion of a simulation, the program gives the lift, drag, and moment coefficients as well as the pressure and velocity around the airfoil. The simulation is then repeated across multiple angles of attack to give full lift and drag curves. The results are then compared to previous test data and other CFD predictions. This research will lead to further work involving quasi-steady 2D simulations incorporating NASTRAN to model aeroelastic deformation and eventually to 3D aeroelastic simulations. NSF ECE Grant #1358991 supported the first author as an REU student.
NASA Astrophysics Data System (ADS)
Dai, Yu; Xue, Yuan; Zhang, Jianxun
2016-01-01
Impulsive noise caused by some random events has the main character of short rise-time and wide frequency spectrum range, so it has the potential to degrade the performance and reliability of the harmonic estimation. This paper focuses on the harmonic estimation procedure based on continuous wavelet transform (CWT) when the analyzed signal is corrupted by the impulsive noise. The digital CWT of both the time-varying sinusoidal signal and the impulsive noise are analyzed, and there are two cross ridges in the time-frequency plane of CWT, which are generated by the signal and the noise separately. In consideration of the amplitude of the noise and the number of the spike event, two inequalities are derived to provide limitations on the wavelet parameters. Based on the amplitude distribution of the noise, the optimal wavelet parameters determined by solving these inequalities are used to suppress the contamination of the noise, as well as increase the amplitude of the ridge corresponding to the signal, so the parameters of each harmonic component can be estimated accurately. The proposed procedure is applied to a numerical simulation and a bone vibration signal test giving satisfactory results of stationary and time-varying harmonic parameter estimation.
Yang, W.; Wu, H.; Cao, L.
2012-07-01
More and more MOX fuels are used in all over the world in the past several decades. Compared with UO{sub 2} fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for {sup 240}Pu and {sup 242}Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)
Multi-method determination of continuous 2D velocity profiles from the surface to 1 km
NASA Astrophysics Data System (ADS)
Peterie, S.; Miller, R. D.; Ivanov, J.; Schwenk, J.; Bailey, B. L.; Schwarzer, J.; Markiewicz, R.
2012-12-01
Compressional and shear reflection data provide critical measurements of velocity and attenuation that are necessary for numerical simulations of site response from earthquake energy and seismic investigations to lithologic and pore characterizations. Imperative for accurate site response models is a seismic velocity model extending from the surface to the depth of interest that is representative of the true subsurface. In general, no seismic method can be used to characterize the shallowest (< 30 m) and deepest (30 m to 1 km) portions of the subsurface in a single pass with a consistent set of equipment and acquisition parameters. With four unique seismic surveys targeting different portions of the subsurface and different components of the seismic wavefield, we were able to build a comprehensive dataset that facilitated continuous 2D velocity profiles. The upper kilometer underlying our study site consists of Lake Bonneville lucustrine sediments and post-Bonneville alluvium and colluvium from the nearby Wasatch Front in north central Utah (Eardley, 1938; Hintze, 2005). Four unique seismic surveys were acquired along each of two 1.5 km lines located approximately 3 km apart. Data for tomography and multi-channel analysis of surface waves (MASW) were acquired with a bungee accelerated weight drop and 4.5 Hz compressional geophones. P-wave and S-wave reflection data were acquired with an IVI minivib 1 and 28 Hz compressional and 14 Hz SH geophones, respectively. P-wave and S-wave velocities from the surface to 30 m were determined using tomography and MASW, respectively. Stacking velocities of reflections on common midpoint gathers from the vibroseis data were used to determine Vp and Vs from approximately 30 m to nearly 1 km below ground surface. Each Vp and Vs dataset were merged to generate continuous interval and average velocity profiles. The sutured velocity cross-sections were produced for both P- and S-waves in a fashion not previously described in the
NASA Astrophysics Data System (ADS)
Qian, Jinfang; Zhang, Changjiang
2014-11-01
An efficient algorithm based on continuous wavelet transform combining with pre-knowledge, which can be used to detect the defect of glass bottle mouth, is proposed. Firstly, under the condition of ball integral light source, a perfect glass bottle mouth image is obtained by Japanese Computar camera through the interface of IEEE-1394b. A single threshold method based on gray level histogram is used to obtain the binary image of the glass bottle mouth. In order to efficiently suppress noise, moving average filter is employed to smooth the histogram of original glass bottle mouth image. And then continuous wavelet transform is done to accurately determine the segmentation threshold. Mathematical morphology operations are used to get normal binary bottle mouth mask. A glass bottle to be detected is moving to the detection zone by conveyor belt. Both bottle mouth image and binary image are obtained by above method. The binary image is multiplied with normal bottle mask and a region of interest is got. Four parameters (number of connected regions, coordinate of centroid position, diameter of inner cycle, and area of annular region) can be computed based on the region of interest. Glass bottle mouth detection rules are designed by above four parameters so as to accurately detect and identify the defect conditions of glass bottle. Finally, the glass bottles of Coca-Cola Company are used to verify the proposed algorithm. The experimental results show that the proposed algorithm can accurately detect the defect conditions of the glass bottles and have 98% detecting accuracy.
NASA Astrophysics Data System (ADS)
G, A., Major; Fretwell, H. M.; Dugdale, S. B.; Alam, M. A.
1998-11-01
A novel method for reconstructing the Fermi surface from experimental two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) projections is proposed. In this algorithm, the 3D electron momentum-density distribution is expanded in terms of a basis of wavelet-like functions. The parameters of the model, the wavelet coefficients, are determined by maximizing the likelihood function corresponding to the experimental data and the projections calculated from the model. In contrast to other expansions, in the case of that in terms of wavelets a relatively small number of model parameters are sufficient for representing the relevant parts of the 3D distribution, thus keeping computation times reasonably short. Unlike other reconstruction methods, this algorithm takes full account of the statistical information content of the data and therefore may help to reduce the amount of time needed for data acquisition. An additional advantage of wavelet expansion may be the possibility of retrieving the Fermi surface directly from the wavelet coefficients rather than indirectly using the reconstructed 3D distribution.
Instrument-independent analysis of music by means of the continuous wavelet transform
NASA Astrophysics Data System (ADS)
Olmo, Gabriella; Dovis, Fabio; Benotto, Paolo; Calosso, Claudio; Passaro, Pierluigi
1999-10-01
This paper deals with the problem of automatic recognition of music. Segments of digitized music are processed by means of a Continuous Wavelet Transform, properly chosen so as to match the spectral characteristics of the signal. In order to achieve a good time-scale representation of the signal components a novel wavelet has been designed suited to the musical signal features. particular care has been devoted towards an efficient implementation, which operates in the frequency domain, and includes proper segmentation and aliasing reduction techniques to make the analysis of long signals feasible. The method achieves very good performance in terms of both time and frequency selectivity, and can yield the estimate and the localization in time of both the fundamental frequency and the main harmonics of each tone. The analysis is used as a preprocessing step for a recognition algorithm, which we show to be almost independent on the instrument reproducing the sounds. Simulations are provided to demonstrate the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Sohrabi, Mahmoud Reza; Abdolmaleki, Parviz; Esmaeili, Elmira Abdollahzade
2010-09-01
In this study a zero crossing technique based on continuous wavelet transform (CWT) as well as classical derivative spectrophotometry (CDS) is presented for simultaneous determination of cyproterone acetate and ethinyl estradiol in binary mixtures and commercial dosage of drug, without using prior chemical pre-treatment. Absorption spectra were recorded in the wavelength range 200-400 nm. Absorbance data were subjected to various mother wavelets from continuous wavelet transform family to find the optimum point of the wavelet signal processing (Matlab 7.5) gaus 15 and morl wavelet functions with scaling factor, a = 70 and 3rd derivative with Δ λ = 10 nm, were selected. Optimum value of scaling factor was chosen to obtain an appropriate calibration for each method. The validation of proposed methods was investigated by several synthetic mixtures and obtained results were successfully compared among each other. Mean recovery values were found between 96.93% and 101.7% for CWT and 95.55% and 104.22% for DS, respectively for the determination of cyproterone acetate and ethinyl estradiol in synthetic mixtures. The developed methods are rapid, precise and easy to apply for the analysis of overlapping signals of the components in the mixtures. Obtained results from the CWT were compared to those yielded by CDS which were in good agreement and therefore led to a successful determination.
Lahmiri, Salim; Gargour, Christian S; Gabrea, Marcel
2014-10-01
An automated diagnosis system that uses complex continuous wavelet transform (CWT) to process retina digital images and support vector machines (SVMs) for classification purposes is presented. In particular, each retina image is transformed into two one-dimensional signals by concatenating image rows and columns separately. The mathematical norm of phase angles found in each one-dimensional signal at each level of CWT decomposition are relied on to characterise the texture of normal images against abnormal images affected by exudates, drusen and microaneurysms. The leave-one-out cross-validation method was adopted to conduct experiments and the results from the SVM show that the proposed approach gives better results than those obtained by other methods based on the correct classification rate, sensitivity and specificity. PMID:26609393
Ullah, Saleem; Skidmore, Andrew K; Naeem, Mohammad; Schlerf, Martin
2012-10-15
Leaf water content determines plant health, vitality, photosynthetic efficiency and is an important indicator of drought assessment. The retrieval of leaf water content from the visible to shortwave infrared spectra is well known. Here for the first time, we estimated leaf water content from the mid to thermal infrared (2.5-14.0 μm) spectra, based on continuous wavelet analysis. The dataset comprised 394 spectra from nine plant species, with different water contents achieved through progressive drying. To identify the spectral feature most sensitive to the variations in leaf water content, first the Directional Hemispherical Reflectance (DHR) spectra were transformed into a wavelet power scalogram, and then linear relations were established between the wavelet power scalogram and leaf water content. The six individual wavelet features identified in the mid infrared yielded high correlations with leaf water content (R(2)=0.86 maximum, 0.83 minimum), as well as low RMSE (minimum 8.56%, maximum 9.27%). The combination of four wavelet features produced the most accurate model (R(2)=0.88, RMSE=8.00%). The models were consistent in terms of accuracy estimation for both calibration and validation datasets, indicating that leaf water content can be accurately retrieved from the mid to thermal infrared domain of the electromagnetic radiation. PMID:22940042
NASA Astrophysics Data System (ADS)
Cheng, Tao; Rivard, Benoit; Sánchez-Azofeifa, Arturo G.; Féret, Jean-Baptiste; Jacquemoud, Stéphane; Ustin, Susan L.
2014-01-01
Leaf mass per area (LMA), the ratio of leaf dry mass to leaf area, is a trait of central importance to the understanding of plant light capture and carbon gain. It can be estimated from leaf reflectance spectroscopy in the infrared region, by making use of information about the absorption features of dry matter. This study reports on the application of continuous wavelet analysis (CWA) to the estimation of LMA across a wide range of plant species. We compiled a large database of leaf reflectance spectra acquired within the framework of three independent measurement campaigns (ANGERS, LOPEX and PANAMA) and generated a simulated database using the PROSPECT leaf optical properties model. CWA was applied to the measured and simulated databases to extract wavelet features that correlate with LMA. These features were assessed in terms of predictive capability and robustness while transferring predictive models from the simulated database to the measured database. The assessment was also conducted with two existing spectral indices, namely the Normalized Dry Matter Index (NDMI) and the Normalized Difference index for LMA (NDLMA). Five common wavelet features were determined from the two databases, which showed significant correlations with LMA (R2: 0.51-0.82, p < 0.0001). The best robustness (R2 = 0.74, RMSE = 18.97 g/m2 and Bias = 0.12 g/m2) was obtained using a combination of two low-scale features (1639 nm, scale 4) and (2133 nm, scale 5), the first being predominantly important. The transferability of the wavelet-based predictive model to the whole measured database was either better than or comparable to those based on spectral indices. Additionally, only the wavelet-based model showed consistent predictive capabilities among the three measured data sets. In comparison, the models based on spectral indices were sensitive to site-specific data sets. Integrating the NDLMA spectral index and the two robust wavelet features improved the LMA prediction. One of the bands
Energy Science and Technology Software Center (ESTSC)
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
NASA Astrophysics Data System (ADS)
Hirasawa, T.; Ishihara, M.; Tsujita, K.; Hirota, K.; Irisawa, K.; Kitagaki, M.; Fujita, M.; Kikuchi, M.
2012-02-01
In photo-acoustic (PA) imaging, valuable medical applications based on optical absorption spectrum such as contrast agent imaging and blood oxygen saturation measurement have been investigated. In these applications, there is an essential requirement to determine optical absorption coefficients accurately. In present, PA signal intensities have been commonly used to determine optical absorption coefficients. This method achieves practical accuracy by combining with radiative transfer analysis. However, time consumption of radiative transfer analysis and effects of signal generation efficiencies were problems of this method. In this research, we propose a new method to determine optical absorption coefficients using continuous wavelet transform (CWT). We used CWT to estimate instantaneous frequencies of PA signals which reflects optical absorption distribution. We validated the effectiveness of CWT in determination of optical absorption coefficients through an experiment. In the experiment, planar shaped samples were illuminated to generate PA signal. The PA signal was measured by our fabricated PA probe in which an optical fiber and a ring shaped P(VDFTrFE) ultrasound sensor were coaxially aligned. Optical properties of samples were adjusted by changing the concentration of dye solution. Tunable Ti:Sapphire laser (690 - 1000 nm) was used as illumination source. As a result, we confirmed strong correlation between optical absorption coefficients of samples and the instantaneous frequency of PA signal obtained by CWT. Advantages of this method were less interference of light transfer and signal generation efficiency.
Paul, Sabyasachi; Rao, D D; Sarkar, P K
2012-11-01
Measurement of environmental dose in the vicinity of a nuclear power plant site (Tarapur, India) is carried out continuously for the years 2007-2010 and attempts have been made to quantify the additional contributions from nuclear power plants over natural background by segregating the background fluctuations from the events due to plume passage using a non-decimated wavelet approach. A conservative estimate obtained using wavelet based analysis has shown a maximum annual dose of 38 μSv in a year at 1.6 km and 4.8 μSv at 10 km from the installation. The detected events within a year are in good agreement with the month wise wind-rose profile indicating reliability of the algorithm for proper detection of an event from the continuous dose rate measurements. The results were validated with the dispersion model dose predictions using the source term from routine monitoring data and meteorological parameters. PMID:22940411
NASA Astrophysics Data System (ADS)
Adhikari, B.; Mendes, O., Jr.; Domingues, M. O.; Echer, E.
2014-12-01
Around the solar maximum, the dominant structures emanating from the sun are sporadic coronal mass ejection (CMEs) and their interplanetary counterparts (ICMEs). In the descending and minimum phases of solar cycle, the geomagnetic activities are mostly influenced by corotating high speed streams. These high speed streams are embedded with highly fluctuated Alfven waves.When these fluctuation of Alfven waves in IMF (Bz) diminish, the storm starts its long recovery phase. The Earth's equatorial magnetic field monitored by the Dst (disturbed storm time) index found to be below than its quiet day value for days. This phenomena is called high-intensity, long duration, continuous AE activity or HILDCAA. In this work, we discuss the ground magnetometers signatures obtained from five longitudinal stations during three HILDCAA events of different interplanetary causes. The concepts of wavelet analysis (CWT, DWT and modulus correlation) have been used in order to get some common signatures on these stations. The CWT is an integral transform, it explores time frequency representation of the horizontal component of geomagnetic field. The objective of DWT is to highlight the disturbances associated during HILDCAA.The Daubechies orthogonal wavelet transform of order 2 with wavelet coefficient magnitudes at seven levels have been studied. In terms of wavelet coefficients the fluctuations present in the horizontal component of geomagnetic field have been analyzed. Both CWT and DWT have proved to be a useful tool in order to get some common features on these stations during the events . We also used wavelet modulus correlation to study the correlation between H-component from five longitudinal stations with IMF-Bz. These results show that the H-component for all stations are highly correlated with IMF-Bz during HILDCAAs.
NASA Astrophysics Data System (ADS)
Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I.
2016-03-01
Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
Adaptive Multilinear Tensor Product Wavelets.
Weiss, Kenneth; Lindstrom, Peter
2016-01-01
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 to 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. 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. PMID:26529742
Continuous wavelet transform analysis of one-dimensional quantum bound states from first principles
Handy, C.R.; Murenzi, R.
1996-11-01
Over the last decade, Handy and Bessis have developed a moment-problem-based, multiscale quantization theory, the eigenvalue moment method (EMM), which has proven effective in solving singular, strongly coupled, multidimensional Schr{umlt o}dinger Hamiltonians. We extend the scope of EMM by demonstrating its essential role in the generation of wavelet transforms for one-dimensional quantum systems. Combining this with the function-wavelet reconstruction formulas currently available, we are able to recover the wave function systematically, from first principles, through a multiscale process proceeding from large spatial scales to smaller ones. This accomplishment also addresses another outstanding problem, that of reconstructing a function from its moments. For the class of problems considered, the combined EMM-wavelet analysis yields a definitive solution. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Gallego, A.; Moreno-García, P.; Casanova, Cesar F.
2013-06-01
Structural studies to find defects (in particular delaminations) in composite plates have been very prevalent in the Structural Health Monitoring field. The present work develops a new method to detect delaminations in CFRP (Carbon Fiber Reinforced Polymer) plates. In this paper the method is validated with numerical simulations, which come to support its adequacy for use with real acquisition data. This is done firstly through the implementation of a delaminated plate finite element. Using the classical lamination plate theory, delamination is considered in the kinematic equations through jump functions and additional degrees of freedom. The element allows the introduction of nd delaminations through its thickness. Classical QMITC (Quadrilateral Mixed Interpolation Tensorial Components) and DKQ (Discrete Kirchhoff Quadrilateral) elements are used for the membrane and bending FEM (Finite Element Method) formulation. Second, using the vibration modes obtained with the FEM, a damage location technique based on the variational Ritz method and Wavelet Analysis is proposed. The approach has the advantage of requiring only damaged modes and not the healthy ones. Both FEM simulations and Ritz/Wavelet damage detection schemes are applied in an orthotropic CFRP plate with the stacking sequence [0/90]3S. In addition, the influence of delamination thickness position, boundary conditions and added noise (in order to simulate experimental measures) was studied.
NASA Astrophysics Data System (ADS)
Baluyev, R. V.
2006-02-01
At the present time (September, 2005) more than 150 exoplanetary candidate companions to solar-type stars are known. Such data amount is hardly sufficient for statistical researches. The classical statistical technique (histograms, cumulative distribution, etc.) provides low precision when using for comparison different distribution function values (for example, testing the distribution on structures like heterogeneities). The reason lies in a fact that a way to represent distribution function as a collection of its values is not suitable for such situation. In the present work an approach based on an effective technique of data analysis using wavelet transformations is built. General features of the wavelet analysis of statistical data are described, the practically important statistical tests are constructed. A number of univariate distributions of basic parameters (exoplanetary minimum masses, orbital periods, semi-major axes and eccentricities) are examined. The possible prospects for this technique development are discussed.
NASA Astrophysics Data System (ADS)
Singer, H. M.; Singer, I.
2006-09-01
The phase-field-crystal model [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)] produces multigrain structures on atomistic length scale but on diffusive time scales. Since individual atoms are resolved but are treated identically it is difficult to distinguish the exact position of grain boundaries and defects within grains. In order to analyze and visualize the whole grains a two-dimensional wavelet transform has been developed, which is capable of extracting grain boundaries and the lattice orientation of a grain relative to a laboratory frame of reference. This transformation makes it possible not only to easily visualize the multigrain structure, but also to perform exact measurements on low- and high-angle boundaries, grain size distributions and boundary-angle distributions, which can then be compared to experimental data. The presented wavelet transform can also be applied to results of other atomistic simulations, e.g., molecular dynamics or granular materials.
Hu, Ying; Mo, Wenqin; Dong, Kaifeng; Jin, Fang; Song, Junlei
2016-06-10
The maximum spectrum of the continuous wavelet transform (MSCWT) is proposed to demodulate the central wavelengths for the overlapped spectrum in a serial fiber Bragg grating (FBG) sensing system. We describe the operation principle of the MSCWT method. Moreover, the influence of the interval gap between two FBG wavelengths, 3 dB bandwidths, and optical powers of the reflected spectra are discussed. The simulation and experimental results indicate that the MSCWT can resolve an overlapped spectrum and decode the central wavelength with high accuracy. More importantly, the proposed peak detection method can enhance the sensing capacity of a wavelength division multiplexing FBG sensor network. PMID:27409024
Abid, Abdulbasit
2013-03-01
This paper presents a thorough discussion of the proposed field-programmable gate array (FPGA) implementation for fringe pattern demodulation using the one-dimensional continuous wavelet transform (1D-CWT) algorithm. This algorithm is also known as wavelet transform profilometry. Initially, the 1D-CWT is programmed using the C programming language and compiled into VHDL using the ImpulseC tool. This VHDL code is implemented on the Altera Cyclone IV GX EP4CGX150DF31C7 FPGA. A fringe pattern image with a size of 512×512 pixels is presented to the FPGA, which processes the image using the 1D-CWT algorithm. The FPGA requires approximately 100 ms to process the image and produce a wrapped phase map. For performance comparison purposes, the 1D-CWT algorithm is programmed using the C language. The C code is then compiled using the Intel compiler version 13.0. The compiled code is run on a Dell Precision state-of-the-art workstation. The time required to process the fringe pattern image is approximately 1 s. In order to further reduce the execution time, the 1D-CWT is reprogramed using Intel Integrated Primitive Performance (IPP) Library Version 7.1. The execution time was reduced to approximately 650 ms. This confirms that at least sixfold speedup was gained using FPGA implementation over a state-of-the-art workstation that executes heavily optimized implementation of the 1D-CWT algorithm. PMID:23458800
NASA Astrophysics Data System (ADS)
Debenjak, Andrej; Boškoski, Pavle; Musizza, Bojan; Petrovčič, Janko; Juričić, Đani
2014-05-01
This paper proposes an approach to the estimation of PEM fuel cell impedance by utilizing pseudo-random binary sequence as a perturbation signal and continuous wavelet transform with Morlet mother wavelet. With the approach, the impedance characteristic in the frequency band from 0.1 Hz to 500 Hz is identified in 60 seconds, approximately five times faster compared to the conventional single-sine approach. The proposed approach was experimentally evaluated on a single PEM fuel cell of a larger fuel cell stack. The quality of the results remains at the same level compared to the single-sine approach.
NASA Astrophysics Data System (ADS)
Qiu, Bingwen; Feng, Min; Tang, Zhenghong
2016-05-01
This study proposed a simple Smoother without any local adjustments based on Continuous Wavelet Transform (SCWT). And then it evaluated its performance together with other commonly applied techniques in phenological estimation. These noise reduction methods included Savitzky-Golay filter (SG), Double Logistic function (DL), Asymmetric Gaussian function (AG), Whittaker Smoother (WS) and Harmonic Analysis of Time-Series (HANTS). They were evaluated based on fidelity and smoothness, and their efficiencies in deriving phenological parameters through the inflexion point-based method with the 8-day composite Moderate Resolution Imaging Spectroradiometer (MODIS) 2-band Enhanced Vegetation Index (EVI2) in 2013 in China. The following conclusions were drawn: (1) The SG method exhibited strong fidelity, but weak smoothness and spatial continuity. (2) The HANTS method had very robust smoothness but weak fidelity. (3) The AG and DL methods performed weakly for vegetation with more than one growth cycle (i.e., multiple crops). (4) The WS and SCWT smoothers outperformed others with combined considerations of fidelity and smoothness, and consistent phenological patterns (correlation coefficients greater than 0.8 except evergreen broadleaf forests (0.68)). (5) Compared with WS methods, the SCWT smoother was capable in preservation of real local minima and maxima with fewer inflexions. (6) Large discrepancy was examined from the estimated phenological dates with SG and HANTS methods, particularly in evergreen forests and multiple cropping regions (the absolute mean deviation rates were 6.2-17.5 days and correlation coefficients less than 0.34 for estimated start dates).
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…
NASA Astrophysics Data System (ADS)
Esposito, Angelo; Russo, Luigi; Kändler, Christoph; Pianese, Cesare; Ludwig, Bastian; Steiner, Nadia Yousfi
2016-06-01
The on-line diagnostics of Solid Oxide Fuel Cells (SOFCs) is a critical tool to achieve optimal performance and extend the lifetime. The Continuous Wavelet Transform (CWT) methodology was applied to the SOFC voltage signal to detect signatures that reveal the presence of a fault in the cell/stack. The selected fault was anode re-oxidation caused by high Fuel Utilization (FU) (higher then nominal). To experimentally emulate the high FU faults, a standard test procedure was developed, which was used to characterize a μ-CHP system at high FU operation. To complete the analysis, data collected on Single Cells were exploited too. The CWT was applied to the voltage signal for each FU level to verify the qualitative difference (signature) between the signals at different FU's within the same tests as well as the correspondence between the same conditions over different tests. A statistical study was performed to quantify the observed differences and to determine the correspondence between CWT coefficients and operating conditions. The approach proves to be suitable to diagnose high FU in SOFC, showing a successful detection rate above 76%. The results show the good potential of using the CWT methodology as diagnostic tools for SOFCs from cell to stack level.
Elzanfaly, Eman S; Hassan, Said A; Salem, Maissa Y; El-Zeany, Badr A
2015-12-01
A comparative study was established between two signal processing techniques showing the theoretical algorithm for each method and making a comparison between them to indicate the advantages and limitations. The methods under study are Numerical Differentiation (ND) and Continuous Wavelet Transform (CWT). These methods were studied as spectrophotometric resolution tools for simultaneous analysis of binary and ternary mixtures. To present the comparison, the two methods were applied for the resolution of Bisoprolol (BIS) and Hydrochlorothiazide (HCT) in their binary mixture and for the analysis of Amlodipine (AML), Aliskiren (ALI) and Hydrochlorothiazide (HCT) as an example for ternary mixtures. By comparing the results in laboratory prepared mixtures, it was proven that CWT technique is more efficient and advantageous in analysis of mixtures with severe overlapped spectra than ND. The CWT was applied for quantitative determination of the drugs in their pharmaceutical formulations and validated according to the ICH guidelines where accuracy, precision, repeatability and robustness were found to be within the acceptable limit. PMID:26186613
NASA Astrophysics Data System (ADS)
Nardi, F.; Grimaldi, S.; Petroselli, A.
2012-12-01
Remotely sensed Digital Elevation Models (DEMs), largely available at high resolution, and advanced terrain analysis techniques built in Geographic Information Systems (GIS), provide unique opportunities for DEM-based hydrologic and hydraulic modelling in data-scarce river basins paving the way for flood mapping at the global scale. This research is based on the implementation of a fully continuous hydrologic-hydraulic modelling optimized for ungauged basins with limited river flow measurements. The proposed procedure is characterized by a rainfall generator that feeds a continuous rainfall-runoff model producing flow time series that are routed along the channel using a bidimensional hydraulic model for the detailed representation of the inundation process. The main advantage of the proposed approach is the characterization of the entire physical process during hydrologic extreme events of channel runoff generation, propagation, and overland flow within the floodplain domain. This physically-based model neglects the need for synthetic design hyetograph and hydrograph estimation that constitute the main source of subjective analysis and uncertainty of standard methods for flood mapping. Selected case studies show results and performances of the proposed procedure as respect to standard event-based approaches.
A Numerical Study of Continuous Data Assimilation for the 2D-NS Equations Using Nodal Points
NASA Astrophysics Data System (ADS)
Gesho, Masakazu
This thesis conducts a number of numerical experiments using massively parallel GPU computations to study a new continuous data assimilation algorithm. We test the algorithm on two-dimensional incompressible fluid flows given by the Navier--Stokes equations. In this context, observations of the Eulerian velocity field given at a finite resolution of nodal points in space may be used to recover the exact velocity field over time. We also consider nodal measurements of the vorticity field and stream function. The main difference between this new algorithm and previous continuous data assimilation methods is the inclusion of a relaxation parameter micro that controls the rate at which the approximate solution is forced toward the observational measurements. If micro is too small, the approximate solution obtained by data assimilation may not converge to the reference solution; however, if micro is too large then high frequency spill-over from the observations may contaminate the approximate solution. Our focus is on the resolution of the nodal points necessary for the algorithm to recover the exact velocity field and how best to choose the parameter micro.
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. PMID:26573647
Tsanas, Athanasios; Clifford, Gari D.
2015-01-01
Sleep spindles are critical in characterizing sleep and have been associated with cognitive function and pathophysiological assessment. Typically, their detection relies on the subjective and time-consuming visual examination of electroencephalogram (EEG) signal(s) by experts, and has led to large inter-rater variability as a result of poor definition of sleep spindle characteristics. Hitherto, many algorithmic spindle detectors inherently make signal stationarity assumptions (e.g., Fourier transform-based approaches) which are inappropriate for EEG signals, and frequently rely on additional information which may not be readily available in many practical settings (e.g., more than one EEG channels, or prior hypnogram assessment). This study proposes a novel signal processing methodology relying solely on a single EEG channel, and provides objective, accurate means toward probabilistically assessing the presence of sleep spindles in EEG signals. We use the intuitively appealing continuous wavelet transform (CWT) with a Morlet basis function, identifying regions of interest where the power of the CWT coefficients corresponding to the frequencies of spindles (11–16 Hz) is large. The potential for assessing the signal segment as a spindle is refined using local weighted smoothing techniques. We evaluate our findings on two databases: the MASS database comprising 19 healthy controls and the DREAMS sleep spindle database comprising eight participants diagnosed with various sleep pathologies. We demonstrate that we can replicate the experts' sleep spindles assessment accurately in both databases (MASS database: sensitivity: 84%, specificity: 90%, false discovery rate 83%, DREAMS database: sensitivity: 76%, specificity: 92%, false discovery rate: 67%), outperforming six competing automatic sleep spindle detection algorithms in terms of correctly replicating the experts' assessment of detected spindles. PMID:25926784
Tsanas, Athanasios; Clifford, Gari D
2015-01-01
Sleep spindles are critical in characterizing sleep and have been associated with cognitive function and pathophysiological assessment. Typically, their detection relies on the subjective and time-consuming visual examination of electroencephalogram (EEG) signal(s) by experts, and has led to large inter-rater variability as a result of poor definition of sleep spindle characteristics. Hitherto, many algorithmic spindle detectors inherently make signal stationarity assumptions (e.g., Fourier transform-based approaches) which are inappropriate for EEG signals, and frequently rely on additional information which may not be readily available in many practical settings (e.g., more than one EEG channels, or prior hypnogram assessment). This study proposes a novel signal processing methodology relying solely on a single EEG channel, and provides objective, accurate means toward probabilistically assessing the presence of sleep spindles in EEG signals. We use the intuitively appealing continuous wavelet transform (CWT) with a Morlet basis function, identifying regions of interest where the power of the CWT coefficients corresponding to the frequencies of spindles (11-16 Hz) is large. The potential for assessing the signal segment as a spindle is refined using local weighted smoothing techniques. We evaluate our findings on two databases: the MASS database comprising 19 healthy controls and the DREAMS sleep spindle database comprising eight participants diagnosed with various sleep pathologies. We demonstrate that we can replicate the experts' sleep spindles assessment accurately in both databases (MASS database: sensitivity: 84%, specificity: 90%, false discovery rate 83%, DREAMS database: sensitivity: 76%, specificity: 92%, false discovery rate: 67%), outperforming six competing automatic sleep spindle detection algorithms in terms of correctly replicating the experts' assessment of detected spindles. PMID:25926784
Source Wavelet Phase Extraction
NASA Astrophysics Data System (ADS)
Naghadeh, Diako Hariri; Morley, Christopher Keith
2016-06-01
Extraction of propagation wavelet phase from seismic data can be conducted using first, second, third and fourth-order statistics. Three new methods are introduced, which are: (1) Combination of different moments, (2) Windowed continuous wavelet transform and (3) Maximum correlation with cosine function. To compare different methods synthetic data with and without noise were chosen. Results show that first, second and third order statistics are not able to preserve wavelet phase. Kurtosis can preserve propagation wavelet phase but signal-to-noise ratio can affect the extracted phase using this method. So for data set with low signal-to-noise ratio, it will be unstable. Using a combination of different moments to extract the phase is more robust than applying kurtosis. The improvement occurs because zero phase wavelets with reverse polarities have equal maximum kurtosis values hence the correct wavelet polarity cannot be identified. Zero-phase wavelets with reverse polarities have minimum and maximum values for a combination of different-moments method. These properties enable the technique to handle a finite data segment and to choose the correct wavelet polarity. Also, the existence of different moments can decrease sensitivity to outliers. A windowed continuous wavelet transform is more sensitive to signal-to-noise ratio than the combination of different-moments method, also if the scale for the wavelet is incorrect it will encounter with more problems to extract phase. When the effects of frequency bandwidth, signal-to-noise ratio and analyzing window length are considered, the results of extracting phase information from data without and with noise demonstrate that combination of different-moments is superior to the other methods introduced here.
Sohrabi, Mahmoud Reza; Darabi, Golnaz
2016-01-01
Flavonoids are γ-benzopyrone derivatives, which are highly regarded in these researchers for their antioxidant property. In this study, two new signals processing methods been coupled with UV spectroscopy for spectral resolution and simultaneous quantitative determination of Myricetin, Kaempferol and Quercetin as flavonoids in Laurel, St. John's Wort and Green Tea without the need for any previous separation procedure. The developed methods are continuous wavelet transform (CWT) and least squares support vector machine (LS-SVM) methods integrated with UV spectroscopy individually. Different wavelet families were tested by CWT method and finally the Daubechies wavelet family (Db4) for Myricetin and the Gaussian wavelet families for Kaempferol (Gaus3) and Quercetin (Gaus7) were selected and applied for simultaneous analysis under the optimal conditions. The LS-SVM was applied to build the flavonoids prediction model based on absorption spectra. The root mean square errors for prediction (RMSEP) of Myricetin, Kaempferol and Quercetin were 0.0552, 0.0275 and 0.0374, respectively. The developed methods were validated by the analysis of the various synthetic mixtures associated with a well- known flavonoid contents. Mean recovery values of Myricetin, Kaempferol and Quercetin, in CWT method were 100.123, 100.253, 100.439 and in LS-SVM method were 99.94, 99.81 and 99.682, respectively. The results achieved by analyzing the real samples from the CWT and LS-SVM methods were compared to the HPLC reference method and the results were very close to the reference method. Meanwhile, the obtained results of the one-way ANOVA (analysis of variance) test revealed that there was no significant difference between the suggested methods. PMID:26241831
NASA Astrophysics Data System (ADS)
Sohrabi, Mahmoud Reza; Darabi, Golnaz
2016-01-01
Flavonoids are γ-benzopyrone derivatives, which are highly regarded in these researchers for their antioxidant property. In this study, two new signals processing methods been coupled with UV spectroscopy for spectral resolution and simultaneous quantitative determination of Myricetin, Kaempferol and Quercetin as flavonoids in Laurel, St. John's Wort and Green Tea without the need for any previous separation procedure. The developed methods are continuous wavelet transform (CWT) and least squares support vector machine (LS-SVM) methods integrated with UV spectroscopy individually. Different wavelet families were tested by CWT method and finally the Daubechies wavelet family (Db4) for Myricetin and the Gaussian wavelet families for Kaempferol (Gaus3) and Quercetin (Gaus7) were selected and applied for simultaneous analysis under the optimal conditions. The LS-SVM was applied to build the flavonoids prediction model based on absorption spectra. The root mean square errors for prediction (RMSEP) of Myricetin, Kaempferol and Quercetin were 0.0552, 0.0275 and 0.0374, respectively. The developed methods were validated by the analysis of the various synthetic mixtures associated with a well- known flavonoid contents. Mean recovery values of Myricetin, Kaempferol and Quercetin, in CWT method were 100.123, 100.253, 100.439 and in LS-SVM method were 99.94, 99.81 and 99.682, respectively. The results achieved by analyzing the real samples from the CWT and LS-SVM methods were compared to the HPLC reference method and the results were very close to the reference method. Meanwhile, the obtained results of the one-way ANOVA (analysis of variance) test revealed that there was no significant difference between the suggested methods.
NASA Astrophysics Data System (ADS)
Ahmad, Mirza Naseer; Rowell, Philip; Sriburee, Suchada
2014-06-01
Fluvial sands host excellent oil and gas reservoirs in various fields throughout the world. However, the lateral heterogeneity of reservoir properties within these reservoirs can be significant and determining the distribution of good reservoirs is a challenge. This study attempts to predict sand distribution within fluvial depositional systems by applying the Continuous Wavelet Transformation technique of spectral decomposition along with full spectrum seismic attributes, to a 3D seismic data set in the Pattani Basin, Gulf of Thailand. Full spectrum seismic attributes such as root mean square and coherency help to effectively map fluvial systems down to certain depth below which imaging is difficult in the intervals of interest in this study. However, continuous wavelet transform used in conjunction with other attributes by applying visualization techniques of transparency and RGB can be used at greater depths to extract from 3D seismic data useful information of fluvial depositional elements. This workflow may help to identify different reservoir compartments within the fluvial systems of the Gulf of Thailand.
General inversion formulas for wavelet transforms
NASA Astrophysics Data System (ADS)
Holschneider, Matthias
1993-09-01
This article is the continuation of a series of articles about group theory and wavelet analysis [A. Grossmann, J. Morlet, and T. Paul, J. Math. Phys. 26, 2473 (1985)]. As is well-known in the case of the afine group, the reconstruction wavelet and the analyzing wavelet need not be identic. In this article it is shown that this holds for arbitrary groups. In addition it is shown that even for nonadmissible analyzing wavelets the wavelet transform may be inverted. Accordingly the image of the wavelet transform can be characterized by many different reproducing kernels.
Hidalgo, D; Sacco, A; Hernández, S; Tommasi, T
2015-11-01
A mixed microbial population naturally presents in seawater was used as active anodic biofilm of two Microbial Fuel Cells (MFCs), employing either a 2D commercial carbon felt or 3D carbon-coated Berl saddles as anode electrodes, with the aim to compare their electrochemical behavior under continuous operation. After an initial increase of the maximum power density, the felt-based cell reduced its performance at 5 months (from 7 to 4 μW cm(-2)), while the saddle-based MFC exceeds 9 μW cm(-2) (after 2 months) and maintained such performance for all the tests. Electrochemical impedance spectroscopy was used to identify the MFCs controlling losses and indicates that the mass-transport limitations at the biofilm-electrolyte interface have the main contribution (>95%) to their internal resistance. The activation resistance was one order of magnitude lower with the Berl saddles than with carbon felt, suggesting an enhanced charge-transfer in the high surface-area 3D electrode, due to an increase in bacteria population growth. PMID:26166463
Schlossnagle, G.; Restrepo, J.M.; Leaf, G.K.
1993-12-01
The properties of periodized Daubechies wavelets on [0,1] are detailed and contrasted against their counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrate 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 several tabulated values are included.
NASA Astrophysics Data System (ADS)
Karacan, C. Özgen; Olea, Ricardo A.
2014-06-01
Prediction of potential methane emission pathways from various sources into active mine workings or sealed gobs from longwall overburden is important for controlling methane and for improving mining safety. The aim of this paper is to infer strata separation intervals and thus gas emission pathways from standard well log data. The proposed technique was applied to well logs acquired through the Mary Lee/Blue Creek coal seam of the Upper Pottsville Formation in the Black Warrior Basin, Alabama, using well logs from a series of boreholes aligned along a nearly linear profile. For this purpose, continuous wavelet transform (CWT) of digitized gamma well logs was performed by using Mexican hat and Morlet, as the mother wavelets, to identify potential discontinuities in the signal. Pointwise Hölder exponents (PHE) of gamma logs were also computed using the generalized quadratic variations (GQV) method to identify the location and strength of singularities of well log signals as a complementary analysis. PHEs and wavelet coefficients were analyzed to find the locations of singularities along the logs. Using the well logs in this study, locations of predicted singularities were used as indicators in single normal equation simulation (SNESIM) to generate equi-probable realizations of potential strata separation intervals. Horizontal and vertical variograms of realizations were then analyzed and compared with those of indicator data and training image (TI) data using the Kruskal-Wallis test. A sum of squared differences was employed to select the most probable realization representing the locations of potential strata separations and methane flow paths. Results indicated that singularities located in well log signals reliably correlated with strata transitions or discontinuities within the strata. Geostatistical simulation of these discontinuities provided information about the location and extents of the continuous channels that may form during mining. If there is a gas
NASA Astrophysics Data System (ADS)
Conde, Vladimir; Bredemeyer, Stefan; Saballos, J. Armando; Galle, Bo; Hansteen, Thor H.
2016-07-01
San Cristóbal volcano is the highest and one of the most active volcanoes in Nicaragua. Its persistently high activity during the past decade is characterized by strong degassing and almost annual VEI 1-2 explosions, which present a threat to the local communities. Following an eruption on 8 September 2012, the intervals between eruptions decreased significantly, which we interpret as the start of a new eruptive phase. We present here the results of semi-continuous SO2 flux measurements covering a period of 18 months, obtained by two scanning UV-DOAS instruments installed as a part of the network for observation of volcanic and atmospheric change project, and the results of real-time seismic amplitude measurements (RSAM) data. Our data comprise a series of small to moderately explosive events in December 2012, June 2013 and February 2014, which were accompanied by increased gas emissions and seismicity. In order to approach an early warning strategy, we present a statistical method for the joint analysis of gas flux and seismic data, by using continuous wavelet transform and cross-wavelet transform (XWT) methods. This analysis shows that the XWT coefficients of SO2 flux and RSAM are in good agreement with the occurrence of eruptive events and thus may be used to indicate magma ascent into the volcano edifice. Such multi-parameter surveillance efforts can be useful for the interpretation and surveillance of possible eruptive events and could thus be used by local institutions for the prediction of upcoming volcanic unrest.
NASA Astrophysics Data System (ADS)
Conde, Vladimir; Bredemeyer, Stefan; Saballos, J. Armando; Galle, Bo; Hansteen, Thor H.
2015-11-01
San Cristóbal volcano is the highest and one of the most active volcanoes in Nicaragua. Its persistently high activity during the past decade is characterized by strong degassing and almost annual VEI 1-2 explosions, which present a threat to the local communities. Following an eruption on 8 September 2012, the intervals between eruptions decreased significantly, which we interpret as the start of a new eruptive phase. We present here the results of semi-continuous SO2 flux measurements covering a period of 18 months, obtained by two scanning UV-DOAS instruments installed as a part of the network for observation of volcanic and atmospheric change project, and the results of real-time seismic amplitude measurements (RSAM) data. Our data comprise a series of small to moderately explosive events in December 2012, June 2013 and February 2014, which were accompanied by increased gas emissions and seismicity. In order to approach an early warning strategy, we present a statistical method for the joint analysis of gas flux and seismic data, by using continuous wavelet transform and cross-wavelet transform (XWT) methods. This analysis shows that the XWT coefficients of SO2 flux and RSAM are in good agreement with the occurrence of eruptive events and thus may be used to indicate magma ascent into the volcano edifice. Such multi-parameter surveillance efforts can be useful for the interpretation and surveillance of possible eruptive events and could thus be used by local institutions for the prediction of upcoming volcanic unrest.
A Mellin transform approach to wavelet analysis
NASA Astrophysics Data System (ADS)
Alotta, Gioacchino; Di Paola, Mario; Failla, Giuseppe
2015-11-01
The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.
Mohd, Shukri; Holford, Karen M.; Pullin, Rhys
2014-02-12
Source location is an important feature of acoustic emission (AE) damage monitoring in nuclear piping. The ability to accurately locate sources can assist in source characterisation and early warning of failure. This paper describe the development of a novelAE source location technique termed 'Wavelet Transform analysis and Modal Location (WTML)' based on Lamb wave theory and time-frequency analysis that can be used for global monitoring of plate like steel structures. Source location was performed on a steel pipe of 1500 mm long and 220 mm outer diameter with nominal thickness of 5 mm under a planar location test setup using H-N sources. The accuracy of the new technique was compared with other AE source location methods such as the time of arrival (TOA) techniqueand DeltaTlocation. Theresults of the study show that the WTML method produces more accurate location resultscompared with TOA and triple point filtering location methods. The accuracy of the WTML approach is comparable with the deltaT location method but requires no initial acoustic calibration of the structure.
Tryptic digests of human serum albumin (HSA) and human lung epithelial cell lysates were used as test samples in a novel proteomics study. Peptides were separated and analyzed using 2D-nano-LC/MSMS with strong cation exchange (SCX) and reverse phase (RP) chromatography and contin...
Adaptive wavelets and relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hirschmann, Eric; Neilsen, David; Anderson, Matthe; Debuhr, Jackson; Zhang, Bo
2016-03-01
We present a method for integrating the relativistic magnetohydrodynamics equations using iterated interpolating wavelets. Such provide an adaptive implementation for simulations in multidimensions. A measure of the local approximation error for the solution is provided by the wavelet coefficients. They place collocation points in locations naturally adapted to the flow while providing expected conservation. We present demanding 1D and 2D tests includingthe Kelvin-Helmholtz instability and the Rayleigh-Taylor instability. Finally, we consider an outgoing blast wave that models a GRB outflow.
Image denoising with the dual-tree complex wavelet transform
NASA Astrophysics Data System (ADS)
Yaseen, Alauldeen S.; Pavlova, Olga N.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-04-01
The purpose of this study is to compare image denoising techniques based on real and complex wavelet-transforms. Possibilities provided by the classical discrete wavelet transform (DWT) with hard and soft thresholding are considered, and influences of the wavelet basis and image resizing are discussed. The quality of image denoising for the standard 2-D DWT and the dual-tree complex wavelet transform (DT-CWT) is studied. It is shown that DT-CWT outperforms 2-D DWT at the appropriate selection of the threshold level.
NASA Astrophysics Data System (ADS)
Hegazy, Maha A.; Lotfy, Hayam M.; Mowaka, Shereen; Mohamed, Ekram Hany
2016-07-01
Wavelets have been adapted for a vast number of signal-processing applications due to the amount of information that can be extracted from a signal. In this work, a comparative study on the efficiency of continuous wavelet transform (CWT) as a signal processing tool in univariate regression and a pre-processing tool in multivariate analysis using partial least square (CWT-PLS) was conducted. These were applied to complex spectral signals of ternary and quaternary mixtures. CWT-PLS method succeeded in the simultaneous determination of a quaternary mixture of drotaverine (DRO), caffeine (CAF), paracetamol (PAR) and p-aminophenol (PAP, the major impurity of paracetamol). While, the univariate CWT failed to simultaneously determine the quaternary mixture components and was able to determine only PAR and PAP, the ternary mixtures of DRO, CAF, and PAR and CAF, PAR, and PAP. During the calculations of CWT, different wavelet families were tested. The univariate CWT method was validated according to the ICH guidelines. While for the development of the CWT-PLS model a calibration set was prepared by means of an orthogonal experimental design and their absorption spectra were recorded and processed by CWT. The CWT-PLS model was constructed by regression between the wavelet coefficients and concentration matrices and validation was performed by both cross validation and external validation sets. Both methods were successfully applied for determination of the studied drugs in pharmaceutical formulations.
Hegazy, Maha A; Lotfy, Hayam M; Mowaka, Shereen; Mohamed, Ekram Hany
2016-07-01
Wavelets have been adapted for a vast number of signal-processing applications due to the amount of information that can be extracted from a signal. In this work, a comparative study on the efficiency of continuous wavelet transform (CWT) as a signal processing tool in univariate regression and a pre-processing tool in multivariate analysis using partial least square (CWT-PLS) was conducted. These were applied to complex spectral signals of ternary and quaternary mixtures. CWT-PLS method succeeded in the simultaneous determination of a quaternary mixture of drotaverine (DRO), caffeine (CAF), paracetamol (PAR) and p-aminophenol (PAP, the major impurity of paracetamol). While, the univariate CWT failed to simultaneously determine the quaternary mixture components and was able to determine only PAR and PAP, the ternary mixtures of DRO, CAF, and PAR and CAF, PAR, and PAP. During the calculations of CWT, different wavelet families were tested. The univariate CWT method was validated according to the ICH guidelines. While for the development of the CWT-PLS model a calibration set was prepared by means of an orthogonal experimental design and their absorption spectra were recorded and processed by CWT. The CWT-PLS model was constructed by regression between the wavelet coefficients and concentration matrices and validation was performed by both cross validation and external validation sets. Both methods were successfully applied for determination of the studied drugs in pharmaceutical formulations. PMID:27070527
Wavelet transforms as solutions of partial differential equations
Zweig, G.
1997-10-01
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 continuous 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.
Adapting overcomplete wavelet models to natural images
NASA Astrophysics Data System (ADS)
Sallee, Phil; Olshausen, Bruno A.
2003-11-01
Overcomplete wavelet representations have become increasingly popular for their ability to provide highly sparse and robust descriptions of natural signals. We describe a method for incorporating an overcomplete wavelet representation as part of a statistical model of images which includes a sparse prior distribution over the wavelet coefficients. The wavelet basis functions are parameterized by a small set of 2-D functions. These functions are adapted to maximize the average log-likelihood of the model for a large database of natural images. When adapted to natural images, these functions become selective to different spatial orientations, and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Inference with the learned model is demonstrated for applications such as denoising, with results that compare favorably with other methods.
Optical wavelet transform for fingerprint identification
NASA Astrophysics Data System (ADS)
MacDonald, Robert P.; Rogers, Steven K.; Burns, Thomas J.; Fielding, Kenneth H.; Warhola, Gregory T.; Ruck, Dennis W.
1994-03-01
The Federal Bureau of Investigation (FBI) has recently sanctioned a wavelet fingerprint image compression algorithm developed for reducing storage requirements of digitized fingerprints. This research implements an optical wavelet transform of a fingerprint image, as the first step in an optical fingerprint identification process. Wavelet filters are created from computer- generated holograms of biorthogonal wavelets, the same wavelets implemented in the FBI algorithm. Using a detour phase holographic technique, a complex binary filter mask is created with both symmetry and linear phase. The wavelet transform is implemented with continuous shift using an optical correlation between binarized fingerprints written on a Magneto-Optic Spatial Light Modulator and the biorthogonal wavelet filters. A telescopic lens combination scales the transformed fingerprint onto the filters, providing a means of adjusting the biorthogonal wavelet filter dilation continuously. The wavelet transformed fingerprint is then applied to an optical fingerprint identification process. Comparison between normal fingerprints and wavelet transformed fingerprints shows improvement in the optical identification process, in terms of rotational invariance.
On alternative wavelet reconstruction formula: a case study of approximate wavelets.
Lebedeva, Elena A; Postnikov, Eugene B
2014-10-01
The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed. PMID:26064533
Integrated wavelets for medical image analysis
NASA Astrophysics Data System (ADS)
Heinlein, Peter; Schneider, Wilfried
2003-11-01
Integrated wavelets are a new method for discretizing the continuous wavelet transform (CWT). Independent of the choice of discrete scale and orientation parameters they yield tight families of convolution operators. Thus these families can easily be adapted to specific problems. After presenting the fundamental ideas, we focus primarily on the construction of directional integrated wavelets and their application to medical images. We state an exact algorithm for implementing this transform and present applications from the field of digital mammography. The first application covers the enhancement of microcalcifications in digital mammograms. Further, we exploit the directional information provided by integrated wavelets for better separation of microcalcifications from similar structures.
Compression of echocardiographic scan line data using wavelet packet transform
NASA Technical Reports Server (NTRS)
Hang, X.; Greenberg, N. L.; Qin, J.; Thomas, J. D.
2001-01-01
An efficient compression strategy is indispensable for digital echocardiography. Previous work has suggested improved results utilizing wavelet transforms in the compression of 2D echocardiographic images. Set partitioning in hierarchical trees (SPIHT) was modified to compress echocardiographic scanline data based on the wavelet packet transform. A compression ratio of at least 94:1 resulted in preserved image quality.
Wavelet analysis of hemispheroid flow separation toward understanding human vocal fold pathologies
NASA Astrophysics Data System (ADS)
Plesniak, Daniel H.; Carr, Ian A.; Bulusu, Kartik V.; Plesniak, Michael W.
2014-11-01
Physiological flows observed in human vocal fold pathologies, such as polyps and nodules, can be modeled by flow over a wall-mounted protuberance. The experimental investigation of flow separation over a surface-mounted hemispheroid was performed using particle image velocimetry (PIV) and measurements of surface pressure in a low-speed wind tunnel. This study builds on the hypothesis that the signatures of vortical structures associated with flow separation are imprinted on the surface pressure distributions. Wavelet decomposition methods in one- and two-dimensions were utilized to elucidate the flow behavior. First, a complex Gaussian wavelet was used for the reconstruction of surface pressure time series from static pressure measurements acquired from ports upstream, downstream, and on the surface of the hemispheroid. This was followed by the application of a novel continuous wavelet transform algorithm (PIVlet 1.2) using a 2D-Ricker wavelet for coherent structure detection on instantaneous PIV-data. The goal of this study is to correlate phase shifts in surface pressure with Strouhal numbers associated with the vortex shedding. Ultimately, the wavelet-based analytical framework will be aimed at addressing pulsatile flows. This material is based in part upon work supported by the National Science Foundation under Grant Number CBET-1236351, and GW Center for Biomimetics and Bioinspired Engineering (COBRE).
Image-based scene representation using wavelet-based interval morphing
NASA Astrophysics Data System (ADS)
Bao, Paul; Xu, Dan
1999-07-01
Scene appearance for a continuous range of viewpoint can be represented by a discrete set of images via image morphing. In this paper, we present a new robust image morphing scheme based on 2D wavelet transform and interval field interpolation. Traditional mesh-base and field-based morphing algorithms, usually designed in the spatial image space, suffer from very high time complexity and therefore make themselves impractical in real-time virtual environment applications. Compared with traditional morphing methods, the proposed wavelet-based interval morphing scheme performs interval interpolation in both the frequency and spatial spaces. First, the images of the scene can be significantly compressed in the frequency domain with little degradation in visual quality and therefore the complexity of the scene can be significantly reduced. Second, since a feature point in the image may correspond to a neighborhood in a subband image in the wavelet domain, we define feature interval for the wavelet-transformed images for an accurate feature matching between the morphing images. Based on the feature intervals, we employ the interval field interpolation to morph the images progressively in a coarse-to-fine process. Finally, we use a post-warping procedure to transform the interpolated views to its desired position. A nice future of using wavelet transformation is its multiresolution representation mode, which enables the progressive morphing of scene.
Analysis of autostereoscopic three-dimensional images using multiview wavelets.
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. PMID:27534470
Wavelet frames and admissibility in higher dimensions
Fuehr, H.
1996-12-01
This paper is concerned with the relations between discrete and continuous wavelet transforms on {ital k}-dimensional Euclidean space. We start with the construction of continuous wavelet transforms with the help of square-integrable representations of certain semidirect products, thereby generalizing results of Bernier and Taylor. We then turn to frames of L{sup 2}({bold R}{sup {ital k}}) and to the question, when the functions occurring in a given frame are admissible for a given continuous wavelet transform. For certain frames we give a characterization which generalizes a result of Daubechies to higher dimensions. {copyright} {ital 1996 American Institute of Physics.}
Perception-based reversible watermarking for 2D vector maps
NASA Astrophysics Data System (ADS)
Men, Chaoguang; Cao, Liujuan; Li, Xiang
2010-07-01
This paper presents an effective and reversible watermarking approach for digital copyright protection of 2D-vector maps. To ensure that the embedded watermark is insensitive for human perception, we only select the noise non-sensitive regions for watermark embedding by estimating vertex density within each polyline. To ensure the exact recovery of original 2D-vector map after watermark extraction, we introduce a new reversible watermarking scheme based on reversible high-frequency wavelet coefficients modification. Within the former-selected non-sensitive regions, our watermarking operates on the lower-order vertex coordinate decimals with integer wavelet transform. Such operation further reduces the visual distortion caused by watermark embedding. We have validated the effectiveness of our scheme on our real-world city river/building 2D-vector maps. We give extensive experimental comparisons with state-of-the-art methods, including embedding capability, invisibility, and robustness over watermark attacking.
Davis, A.B.
1998-12-01
The authors compare several ways of uncovering multifractal properties of data in 1D and 2D using wavelet transforms. The WTMM or (Continuous) Wavelet Transform Maximum Modulus method has been extensively documented and widely applied by Dr. Alain Arneodo`s (Bordeaux) group, to the point where their successes have overshadowed simpler techniques that use the Discrete WT. What the latter lack in robustness is gained in efficiency, thus enabling virtually real-time multifractal analysis of data as it is collected. Another advantage of DWT-based approaches is that tensor products of dyadic and triadic branching schemes enable a straightforward attack on strong anisotropy in natural and artificial 2D random fields.
Directional spherical multipole wavelets
Hayn, Michael; Holschneider, Matthias
2009-07-15
We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets.
NASA Astrophysics Data System (ADS)
Jones, B. J. T.
Wavelet analysis has become a major tool in many aspects of data handling, whether it be statistical analysis, noise removal or image reconstruction. Wavelet analysis has worked its way into fields as diverse as economics, medicine, geophysics, music and cosmology.
Wavelet periodicity detection algorithms
NASA Astrophysics Data System (ADS)
Benedetto, John J.; Pfander, Goetz E.
1998-10-01
This paper deals with the analysis of time series with respect to certain known periodicities. In particular, we shall present a fast method aimed at detecting periodic behavior inherent in noise data. The method is composed of three steps: (1) Non-noisy data are analyzed through spectral and wavelet methods to extract specific periodic patterns of interest. (2) Using these patterns, we construct an optimal piecewise constant wavelet designed to detect the underlying periodicities. (3) We introduce a fast discretized version of the continuous wavelet transform, as well as waveletgram averaging techniques, to detect occurrence and period of these periodicities. The algorithm is formulated to provide real time implementation. Our procedure is generally applicable to detect locally periodic components in signals s which can be modeled as s(t) equals A(t)F(h(t)) + N(t) for t in I, where F is a periodic signal, A is a non-negative slowly varying function, and h is strictly increasing with h' slowly varying, N denotes background activity. For example, the method can be applied in the context of epileptic seizure detection. In this case, we try to detect seizure periodics in EEG and ECoG data. In the case of ECoG data, N is essentially 1/f noise. In the case of EEG data and for t in I,N includes noise due to cranial geometry and densities. In both cases N also includes standard low frequency rhythms. Periodicity detection has other applications including ocean wave prediction, cockpit motion sickness prediction, and minefield detection.
Fryer, M.O.
1997-05-01
This paper describes the use of wavelet transform techniques to analyze typical data found in industrial applications. A way of detecting system changes using wavelet transforms is described. The results of applying this method are described for several typical applications. The wavelet technique is compared with the use of Fourier transform methods.
Szu, H.; Hsu, C.
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
Energy Science and Technology Software Center (ESTSC)
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
Symplectic wavelet transformation.
Fan, Hong-Yi; Lu, Hai-Liang
2006-12-01
Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi(*)(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi(*)(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version. PMID:17099740
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.
Multiresolution local tomography in dental radiology using wavelets.
Niinimäki, K; Siltanen, S; Kolehmainen, V
2007-01-01
A Bayesian multiresolution model for local tomography in dental radiology is proposed. In this model a wavelet basis is used to present dental structures and the prior information is modeled in terms of Besov norm penalty. The proposed wavelet-based multiresolution method is used to reduce the number of unknowns in the reconstruction problem by abandoning fine-scale wavelets outside the region of interest (ROI). This multiresolution model allows significant reduction in the number of unknowns without the loss of reconstruction accuracy inside the ROI. The feasibility of the proposed method is tested with two-dimensional (2D) examples using simulated and experimental projection data from dental specimens. PMID:18002604
Wavelet analysis and scaling properties of time series.
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. PMID:16383481
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.
2D Seismic Reflection Data across Central Illinois
Smith, Valerie; Leetaru, Hannes
2014-09-30
In a continuing collaboration with the Midwest Geologic Sequestration Consortium (MGSC) on the Evaluation of the Carbon Sequestration Potential of the Cambro-Ordovician Strata of the Illinois and Michigan Basins project, Schlumberger Carbon Services and WesternGeco acquired two-dimensional (2D) seismic data in the Illinois Basin. This work included the design, acquisition and processing of approximately 125 miles of (2D) seismic reflection surveys running west to east in the central Illinois Basin. Schlumberger Carbon Services and WesternGeco oversaw the management of the field operations (including a pre-shoot planning, mobilization, acquisition and de-mobilization of the field personnel and equipment), procurement of the necessary permits to conduct the survey, post-shoot closure, processing of the raw data, and provided expert consultation as needed in the interpretation of the delivered product. Three 2D seismic lines were acquired across central Illinois during November and December 2010 and January 2011. Traversing the Illinois Basin, this 2D seismic survey was designed to image the stratigraphy of the Cambro-Ordovician sections and also to discern the basement topography. Prior to this survey, there were no regionally extensive 2D seismic data spanning this section of the Illinois Basin. Between the NW side of Morgan County and northwestern border of Douglas County, these seismic lines ran through very rural portions of the state. Starting in Morgan County, Line 101 was the longest at 93 miles in length and ended NE of Decatur, Illinois. Line 501 ran W-E from the Illinois Basin – Decatur Project (IBDP) site to northwestern Douglas County and was 25 miles in length. Line 601 was the shortest and ran N-S past the IBDP site and connected lines 101 and 501. All three lines are correlated to well logs at the IBDP site. Originally processed in 2011, the 2D seismic profiles exhibited a degradation of signal quality below ~400 millisecond (ms) which made
Manchanda, P.; Meenakshi
2009-07-02
Recently Manchanda, Meenakshi and Siddiqi have studied Haar-Vilenkin wavelet and a special type of non-uniform multiresolution analysis. Haar-Vilenkin wavelet is a generalization of Haar wavelet. Motivated by the paper of Gabardo and Nashed we have introduced a class of multiresolution analysis extending the concept of classical multiresolution analysis. We present here a resume of these results. We hope that applications of these concepts to some significant real world problems could be found.
An efficient 2D-WTMM and PNN approach to remove spurious radar echoes
NASA Astrophysics Data System (ADS)
Khider, Mohamed; Haddad, Boualem
2013-03-01
The proposed method aims to reduce the spurious echoes in weather radar images collected at Melbourne radar site, using parameters from 2D-WTMM method based on the continuous wavelet transform, and including the PNN probabilistic neural network for the classification of pixels into two types of echoes : precipitation or parasite. Indeed, we propose the introduction of parameters related to wavelet transform skeletons, these parameters are proportional to the image texture roughness, anisotropy and the distance of separation between non-zero radar echoes cells and give good separation between rain and non-rain echoes. Radar image is first segmented with Voronoi's cells according to the spatial distribution of Holder exponents. By comparing with a direct method of classification which takes into account only one parameter at a time by using a threshold, it was found that the combination of these three parameters with PNN approach improves the final results in terms of preserving precipitation echoes and elimination of weather radar clutter. Initial results show approximately the removal of 98% of clutter and preservation of 97% of precipitation echoes.
Comparative study of different wavelet based neural network models for rainfall-runoff modeling
NASA Astrophysics Data System (ADS)
Shoaib, Muhammad; Shamseldin, Asaad Y.; Melville, Bruce W.
2014-07-01
The use of wavelet transformation in rainfall-runoff modeling has become popular because of its ability to simultaneously deal with both the spectral and the temporal information contained within time series data. The selection of an appropriate wavelet function plays a crucial role for successful implementation of the wavelet based rainfall-runoff artificial neural network models as it can lead to further enhancement in the model performance. The present study is therefore conducted to evaluate the effects of 23 mother wavelet functions on the performance of the hybrid wavelet based artificial neural network rainfall-runoff models. The hybrid Multilayer Perceptron Neural Network (MLPNN) and the Radial Basis Function Neural Network (RBFNN) models are developed in this study using both the continuous wavelet and the discrete wavelet transformation types. The performances of the 92 developed wavelet based neural network models with all the 23 mother wavelet functions are compared with the neural network models developed without wavelet transformations. It is found that among all the models tested, the discrete wavelet transform multilayer perceptron neural network (DWTMLPNN) and the discrete wavelet transform radial basis function (DWTRBFNN) models at decomposition level nine with the db8 wavelet function has the best performance. The result also shows that the pre-processing of input rainfall data by the wavelet transformation can significantly increases performance of the MLPNN and the RBFNN rainfall-runoff models.
A 2-D orientation-adaptive prediction filter in lifting structures for image coding.
Gerek, Omer N; Cetin, A Enis
2006-01-01
Lifting-style implementations of wavelets are widely used in image coders. A two-dimensional (2-D) edge adaptive lifting structure, which is similar to Daubechies 5/3 wavelet, is presented. The 2-D prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image. Consequently, the prediction domain is allowed to rotate +/-45 degrees in regions with diagonal gradient. The gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction, and no multiplications are required. PMID:16435541
Three-dimensional compression scheme based on wavelet transform
NASA Astrophysics Data System (ADS)
Yang, Wu; Xu, Hui; Liao, Mengyang
1999-03-01
In this paper, a 3D compression method based on separable wavelet transform is discussed in detail. The most commonly used digital modalities generate multiple slices in a single examination, which are normally anatomically or physiologically correlated to each other. 3D wavelet compression methods can achieve more efficient compression by exploring the correlation between slices. The first step is based on a separable 3D wavelet transform. Considering the difference between pixel distances within a slice and those between slices, one biorthogonal Antoninin filter bank is applied within 2D slices and a second biorthogonal Villa4 filter bank on the slice direction. Then, S+P transform is applied in the low-resolution wavelet components and an optimal quantizer is presented after analysis of the quantization noise. We use an optimal bit allocation algorithm, which, instead of eliminating the coefficients of high-resolution components in smooth areas, minimizes the system reconstruction distortion at a given bit-rate. Finally, to remain high coding efficiency and adapt to different properties of each component, a comprehensive entropy coding method is proposed, in which arithmetic coding method is applied in high-resolution components and adaptive Huffman coding method in low-resolution components. Our experimental results are evaluated by several image measures and our 3D wavelet compression scheme is proved to be more efficient than 2D wavelet compression.
Texture image retrieval using new rotated complex wavelet filters.
Kokare, Manesh; Biswas, P K; Chatterji, B N
2005-12-01
A new set of two-dimensional (2-D) rotated complex wavelet filters (RCWFs) are designed with complex wavelet filter coefficients, which gives texture information strongly oriented in six different directions (45 degrees apart from complex wavelet transform). The 2-D RCWFs are nonseparable and oriented, which improves characterization of oriented textures. Most texture image retrieval systems are still incapable of providing retrieval result with high retrieval accuracy and less computational complexity. To address this problem, we propose a novel approach for texture image retrieval by using a set of dual-tree rotated complex wavelet filter (DT-RCWF) and dual-tree-complex wavelet transform (DT-CWT) jointly, which obtains texture features in 12 different directions. The information provided by DT-RCWF complements the information generated by DT-CWT. Features are obtained by computing the energy and standard deviation on each subband of the decomposed image. To check the retrieval performance, texture database D1 of 1856 textures from Brodatz album and database D2 of 640 texture images from VisTex image database is created. Experimental results indicates that the proposed method improves retrieval rate from 69.61% to 77.75% on database D1, and from 64.83% to 82.81% on database D2, in comparing with traditional discrete wavelet transform based approach. The proposed method also retains comparable levels of computational complexity. PMID:16366243
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.
Recent advances in wavelet analyses: Part 1. A review of concepts
NASA Astrophysics Data System (ADS)
Labat, David
2005-11-01
This contribution provides a review of the most recent wavelet applications in the field of earth sciences and is devoted to introducing and illustrating new wavelet analysis methods in the field of hydrology. Wavelet analysis remains unknown in the field of hydrology even though it clearly overcomes the well-known limits of the classical Fourier analysis. New wavelet-based tools are proposed to hydrologists in order to make wavelet analysis more attractive. First, a multiresolution continuous wavelet analysis method is shown to significantly improve the determination of the temporal-scale structure of a given signal. Second, the concept of wavelet entropy in both continuous and multiresolution frameworks is introduced allowing for an estimation of the temporal evolution of a given hydrological or climatologic signal's complexity. New insights in the scale-dependence of the relationship are exposed by introducing wavelet cross-correlation and wavelet coherence. Continuous wavelet cross-correlation provides a time-scale distribution of the correlation between two signals, whereas continuous wavelet coherence provides a qualitative estimator of the temporal evolution of the degree of linearity of the relationship between two signals on a given scale. These methods are applied to four large river runoffs and two global climatic indexes in a companion paper.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
NASA Astrophysics Data System (ADS)
Abbasi Tarighat, Maryam; Nabavi, Masoume; Mohammadizadeh, Mohammad Reza
2015-06-01
A new multi-component analysis method based on zero-crossing point-continuous wavelet transformation (CWT) was developed for simultaneous spectrophotometric determination of Cu2+ and Pb2+ ions based on the complex formation with 2-benzyl espiro[isoindoline-1,5oxasolidine]-2,3,4 trione (BSIIOT). The absorption spectra were evaluated with respect to synthetic ligand concentration, time of complexation and pH. Therefore according the absorbance values, 0.015 mmol L-1 BSIIOT, 10 min after mixing and pH 8.0 were used as optimum values. The complex formation between BSIIOT ligand and the cations Cu2+ and Pb2+ by application of rank annihilation factor analysis (RAFA) were investigated. Daubechies-4 (db4), discrete Meyer (dmey), Morlet (morl) and Symlet-8 (sym8) continuous wavelet transforms for signal treatments were found to be suitable among the wavelet families. The applicability of new synthetic ligand and selected mother wavelets were used for the simultaneous determination of strongly overlapped spectra of species without using any pre-chemical treatment. Therefore, CWT signals together with zero crossing technique were directly applied to the overlapping absorption spectra of Cu2+ and Pb2+. The calibration graphs for estimation of Pb2+ and Cu 2+were obtained by measuring the CWT amplitudes at zero crossing points for Cu2+ and Pb2+ at the wavelet domain, respectively. The proposed method was validated by simultaneous determination of Cu2+ and Pb2+ ions in red beans, walnut, rice, tea and soil samples. The obtained results of samples with proposed method have been compared with those predicted by partial least squares (PLS) and flame atomic absorption spectrophotometry (FAAS).
Abbasi Tarighat, Maryam; Nabavi, Masoume; Mohammadizadeh, Mohammad Reza
2015-06-15
A new multi-component analysis method based on zero-crossing point-continuous wavelet transformation (CWT) was developed for simultaneous spectrophotometric determination of Cu(2+) and Pb(2+) ions based on the complex formation with 2-benzyl espiro[isoindoline-1,5 oxasolidine]-2,3,4 trione (BSIIOT). The absorption spectra were evaluated with respect to synthetic ligand concentration, time of complexation and pH. Therefore according the absorbance values, 0.015 mmol L(-1) BSIIOT, 10 min after mixing and pH 8.0 were used as optimum values. The complex formation between BSIIOT ligand and the cations Cu(2+) and Pb(2+) by application of rank annihilation factor analysis (RAFA) were investigated. Daubechies-4 (db4), discrete Meyer (dmey), Morlet (morl) and Symlet-8 (sym8) continuous wavelet transforms for signal treatments were found to be suitable among the wavelet families. The applicability of new synthetic ligand and selected mother wavelets were used for the simultaneous determination of strongly overlapped spectra of species without using any pre-chemical treatment. Therefore, CWT signals together with zero crossing technique were directly applied to the overlapping absorption spectra of Cu(2+) and Pb(2+). The calibration graphs for estimation of Pb(2+) and Cu (2+)were obtained by measuring the CWT amplitudes at zero crossing points for Cu(2+) and Pb(2+) at the wavelet domain, respectively. The proposed method was validated by simultaneous determination of Cu(2+) and Pb(2+) ions in red beans, walnut, rice, tea and soil samples. The obtained results of samples with proposed method have been compared with those predicted by partial least squares (PLS) and flame atomic absorption spectrophotometry (FAAS). PMID:25766479
Multiresolution With Super-Compact Wavelets
NASA Technical Reports Server (NTRS)
Lee, Dohyung
2000-01-01
approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.
3D Wavelet-Based Filter and Method
Moss, William C.; Haase, Sebastian; Sedat, John W.
2008-08-12
A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.
Periodized Daubechies wavelets
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.
Two-dimensional quantum propagation using wavelets in space and time
Sparks, Douglas K.; Johnson, Bruce R.
2006-09-21
A recent method for solving the time-dependent Schroedinger equation has been developed using expansions in compact-support wavelet bases in both space and time [H. Wang et al., J. Chem. Phys. 121, 7647 (2004)]. This method represents an exact quantum mixed time-frequency approach, with special initial temporal wavelets used to solve the initial value problem. The present work is a first extension of the method to multiple spatial dimensions applied to a simple two-dimensional (2D) coupled anharmonic oscillator problem. A wavelet-discretized version of norm preservation for time-independent Hamiltonians discovered in the earlier one-dimensional investigation is verified to hold as well in 2D and, by implication, in higher numbers of spatial dimensions. The wavelet bases are not restricted to rectangular domains, a fact which is exploited here in a 2D adaptive version of the algorithm.
NASA Technical Reports Server (NTRS)
Kempel, Leo C.
1992-01-01
Wavelets are an exciting new topic in applied mathematics and signal processing. This paper will provide a brief review of wavelets which are also known as families of functions with an emphasis on interpretation rather than rigor. We will derive an indirect use of wavelets for the solution of integral equations based techniques adapted from image processing. Examples for resistive strips will be given illustrating the effect of these techniques as well as their promise in reducing dramatically the requirement in order to solve an integral equation for large bodies. We also will present a direct implementation of wavelets to solve an integral equation. Both methods suggest future research topics and may hold promise for a variety of uses in computational electromagnetics.
Proximity sensing with wavelet generated video
NASA Astrophysics Data System (ADS)
Noel, Steven E.; Szu, Harold H.
1998-10-01
In this paper we introduce wavelet video processing of proximity sensor signals. Proximity sensing is required for a wide range of military and commercial applications, including weapon fuzzing, robotics, and automotive collision avoidance. While our proposed method temporarily increases signal dimension, it eventually performs data compression through the extraction of salient signal features. This data compression in turn reduces the necessary complexity of the remaining computational processing. We demonstrate our method of wavelet video processing via the proximity sensing of nearby objects through their Doppler shift. In doing this we perform a continuous wavelet transform on the Doppler signal, after subjecting it to a time-varying window. We then extract signal features from the resulting wavelet video, which we use as input to pattern recognition neural networks. The networks are trained to estimate the time- varying Doppler shift from the extracted features. We test the estimation performance of the networks, using different degrees of nonlinearity in the frequency shift over time and different levels of noise. We give the analytical result that the signal-to-noise enhancement of our proposed method is at least as good as the square root of the number of video frames, although more work is needed to completely quantify this. Real-time wavelet-based video processing and compression technology recently developed under the DOD WAVENET program offers an exciting opportunity to more fully investigate our proposed method.
Combining Wavelet Transform and Hidden Markov Models for ECG Segmentation
NASA Astrophysics Data System (ADS)
Andreão, Rodrigo Varejão; Boudy, Jérôme
2006-12-01
This work aims at providing new insights on the electrocardiogram (ECG) segmentation problem using wavelets. The wavelet transform has been originally combined with a hidden Markov models (HMMs) framework in order to carry out beat segmentation and classification. A group of five continuous wavelet functions commonly used in ECG analysis has been implemented and compared using the same framework. All experiments were realized on the QT database, which is composed of a representative number of ambulatory recordings of several individuals and is supplied with manual labels made by a physician. Our main contribution relies on the consistent set of experiments performed. Moreover, the results obtained in terms of beat segmentation and premature ventricular beat (PVC) detection are comparable to others works reported in the literature, independently of the type of the wavelet. Finally, through an original concept of combining two wavelet functions in the segmentation stage, we achieve our best performances.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems. PMID:27104687
Entanglement Renormalization and Wavelets
NASA Astrophysics Data System (ADS)
Evenbly, Glen; White, Steven R.
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Lagrange wavelets for signal processing.
Shi, Z; Wei, G W; Kouri, D J; Hoffman, D K; Bao, Z
2001-01-01
This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing. PMID:18255493
Wavelet spectrum analysis approach to model validation of dynamic systems
NASA Astrophysics Data System (ADS)
Jiang, Xiaomo; Mahadevan, Sankaran
2011-02-01
Feature-based validation techniques for dynamic system models could be unreliable for nonlinear, stochastic, and transient dynamic behavior, where the time series is usually non-stationary. This paper presents a wavelet spectral analysis approach to validate a computational model for a dynamic system. Continuous wavelet transform is performed on the time series data for both model prediction and experimental observation using a Morlet wavelet function. The wavelet cross-spectrum is calculated for the two sets of data to construct a time-frequency phase difference map. The Box-plot, an exploratory data analysis technique, is applied to interpret the phase difference for validation purposes. In addition, wavelet time-frequency coherence is calculated using the locally and globally smoothed wavelet power spectra of the two data sets. Significance tests are performed to quantitatively verify whether the wavelet time-varying coherence is significant at a specific time and frequency point, considering uncertainties in both predicted and observed time series data. The proposed wavelet spectrum analysis approach is illustrated with a dynamics validation challenge problem developed at the Sandia National Laboratories. A comparison study is conducted to demonstrate the advantages of the proposed methodologies over classical frequency-independent cross-correlation analysis and time-independent cross-coherence analysis for the validation of dynamic systems.
Wavelet analysis of atmospheric turbulence
Hudgins, L.H.
1992-12-31
After a brief review of the elementary properties of Fourier Transforms, the Wavelet Transform is defined in Part I. Basic results are given for admissable wavelets. The Multiresolution Analysis, or MRA (a mathematical structure which unifies a large class of wavelets with Quadrature Mirror Filters) is then introduced. Some fundamental aspects of wavelet design are then explored. The Discrete Wavelet Transform is discussed and, in the context of an MRA, is seen to supply a Fast Wavelet Transform which competes with the Fast Fourier Transform for efficiency. In Part II, the Wavelet Transform is developed in terms of the scale number variable s instead of the scale length variable a where a = 1/s. Basic results such as the admissibility condition, conservation of energy, and the reconstruction theorem are proven in this context. After reviewing some motivation for the usual Fourier power spectrum, a definition is given for the wavelet power spectrum. This `spectral density` is then intepreted in the context of spectral estimation theory. Parseval`s theorem for Wavelets then leads naturally to the Wavelet Cross Spectrum, Wavelet Cospectrum, and Wavelet Quadrature Spectrum. Wavelet Transforms are then applied in Part III to the analysis of atmospheric turbulence. Data collected over the ocean is examined in the wavelet transform domain for underlying structure. A brief overview of atmospheric turbulence is provided. Then the overall method of applying Wavelet Transform techniques to time series data is described. A trace study is included, showing some of the aspects of choosing the computational algorithm, and selection of a specific analyzing wavelet. A model for generating synthetic turbulence data is developed, and seen to yield useful results in comparing with real data for structural transitions. Results from the theory of Wavelet Spectral Estimation and Wavelength Cross-Transforms are applied to studying the momentum transport and the heat flux.
Wavelet-RX anomaly detection for dual-band forward-looking infrared imagery.
Mehmood, Asif; Nasrabadi, Nasser M
2010-08-20
This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-looking infrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. The proposed approach, called the wavelet-RX (Reed-Xiaoli) algorithm, consists of a combination of a two-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called the RX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decompose the input image into uniform subbands. A subband-image cube is formed by concatenating together a number of significant subbands (high-energy subbands). The RX algorithm is then applied to the subband-image cube obtained from a wavelet decomposition of the LW or MW sensor data. In the case of the dual band, the RX algorithm is applied to a subband-image cube constructed by concatenating together the high-energy subbands of the LW and MW subband-image cubes. Experimental results are presented for the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detecting anomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor. The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector for both single-band and dual-band FLIR sensors. PMID:20733634
Energy Science and Technology Software Center (ESTSC)
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
Space-based RF signal classification using adaptive wavelet features
Caffrey, M.; Briles, S.
1995-04-01
RF signals are dispersed in frequency as they propagate through the ionosphere. For wide-band signals, this results in nonlinearly- chirped-frequency, transient signals in the VHF portion of the spectrum. This ionospheric dispersion provide a means of discriminating wide-band transients from other signals (e.g., continuous-wave carriers, burst communications, chirped-radar signals, etc.). The transient nature of these dispersed signals makes them candidates for wavelet feature selection. Rather than choosing a wavelet ad hoc, we adaptively compute an optimal mother wavelet via a neural network. Gaussian weighted, linear frequency modulate (GLFM) wavelets are linearly combined by the network to generate our application specific mother wavelet, which is optimized for its capacity to select features that discriminate between the dispersed signals and clutter (e.g., multiple continuous-wave carriers), not for its ability to represent the dispersed signal. The resulting mother wavelet is then used to extract features for a neutral network classifier. The performance of the adaptive wavelet classifier is the compared to an FFT based neural network classifier.
Wavelet based hierarchical coding scheme for radar image compression
NASA Astrophysics Data System (ADS)
Sheng, Wen; Jiao, Xiaoli; He, Jifeng
2007-12-01
This paper presents a wavelet based hierarchical coding scheme for radar image compression. Radar signal is firstly quantized to digital signal, and reorganized as raster-scanned image according to radar's repeated period frequency. After reorganization, the reformed image is decomposed to image blocks with different frequency band by 2-D wavelet transformation, each block is quantized and coded by the Huffman coding scheme. A demonstrating system is developed, showing that under the requirement of real time processing, the compression ratio can be very high, while with no significant loss of target signal in restored radar image.
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.
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Electromagnetic spatial coherence wavelets.
Castaneda, Roman; Garcia-Sucerquia, Jorge
2006-01-01
The recently introduced concept of spatial coherence wavelets is generalized to describe the propagation of electromagnetic fields in the free space. For this aim, the spatial coherence wavelet tensor is introduced as an elementary amount, in terms of which the formerly known quantities for this domain can be expressed. It allows for the analysis of the relationship between the spatial coherence properties and the polarization state of the electromagnetic wave. This approach is completely consistent with the recently introduced unified theory of coherence and polarization for random electromagnetic beams, but it provides further insight about the causal relationship between the polarization states at different planes along the propagation path. PMID:16478063
Dual tree fractional quaternion wavelet transform for disparity estimation.
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. PMID:24388356
Davis, A. B.; Petrov, N. P.; Clothiaux, E. E.; Marshak, A.
2002-01-01
Spatial and/or temporal variabilities of clouds is of paramount importance for at least two in tensely researched sub-problems in global and regional climate modeling: (1) cloud-radiation interaction where correlations can trigger 3D radiative transfer effects; and (2) dynamical cloud modeling where the goal is to realistically reproduce the said correlations. We propose wavelets as a simple yet powerful way of quantifying cloud variability. More precisely, we use 'semi-discrete' wavelet transforms which, at least in the present statistical applications, have advantages over both its continuous and discrete counterparts found in the bulk of the wavelet literature. With the particular choice of normalization we adopt, the scale-dependence of the variance of the wavelet coefficients (i.e,, the wavelet energy spectrum) is always a better discriminator of transition from 'stationary' to 'nonstationary' behavior than conventional methods based on auto-correlation analysis, second-order structure function (a.k.a. the semi-variogram), or Fourier analysis. Indeed, the classic statistics go at best from monotonically scale- or wavenumber-dependent to flat at such a transition; by contrast, the wavelet spectrum changes the sign of its derivative with respect to scale. We apply 1D and 2D semi-discrete wavelet transforms to remote sensing data on cloud structure from two sources: (1) an upward-looking milli-meter cloud radar (MMCR) at DOE's climate observation site in Oklahoma deployed as part of the Atmospheric Radiation Measurement (ARM) Progrm; and (2) DOE's Multispectral Thermal Imager (MTI), a high-resolution space-borne instrument in sunsynchronous orbit that is described in sufficient detail for our present purposes by Weber et al. (1999). For each type of data, we have at least one theoretical prediction - with empirical validation already in existence - for a power-law relation for wavelet statistics with respect to scale. This is what is expected in physical (i
NASA Astrophysics Data System (ADS)
Mayor, Louise
2016-05-01
Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.
50 CFR Table 2d to Part 679 - Species Codes-Non-FMP Species
Code of Federal Regulations, 2012 CFR
2012-10-01
... 50 Wildlife and Fisheries 13 2012-10-01 2012-10-01 false Species Codes-Non-FMP Species 2d Table 2d to Part 679 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION, DEPARTMENT OF COMMERCE (CONTINUED) FISHERIES OF THE EXCLUSIVE ECONOMIC ZONE OFF ALASKA Pt. 679, Table 2d Table 2d to Part...
Ho, Derek; Kim, Sanghoon; Drake, Tyler K.; Eldridge, Will J.; Wax, Adam
2014-01-01
We present a fast approach for size determination of spherical scatterers using the continuous wavelet transform of the angular light scattering profile to address the computational limitations of previously developed sizing techniques. The potential accuracy, speed, and robustness of the algorithm were determined in simulated models of scattering by polystyrene beads and cells. The algorithm was tested experimentally on angular light scattering data from polystyrene bead phantoms and MCF-7 breast cancer cells using a 2D a/LCI system. Theoretical sizing of simulated profiles of beads and cells produced strong fits between calculated and actual size (r2 = 0.9969 and r2 = 0.9979 respectively), and experimental size determinations were accurate to within one micron. PMID:25360350
Spectral Laplace-Beltrami wavelets with applications in medical images.
Tan, Mingzhen; Qiu, Anqi
2015-05-01
The spectral graph wavelet transform (SGWT) has recently been developed to compute wavelet transforms of functions defined on non-Euclidean spaces such as graphs. By capitalizing on the established framework of the SGWT, we adopt a fast and efficient computation of a discretized Laplace-Beltrami (LB) operator that allows its extension from arbitrary graphs to differentiable and closed 2-D manifolds (smooth surfaces embedded in the 3-D Euclidean space). This particular class of manifolds are widely used in bioimaging to characterize the morphology of cells, tissues, and organs. They are often discretized into triangular meshes, providing additional geometric information apart from simple nodes and weighted connections in graphs. In comparison with the SGWT, the wavelet bases constructed with the LB operator are spatially localized with a more uniform "spread" with respect to underlying curvature of the surface. In our experiments, we first use synthetic data to show that traditional applications of wavelets in smoothing and edge detectio can be done using the wavelet bases constructed with the LB operator. Second, we show that multi-resolutional capabilities of the proposed framework are applicable in the classification of Alzheimer's patients with normal subjects using hippocampal shapes. Wavelet transforms of the hippocampal shape deformations at finer resolutions registered higher sensitivity (96%) and specificity (90%) than the classification results obtained from the direct usage of hippocampal shape deformations. In addition, the Laplace-Beltrami method requires consistently a smaller number of principal components (to retain a fixed variance) at higher resolution as compared to the binary and weighted graph Laplacians, demonstrating the potential of the wavelet bases in adapting to the geometry of the underlying manifold. PMID:25343758
Wavelet for Ultrasonic Flaw Enhancement and Image Compression
NASA Astrophysics Data System (ADS)
Cheng, W.; Tsukada, K.; Li, L. Q.; Hanasaki, K.
2003-03-01
Ultrasonic imaging has been widely used in Non-destructive Testing (NDT) and medical application. However, the image is always degraded by blur and noise. Besides, the pressure on both storage and transmission gives rise to the need of image compression. We apply 2-D Discrete Wavelet Transform (DWT) to C-scan 2-D images to realize flaw enhancement and image compression, taking advantage of DWT scale and orientation selectivity. The Wavelet coefficient thresholding and scalar quantization are employed respectively. Furthermore, we realize the unification of flaw enhancement and image compression in one process. The reconstructed image from the compressed data gives a clearer interpretation of the flaws at a much smaller bit rate.
Energy Science and Technology Software Center (ESTSC)
2001-01-31
This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.
NASA Astrophysics Data System (ADS)
Mortarini, Luca; Cava, Daniela; Giostra, Umberto; Anfossi, Domenico
2016-04-01
Meandering is generally defined in terms of large variation of the wind direction due to a complex mix of motions on scales between the main turbulent eddies and the smallest mesoscale motions. There is not a general consensus on the physical causes of the motions responsible of the wind meandering during low-wind speed conditions. They include internal gravity waves, quasi-2D pancake motions, cold air drainage, solitons, vortices with either a horizontal axis or a vertical axis. In this work we present the analysis of wind and temperature data measured with two sonic anemometers in a low-wind stably stratified night observed during the Urban Turbulent Project (Torino, Italy). An original approach to estimate the meandering time scales of the wind velocity and temperature using two complementary methodologies is proposed. In the literature the meandering time-scale is evaluated fitting the Eulerian auto-correlation functions of the wind velocity with an oscillating theoretical behaviour on hourly datasets. First we extend this method considering the dependence of the time-scale on the dataset length considering longer datasets (1, 2, 3, 4 hours) and then we compare these results with a wavelet analysis. The continuous wavelet transform based on the Morlet basis is used to detect and characterize the time-scale of the wavelike oscillations both in the wind velocity and in the temperature signals. Moreover cross-wavelet spectra are used to identify the nature of the wavy patterns in order to discriminate the presence of gravity waves. The wavelet analysis corroborates the results obtained with the auto-correlation functions and opens new promising perspectives for the study of the meandering phenomenon.
Embedded morphological dilation coding for 2D and 3D images
NASA Astrophysics Data System (ADS)
Lazzaroni, Fabio; Signoroni, Alberto; Leonardi, Riccardo
2002-01-01
Current wavelet-based image coders obtain high performance thanks to the identification and the exploitation of the statistical properties of natural images in the transformed domain. Zerotree-based algorithms, as Embedded Zerotree Wavelets (EZW) and Set Partitioning In Hierarchical Trees (SPIHT), offer high Rate-Distortion (RD) coding performance and low computational complexity by exploiting statistical dependencies among insignificant coefficients on hierarchical subband structures. Another possible approach tries to predict the clusters of significant coefficients by means of some form of morphological dilation. An example of a morphology-based coder is the Significance-Linked Connected Component Analysis (SLCCA) that has shown performance which are comparable to the zerotree-based coders but is not embedded. A new embedded bit-plane coder is proposed here based on morphological dilation of significant coefficients and context based arithmetic coding. The algorithm is able to exploit both intra-band and inter-band statistical dependencies among wavelet significant coefficients. Moreover, the same approach is used both for two and three-dimensional wavelet-based image compression. Finally we the algorithms are tested on some 2D images and on a medical volume, by comparing the RD results to those obtained with the state-of-the-art wavelet-based coders.
Nanoimprint lithography: 2D or not 2D? A review
NASA Astrophysics Data System (ADS)
Schift, Helmut
2015-11-01
Nanoimprint lithography (NIL) is more than a planar high-end technology for the patterning of wafer-like substrates. It is essentially a 3D process, because it replicates various stamp topographies by 3D displacement of material and takes advantage of the bending of stamps while the mold cavities are filled. But at the same time, it keeps all assets of a 2D technique being able to pattern thin masking layers like in photon- and electron-based traditional lithography. This review reports about 20 years of development of replication techniques at Paul Scherrer Institut, with a focus on 3D aspects of molding, which enable NIL to stay 2D, but at the same time enable 3D applications which are "more than Moore." As an example, the manufacturing of a demonstrator for backlighting applications based on thermally activated selective topography equilibration will be presented. This technique allows generating almost arbitrary sloped, convex and concave profiles in the same polymer film with dimensions in micro- and nanometer scale.
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
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.
Discrete wavelet analysis of power system transients
Wilkinson, W.A.; Cox, M.D.
1996-11-01
Wavelet analysis is a new method for studying power system transients. Through wavelet analysis, transients are decomposed into a series of wavelet components, each of which is a time-domain signal that covers a specific octave frequency band. This paper presents the basic ideas of discrete wavelet analysis. A variety of actual and simulated transient signals are then analyzed using the discrete wavelet transform that help demonstrate the power of wavelet analysis.
Perceptually Lossless Wavelet Compression
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
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 is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. 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(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose 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.
Zahra, Noor e; Sevindir, Huliya A.; Aslan, Zafar; Siddiqi, A. H.
2012-07-17
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.
NASA Astrophysics Data System (ADS)
Zahra, Noor e.; Sevindir, Huliya A.; Aslan, Zafar; 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.
2D superconductivity by ionic gating
NASA Astrophysics Data System (ADS)
Iwasa, Yoshi
2D superconductivity is attracting a renewed interest due to the discoveries of new highly crystalline 2D superconductors in the past decade. Superconductivity at the oxide interfaces triggered by LaAlO3/SrTiO3 has become one of the promising routes for creation of new 2D superconductors. Also, the MBE grown metallic monolayers including FeSe are also offering a new platform of 2D superconductors. In the last two years, there appear a variety of monolayer/bilayer superconductors fabricated by CVD or mechanical exfoliation. Among these, electric field induced superconductivity by electric double layer transistor (EDLT) is a unique platform of 2D superconductivity, because of its ability of high density charge accumulation, and also because of the versatility in terms of materials, stemming from oxides to organics and layered chalcogenides. In this presentation, the following issues of electric filed induced superconductivity will be addressed; (1) Tunable carrier density, (2) Weak pinning, (3) Absence of inversion symmetry. (1) Since the sheet carrier density is quasi-continuously tunable from 0 to the order of 1014 cm-2, one is able to establish an electronic phase diagram of superconductivity, which will be compared with that of bulk superconductors. (2) The thickness of superconductivity can be estimated as 2 - 10 nm, dependent on materials, and is much smaller than the in-plane coherence length. Such a thin but low resistance at normal state results in extremely weak pinning beyond the dirty Boson model in the amorphous metallic films. (3) Due to the electric filed, the inversion symmetry is inherently broken in EDLT. This feature appears in the enhancement of Pauli limit of the upper critical field for the in-plane magnetic fields. In transition metal dichalcogenide with a substantial spin-orbit interactions, we were able to confirm the stabilization of Cooper pair due to its spin-valley locking. This work has been supported by Grant-in-Aid for Specially
Rodriguez-Hernandez, Miguel A; Gomez-Sacristan, Angel; Sempere-Payá, Víctor M
2016-04-29
Ultrasound diagnosis is a widely used medical tool. Among the various ultrasound techniques, ultrasonic imaging is particularly relevant. This paper presents an improvement to a two-dimensional (2D) ultrasonic system using measurements taken from perpendicular planes, where digital signal processing techniques are used to combine one-dimensional (1D) A-scans were acquired by individual transducers in arrays located in perpendicular planes. An algorithm used to combine measurements is improved based on the wavelet transform, which includes a denoising step during the 2D representation generation process. The inclusion of this new denoising stage generates higher quality 2D representations with a reduced level of speckling. The paper includes different 2D representations obtained from noisy A-scans and compares the improvements obtained by including the denoising stage. PMID:27163318
Big data extraction with adaptive wavelet analysis (Presentation Video)
NASA Astrophysics Data System (ADS)
Qu, Hongya; Chen, Genda; Ni, Yiqing
2015-04-01
Nondestructive evaluation and sensing technology have been increasingly applied to characterize material properties and detect local damage in structures. More often than not, they generate images or data strings that are difficult to see any physical features without novel data extraction techniques. In the literature, popular data analysis techniques include Short-time Fourier Transform, Wavelet Transform, and Hilbert Transform for time efficiency and adaptive recognition. In this study, a new data analysis technique is proposed and developed by introducing an adaptive central frequency of the continuous Morlet wavelet transform so that both high frequency and time resolution can be maintained in a time-frequency window of interest. The new analysis technique is referred to as Adaptive Wavelet Analysis (AWA). This paper will be organized in several sections. In the first section, finite time-frequency resolution limitations in the traditional wavelet transform are introduced. Such limitations would greatly distort the transformed signals with a significant frequency variation with time. In the second section, Short Time Wavelet Transform (STWT), similar to Short Time Fourier Transform (STFT), is defined and developed to overcome such shortcoming of the traditional wavelet transform. In the third section, by utilizing the STWT and a time-variant central frequency of the Morlet wavelet, AWA can adapt the time-frequency resolution requirement to the signal variation over time. Finally, the advantage of the proposed AWA is demonstrated in Section 4 with a ground penetrating radar (GPR) image from a bridge deck, an analytical chirp signal with a large range sinusoidal frequency change over time, the train-induced acceleration responses of the Tsing-Ma Suspension Bridge in Hong Kong, China. The performance of the proposed AWA will be compared with the STFT and traditional wavelet transform.
Data compression by wavelet transforms
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1992-01-01
A wavelet transform algorithm is applied to image compression. It is observed that the algorithm does not suffer from the blockiness characteristic of the DCT-based algorithms at compression ratios exceeding 25:1, but the edges do not appear as sharp as they do with the latter method. Some suggestions for the improved performance of the wavelet transform method are presented.
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.
Entropy-based optimization of wavelet spatial filters.
Farina, Darino; Kamavuako, Ernest Nlandu; Wu, Jian; Naddeo, Francesco
2008-03-01
A new class of spatial filters for surface electromyographic (EMG) signal detection is proposed. These filters are based on the 2-D spatial wavelet decomposition of the surface EMG recorded with a grid of electrodes and inverse transformation after zeroing a subset of the transformation coefficients. The filter transfer function depends on the selected mother wavelet in the two spatial directions. Wavelet parameterization is proposed with the aim of signal-based optimization of the transfer function of the spatial filter. The optimization criterion was the minimization of the entropy of the time samples of the output signal. The optimized spatial filter is linear and space invariant. In simulated and experimental recordings, the optimized wavelet filter showed increased selectivity with respect to previously proposed filters. For example, in simulation, the ratio between the peak-to-peak amplitude of action potentials generated by motor units 20 degrees apart in the transversal direction was 8.58% (with monopolar recording), 2.47% (double differential), 2.59% (normal double differential), and 0.47% (optimized wavelet filter). In experimental recordings, the duration of the detected action potentials decreased from (mean +/- SD) 6.9 +/- 0.3 ms (monopolar recording), to 4.5 +/- 0.2 ms (normal double differential), 3.7 +/- 0.2 (double differential), and 3.0 +/- 0.1 ms (optimized wavelet filter). In conclusion, the new class of spatial filters with the proposed signal-based optimization of the transfer function allows better discrimination of individual motor unit activities in surface EMG recordings than it was previously possible. PMID:18334382
Resolution enhancement of composite spectra using wavelet-based derivative spectrometry.
Kharintsev, S S; Kamalova, D I; Salakhov, M Kh; Sevastianov, A A
2005-01-01
An approach based on the using of the continuous wavelet transform (CWT) in derivative spectrometry (DS) is considered. Within the framework of the approach we develop a numerical differentiation algorithm with continuous wavelets for improving resolution of composite spectra. The wavelet-based derivative spectrometry (WDS) method results in best contrast in differential curves compared to the conventional derivative spectrometry method. A main advantage is that, as opposed to DS, WDS gives stable estimations of derivative in the wavelet domain without using the regularization. A wavelet shape and the information redundancy are of the greatest importance when the continuous wavelet transform is used. As an appropriate wavelet we offer to utilize the nth derivative of a component with a priori known shape. The energy distribution into scales allows one to determine a unique wavelet projection and in that way to avoid the information redundancy. A comparative study of WDS and DS with the statistical regularization method (SRM) is made; in particular, limits of applicability of these are given. Examples of the application of both DS and WDS for improving resolution of synthetic composite bands and real-world composite ones coming from molecular spectroscopy are given. PMID:15556433
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Wavelets can provide a basis set in which the basis functions are constructed by dilating and translating a fixed function known as the mother wavelet. The mother wavelet can be seen as a high pass filter in the frequency domain. The process of dilating and expanding this high-pass filter can be seen as altering the frequency range that is 'passed' or detected. The process of translation moves this high-pass filter throughout the domain, thereby providing a mechanism to detect the frequencies or scales of information at every location. This is exactly the type of information that is needed for effective grid generation. This paper provides motivation to use wavelets for grid generation in addition to providing the final product: source code for wavelet-based grid generation.
Wavelet compression of medical imagery.
Reiter, E
1996-01-01
Wavelet compression is a transform-based compression technique recently shown to provide diagnostic-quality images at compression ratios as great as 30:1. Based on a recently developed field of applied mathematics, wavelet compression has found success in compression applications from digital fingerprints to seismic data. The underlying strength of the method is attributable in large part to the efficient representation of image data by the wavelet transform. This efficient or sparse representation forms the basis for high-quality image compression by providing subsequent steps of the compression scheme with data likely to result in long runs of zero. These long runs of zero in turn compress very efficiently, allowing wavelet compression to deliver substantially better performance than existing Fourier-based methods. Although the lack of standardization has historically been an impediment to widespread adoption of wavelet compression, this situation may begin to change as the operational benefits of the technology become better known. PMID:10165355
A generalized wavelet extrema representation
Lu, Jian; Lades, M.
1995-10-01
The wavelet extrema representation originated by Stephane Mallat is a unique framework for low-level and intermediate-level (feature) processing. In this paper, we present a new form of wavelet extrema representation generalizing Mallat`s original work. The generalized wavelet extrema representation is a feature-based multiscale representation. For a particular choice of wavelet, our scheme can be interpreted as representing a signal or image by its edges, and peaks and valleys at multiple scales. Such a representation is shown to be stable -- the original signal or image can be reconstructed with very good quality. It is further shown that a signal or image can be modeled as piecewise monotonic, with all turning points between monotonic segments given by the wavelet extrema. A new projection operator is introduced to enforce piecewise inonotonicity of a signal in its reconstruction. This leads to an enhancement to previously developed algorithms in preventing artifacts in reconstructed signal.
Fan, Hong-Yi; Lu, Hai-Liang
2007-03-01
The Einstein-Podolsky-Rosen entangled state representation is applied to studying the admissibility condition of mother wavelets for complex wavelet transforms, which leads to a family of new mother wavelets. Mother wavelets thus are classified as the Hermite-Gaussian type for real wavelet transforms and the Laguerre-Gaussian type for the complex case. PMID:17392919
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 and spacetime squeeze
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.; Noz, Marilyn E.
1993-01-01
It is shown that the wavelet is the natural language for the Lorentz covariant description of localized light waves. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta(t))(Delta(w)) is approximately 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.
Classification of FTIR cancer data using wavelets and BPNN
NASA Astrophysics Data System (ADS)
Cheng, Cungui; Tian, Yumei; Zhang, Changjiang
2007-11-01
In this paper, a feature extracting method based on wavelets for horizontal attenuated total reflectance Fourier transform infrared spectroscopy (HATR-FTIR) cancer data analysis and classification using artificial neural network trained with back-propagation algorithm is presented. 168 Spectra were collected from 84 pairs of fresh normal and abnormal lung tissue's samples. After preprocessing, 12 features were extracted with continuous wavelet analysis. Based on BPNN classification, all spectra were classified into two categories : normal or abnormal. The accuracy of identifying normal, early carcinoma, and advanced carcinoma were 100%, 90% and 100% respectively. This result indicated that FTIR with continuous wavelet transform (CWT) and the back-propagation neural network (BPNN) could effectively and easily diagnose lung cancer in its early stages.
Time sequence image analysis of positron emission tomography using wavelet transformation.
Hsu, Chih-Yu; Lai, Yeong-Lin; Chen, Chih-Cheng; Lee, Yu-Tzu; Tseng, Kuo-Kun; Lai, Yeong-Kang; Zheng, Chun-Yi; Jheng, Huai-Cian
2015-01-01
This paper presents the time sequence image analysis technique of positron emission tomography (PET) using a wavelet transformation method. The abdominal cavity of a person taking [18F]Fluoro-2-deoxy-2-D-glucose (18F-FDG) was scanned by the dynamic PET. The organ selection with dynamic PET images was conducted by the wavelet transformation to implement automatic selection of the region of interest (ROI). The image segmentation was carried out by the processes of sampling, wavelet transformation, erosion, dilation, and superimposition. Wavelet constructed image (WCI) contours were created by sampling 512 images from 1960 consecutive dynamic sequence PET images. The image segmentation technology developed can help doctors automatically select ROI, accurately identify lesion locations of organs, and thus effectively reduce human operation time and errors. PMID:26578275
High-order wavelet reconstruction/differentiation filters and Gibbs phenomena
NASA Astrophysics Data System (ADS)
Lombardini, Richard; Acevedo, Ramiro; Kuczala, Alexander; Keys, Kerry; Goodrich, Carl; Johnson, Bruce
2016-03-01
We have developed an efficient method to accurately represent 1D or 2D, smooth or discontinuous, solutions to partial differential equations (PDE's), such as Schrodinger or Maxwell's equations, in an orthogonal Daubechies wavelet basis. This is a crucial step in the future development of a wavelet method that solves these PDE's. There are two main developments from this research. First, a reconstruction transform for smooth functions, discovered in previous works [Keinert and Kwon (1997) and Neelov and Goedecker (2006)], is generalized in order to develop a systematic way of tuning its error. This transform converts the wavelet basis representation back to the actual point values of the function. Since this reconstruction can far exceed the wavelet approximation order, it is shown that shorter wavelets can be used while maintaining a high-order accuracy resulting in an increase of computational efficiency. Second, a new ``truncated'' reconstruction transform is developed, using pieces of wavelets, or ``tail functions'', which can be applied to discontinuous functions. Not only does it avoid the wavelet Gibbs phenomenon, but also maintains a tunable accuracy similar to the smooth function case.
An Introduction to Wavelet Theory and Analysis
Miner, N.E.
1998-10-01
This report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides tiormation about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet amdysis algorithms. The most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelet transforms for signal reconstruction are presented. This report is intended to be approachable by non- mathematicians, although a basic understanding of engineering mathematics is necessary.
Multiscale peak detection in wavelet space.
Zhang, Zhi-Min; Tong, Xia; Peng, Ying; Ma, Pan; Zhang, Ming-Jin; Lu, Hong-Mei; Chen, Xiao-Qing; Liang, Yi-Zeng
2015-12-01
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 . PMID:26514234
Hyperspectral imaging with wavelet transform for classification of colon tissue biopsy samples
NASA Astrophysics Data System (ADS)
Masood, Khalid
2008-08-01
Automatic classification of medical images is a part of our computerised medical imaging programme to support the pathologists in their diagnosis. Hyperspectral data has found its applications in medical imagery. Its usage is increasing significantly in biopsy analysis of medical images. In this paper, we present a histopathological analysis for the classification of colon biopsy samples into benign and malignant classes. The proposed study is based on comparison between 3D spectral/spatial analysis and 2D spatial analysis. Wavelet textural features in the wavelet domain are used in both these approaches for classification of colon biopsy samples. Experimental results indicate that the incorporation of wavelet textural features using a support vector machine, in 2D spatial analysis, achieve best classification accuracy.
Wavelet networks for face processing
NASA Astrophysics Data System (ADS)
Krüger, V.; Sommer, G.
2002-06-01
Wavelet networks (WNs) were introduced in 1992 as a combination of artificial neural radial basis function (RBF) networks and wavelet decomposition. Since then, however, WNs have received only a little attention. We believe that the potential of WNs has been generally underestimated. WNs have the advantage that the wavelet coefficients are directly related to the image data through the wavelet transform. In addition, the parameters of the wavelets in the WNs are subject to optimization, which results in a direct relation between the represented function and the optimized wavelets, leading to considerable data reduction (thus making subsequent algorithms much more efficient) as well as to wavelets that can be used as an optimized filter bank. In our study we analyze some WN properties and highlight their advantages for object representation purposes. We then present a series of results of experiments in which we used WNs for face tracking. We exploit the efficiency that is due to data reduction for face recognition and face-pose estimation by applying the optimized-filter-bank principle of the WNs.
Resnikoff, H.L. )
1993-01-01
The theory of compactly supported wavelets is now 4 yr old. In that short period, it has stimulated significant research in pure mathematics; has been the source of new numerical methods for the solution of nonlinear partial differential equations, including Navier-Stokes; and has been applied to digital signal-processing problems, ranging from signal detection and classification to signal compression for speech, audio, images, seismic signals, and sonar. Wavelet channel coding has even been proposed for code division multiple access digital telephony. In each of these applications, prototype wavelet solutions have proved to be competitive with established methods, and in many cases they are already superior.
Peak finding using biorthogonal wavelets
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 much better than the FBI wavelets.
Generalized orthogonal wavelet phase reconstruction.
Axtell, Travis W; Cristi, Roberto
2013-05-01
Phase reconstruction is used for feedback control in adaptive optics systems. To achieve performance metrics for high actuator density or with limited processing capabilities on spacecraft, a wavelet signal processing technique is advantageous. Previous derivations of this technique have been limited to the Haar wavelet. This paper derives the relationship and algorithms to reconstruct phase with O(n) computational complexity for wavelets with the orthogonal property. This has additional benefits for performance with noise in the measurements. We also provide details on how to handle the boundary condition for telescope apertures. PMID:23695316
Electroencephalography data analysis by using discrete wavelet packet transform
NASA Astrophysics Data System (ADS)
Karim, Samsul Ariffin Abdul; Ismail, Mohd Tahir; Hasan, Mohammad Khatim; Sulaiman, Jumat; Muthuvalu, Mohana Sundaram; Janier Josefina, B.
2015-05-01
Electroencephalography (EEG) is the electrical activity generated by the movement of neurons in the brain. It is categorized into delta waves, theta, alpha, beta and gamma. These waves exist in a different frequency band. This paper is a continuation of our previous research. EEG data will be decomposed using Discrete Wavelet Packet Transform (DWPT). Daubechies wavelets 10 (D10) will be used as the basic functions for research purposes. From the main results, it is clear that the DWPT able to characterize the EEG signal corresponding to each wave at a specific frequency. Furthermore, the numerical results obtained better than the results using DWT. Statistical analysis support our main findings.
Adaptive wavelet-based recognition of oscillatory patterns on electroencephalograms
NASA Astrophysics Data System (ADS)
Nazimov, Alexey I.; Pavlov, Alexey N.; Hramov, Alexander E.; Grubov, Vadim V.; Koronovskii, Alexey A.; Sitnikova, Evgenija Y.
2013-02-01
The problem of automatic recognition of specific oscillatory patterns on electroencephalograms (EEG) is addressed using the continuous wavelet-transform (CWT). A possibility of improving the quality of recognition by optimizing the choice of CWT parameters is discussed. An adaptive approach is proposed to identify sleep spindles (SS) and spike wave discharges (SWD) that assumes automatic selection of CWT-parameters reflecting the most informative features of the analyzed time-frequency structures. Advantages of the proposed technique over the standard wavelet-based approaches are considered.
Design of Steerable Wavelets to Detect Multifold Junctions.
Püspöki, Zsuzsanna; Uhlmann, Virginie; Vonesch, Cédric; Unser, Michael
2016-02-01
We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern analysis. The goal of this paper is to build optimal junction detectors based on 2D steerable wavelets that are polar-separable in the Fourier domain. The approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions. The backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix. We are able to detect M -fold junctions in different scales and orientations. We provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm. PMID:26685237
Birdsong Denoising Using Wavelets.
Priyadarshani, Nirosha; Marsland, Stephen; Castro, Isabel; Punchihewa, Amal
2016-01-01
Automatic recording of birdsong is becoming the preferred way to monitor and quantify bird populations worldwide. Programmable recorders allow recordings to be obtained at all times of day and year for extended periods of time. Consequently, there is a critical need for robust automated birdsong recognition. One prominent obstacle to achieving this is low signal to noise ratio in unattended recordings. Field recordings are often very noisy: birdsong is only one component in a recording, which also includes noise from the environment (such as wind and rain), other animals (including insects), and human-related activities, as well as noise from the recorder itself. We describe a method of denoising using a combination of the wavelet packet decomposition and band-pass or low-pass filtering, and present experiments that demonstrate an order of magnitude improvement in noise reduction over natural noisy bird recordings. PMID:26812391
Birdsong Denoising Using Wavelets
Priyadarshani, Nirosha; Marsland, Stephen; Castro, Isabel; Punchihewa, Amal
2016-01-01
Automatic recording of birdsong is becoming the preferred way to monitor and quantify bird populations worldwide. Programmable recorders allow recordings to be obtained at all times of day and year for extended periods of time. Consequently, there is a critical need for robust automated birdsong recognition. One prominent obstacle to achieving this is low signal to noise ratio in unattended recordings. Field recordings are often very noisy: birdsong is only one component in a recording, which also includes noise from the environment (such as wind and rain), other animals (including insects), and human-related activities, as well as noise from the recorder itself. We describe a method of denoising using a combination of the wavelet packet decomposition and band-pass or low-pass filtering, and present experiments that demonstrate an order of magnitude improvement in noise reduction over natural noisy bird recordings. PMID:26812391
NKG2D ligands as therapeutic targets
Spear, Paul; Wu, Ming-Ru; Sentman, Marie-Louise; Sentman, Charles L.
2013-01-01
The Natural Killer Group 2D (NKG2D) receptor plays an important role in protecting the host from infections and cancer. By recognizing ligands induced on infected or tumor cells, NKG2D modulates lymphocyte activation and promotes immunity to eliminate ligand-expressing cells. Because these ligands are not widely expressed on healthy adult tissue, NKG2D ligands may present a useful target for immunotherapeutic approaches in cancer. Novel therapies targeting NKG2D ligands for the treatment of cancer have shown preclinical success and are poised to enter into clinical trials. In this review, the NKG2D receptor and its ligands are discussed in the context of cancer, infection, and autoimmunity. In addition, therapies targeting NKG2D ligands in cancer are also reviewed. PMID:23833565
Wavelet theory and its applications
Faber, V.; Bradley, JJ.; Brislawn, C.; Dougherty, R.; Hawrylycz, M.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We investigated the theory of wavelet transforms and their relation to Laboratory applications. The investigators have had considerable success in the past applying wavelet techniques to the numerical solution of optimal control problems for distributed- parameter systems, nonlinear signal estimation, and compression of digital imagery and multidimensional data. Wavelet theory involves ideas from the fields of harmonic analysis, numerical linear algebra, digital signal processing, approximation theory, and numerical analysis, and the new computational tools arising from wavelet theory are proving to be ideal for many Laboratory applications. 10 refs.
A wavelet phase filter for emission tomography
Olsen, E.T.; Lin, B.
1995-07-01
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.
A signal invariant wavelet function selection algorithm.
Garg, Girisha
2016-04-01
This paper addresses the problem of mother wavelet selection for wavelet signal processing in feature extraction and pattern recognition. The problem is formulated as an optimization criterion, where a wavelet library is defined using a set of parameters to find the best mother wavelet function. For estimating the fitness function, adopted to evaluate the performance of the wavelet function, analysis of variance is used. Genetic algorithm is exploited to optimize the determination of the best mother wavelet function. For experimental evaluation, solutions for best mother wavelet selection are evaluated on various biomedical signal classification problems, where the solutions of the proposed algorithm are assessed and compared with manual hit-and-trial methods. The results show that the solutions of automated mother wavelet selection algorithm are consistent with the manual selection of wavelet functions. The algorithm is found to be invariant to the type of signals used for classification. PMID:26253283
Semi-orthogonal wavelets for elliptic variational problems
Hardin, D.P.; Roach, D.W.
1998-04-01
In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this basis leads to robust scalable Galerkin discretizations of the model problem which remain well-conditioned independent of {epsilon}, L, and the refinement level K.
Heart Disease Detection Using Wavelets
NASA Astrophysics Data System (ADS)
González S., A.; Acosta P., J. L.; Sandoval M., M.
2004-09-01
We develop a wavelet based method to obtain standardized gray-scale chart of both healthy hearts and of hearts suffering left ventricular hypertrophy. The hypothesis that early bad functioning of heart can be detected must be tested by comparing the wavelet analysis of the corresponding ECD with the limit cases. Several important parameters shall be taken into account such as age, sex and electrolytic changes.
Low-Oscillation Complex Wavelets
NASA Astrophysics Data System (ADS)
ADDISON, P. S.; WATSON, J. N.; FENG, T.
2002-07-01
In this paper we explore the use of two low-oscillation complex wavelets—Mexican hat and Morlet—as powerful feature detection tools for data analysis. These wavelets, which have been largely ignored to date in the scientific literature, allow for a decomposition which is more “temporal than spectral” in wavelet space. This is shown to be useful for the detection of small amplitude, short duration signal features which are masked by much larger fluctuations. Wavelet transform-based methods employing these wavelets (based on both wavelet ridges and modulus maxima) are developed and applied to sonic echo NDT signals used for the analysis of structural elements. A new mobility scalogram and associated reflectogram is defined for analysis of impulse response characteristics of structural elements and a novel signal compression technique is described in which the pertinent signal information is contained within a few modulus maxima coefficients. As an example of its usefulness, the signal compression method is employed as a pre-processor for a neural network classifier. The authors believe that low oscillation complex wavelets have wide applicability to other practical signal analysis problems. Their possible application to two such problems is discussed briefly—the interrogation of arrhythmic ECG signals and the detection and characterization of coherent structures in turbulent flow fields.
Wavelet analysis in virtual colonoscopy
NASA Astrophysics Data System (ADS)
Greenblum, Sharon; Li, Jiang; Huang, Adam; Summers, Ronald M.
2006-03-01
The computed tomographic colonography (CTC) computer aided detection (CAD) program is a new method in development to detect colon polyps in virtual colonoscopy. While high sensitivity is consistently achieved, additional features are desired to increase specificity. In this paper, a wavelet analysis was applied to CTCCAD outputs in an attempt to filter out false positive detections. 52 CTCCAD detection images were obtained using a screen capture application. 26 of these images were real polyps, confirmed by optical colonoscopy and 26 were false positive detections. A discrete wavelet transform of each image was computed with the MATLAB wavelet toolbox using the Haar wavelet at levels 1-5 in the horizontal, vertical and diagonal directions. From the resulting wavelet coefficients at levels 1-3 for all directions, a 72 feature vector was obtained for each image, consisting of descriptive statistics such as mean, variance, skew, and kurtosis at each level and orientation, as well as error statistics based on a linear predictor of neighboring wavelet coefficients. The vectors for each of the 52 images were then run through a support vector machine (SVM) classifier using ten-fold cross-validation training to determine its efficiency in distinguishing polyps from false positives. The SVM results showed 100% sensitivity and 51% specificity in correctly identifying the status of detections. If this technique were added to the filtering process of the CTCCAD polyp detection scheme, the number of false positive results could be reduced significantly.
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.
Spherical wavelet transform: linking global seismic tomography and imaging
NASA Astrophysics Data System (ADS)
Pan, J.
2001-12-01
Each year, numerous seismic tomographic images are published based on either new parameterization, damping schemes or datasets. Though people agree generally on the longer- wavelength seismic structures, large discrepencies still exist among various models. Normally the data is noisy, thus the inverse problem is often ill-conditioned. Sampling rate may be enough to resolve for long-wavelength structures when we parameterize the earth to a low harmonic order. However, higher order signals (slabs, plume-like structures, and local seismic velocity anomalies (SVA)) on a global scale remain under-sampled. Finer discretization of the model space increases the problem size dramatically but does not alleviate the nature of the problem. The main challenge thus is to find an efficient representation of the model space to solve for the lower- and higher- degree SVAs simultaneously. Spherical wavelets are a good choice because of their compact support (locaized) in both spatial and frequency domains. If SVAs can be viewed as an image, they consist of smooth-varying signals superpositioned by small-scale local changes and can be compressed greatly and represented better using spherical wavelets. By mapping the model parameters into a nested multi-resolution analysis (MRA) space, the signals become comparable in size therefore stable solutions can be achieved at every level of the resolution without introducing subjective damping. The efficiency of using wavelets and MRA to denoise and compress signals can be used to reduce the problem size and eliminate effects of noisy data. This new algorithm can achieve better resolving power for 2D and 3D seismic tomography, by linking image processing with inverse theory. Advances in spherical wavelets enable the introduction of wavelet analysis and a new parameterization of MRA into global tomography studies. In this paper, we present the new inversion method based on spherical wavelet transform. An application to 2D surface wave
Tests for Wavelets as a Basis Set
NASA Astrophysics Data System (ADS)
Baker, Thomas; Evenbly, Glen; White, Steven
A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We develop metrics to evaluate wavelets for general problems on test one-dimensional systems. The goal is to eventually use a wavelet basis in electronic structure calculations. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets. We also evaluate a new type of orthogonal wavelet with dilation factor three which is both symmetric and compact in real space. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC008696.
Compression of 3D integral images using wavelet decomposition
NASA Astrophysics Data System (ADS)
Mazri, Meriem; Aggoun, Amar
2003-06-01
This paper presents a wavelet-based lossy compression technique for unidirectional 3D integral images (UII). The method requires the extraction of different viewpoint images from the integral image. A single viewpoint image is constructed by extracting one pixel from each microlens, then each viewpoint image is decomposed using a Two Dimensional Discrete Wavelet Transform (2D-DWT). The resulting array of coefficients contains several frequency bands. The lower frequency bands of the viewpoint images are assembled and compressed using a 3 Dimensional Discrete Cosine Transform (3D-DCT) followed by Huffman coding. This will achieve decorrelation within and between 2D low frequency bands from the different viewpoint images. The remaining higher frequency bands are Arithmetic coded. After decoding and decompression of the viewpoint images using an inverse 3D-DCT and an inverse 2D-DWT, each pixel from every reconstructed viewpoint image is put back into its original position within the microlens to reconstruct the whole 3D integral image. Simulations were performed on a set of four different grey level 3D UII using a uniform scalar quantizer with deadzone. The results for the average of the four UII intensity distributions are presented and compared with previous use of 3D-DCT scheme. It was found that the algorithm achieves better rate-distortion performance, with respect to compression ratio and image quality at very low bit rates.
Perspectives for spintronics in 2D materials
NASA Astrophysics Data System (ADS)
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Sabyasachi; Das, Nandan K.; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.
2014-02-01
The objective of the present work is to diagnose pre-cancer by wavelet transform and multi-fractal de-trended fluctuation analysis of DIC images of normal and different grades of cancer tissues. Our DIC imaging and fluctuation analysis methods (Discrete and continuous wavelet transform, MFDFA) confirm the ability to diagnose and detect the early stage of cancer in cervical tissue.
Group-normalized wavelet packet signal processing
NASA Astrophysics Data System (ADS)
Shi, Zhuoer; Bao, Zheng
1997-04-01
Since the traditional wavelet and wavelet packet coefficients do not exactly represent the strength of signal components at the very time(space)-frequency tilling, group- normalized wavelet packet transform (GNWPT), is presented for nonlinear signal filtering and extraction from the clutter or noise, together with the space(time)-frequency masking technique. The extended F-entropy improves the performance of GNWPT. For perception-based image, soft-logic masking is emphasized to remove the aliasing with edge preserved. Lawton's method for complex valued wavelets construction is extended to generate the complex valued compactly supported wavelet packets for radar signal extraction. This kind of wavelet packets are symmetry and unitary orthogonal. Well-defined wavelet packets are chosen by the analysis remarks on their time-frequency characteristics. For real valued signal processing, such as images and ECG signal, the compactly supported spline or bi- orthogonal wavelet packets are preferred for perfect de- noising and filtering qualities.
Wavelet analysis of Snow course data within the Sierra Nevada Mountains
NASA Astrophysics Data System (ADS)
Rios, T.; Dracup, J. A.
2003-12-01
In recent years, an analytical method known as wavelet analysis has received increasing applications in geophysical fields (Foufoula-Georgiou and Kumar 1994). Wavelet analysis can be used to identify the time and frequency regime in data while still maintaining the time coordinate. By applying the wavelet analysis method to the Mount Shasta snow course for the time period from 1937-1997 using the continuous 1-D wavelet toolbox in MATLAB, we found that several frequency regimes are present within the signal. The inter-annual noise dominates the frequency regime below the seven-year scale, but there is a relatively consistent 9-13 year oscillation that is present within the snow data. This frequency regime is also observed to shift to lower scales as the time series progresses, possibly indicating a shift in the climate variability due to climate change. In addition, analyses of the depth and the water content data exhibit nearly identical wavelet images. We are currently in the process of identifying other climate variables that may exhibit similar periodicity with the continuous 1-D wavelet analysis, such as the PDO and ENSO. Preliminary results show that by analyzing the hydrologic variables of the Sierra Nevada snowpack depth and/or water content using the wavelet method, we may be able to provide useful insights into the synergy and expression of climate change and variability within the California Sierra Nevadas.
2D Turbulence with Complicated Boundaries
NASA Astrophysics Data System (ADS)
Roullet, G.; McWilliams, J. C.
2014-12-01
We examine the consequences of lateral viscous boundary layers on the 2D turbulence that arises in domains with complicated boundaries (headlands, bays etc). The study is carried out numerically with LES. The numerics are carefully designed to ensure all global conservation laws, proper boundary conditions and a minimal range of dissipation scales. The turbulence dramatically differs from the classical bi-periodic case. Boundary layer separations lead to creation of many small vortices and act as a continuing energy source exciting the inverse cascade of energy throughout the domain. The detachments are very intermittent in time. In free decay, the final state depends on the effective numerical resolution: laminar with a single dominant vortex for low Re and turbulent with many vortices for large enough Re. After very long time, the turbulent end-state exhibits a striking tendency for the emergence of shielded vortices which then interact almost elastically. In the forced case, the boundary layers allow the turbulence to reach a statistical steady state without any artificial hypo-viscosity or other large-scale dissipation. Implications are discussed for the oceanic mesoscale and submesoscale turbulence.
Wavelet correlations in the [ital p] model
Greiner, M. Institut fuer Theoretische Physik, Justus Liebig Universitaet, 35392 Geien ); Lipa, P.; Carruthers, P. )
1995-03-01
We suggest applying the concept of wavelet transforms to the study of correlations in multiparticle physics. Both the usual correlation functions as well as the wavelet transformed ones are calculated for the [ital p] model, which is a simple but tractable random cascade model. For this model, the wavelet transform decouples correlations between fluctuations defined on different scales. The advantageous properties of factorial moments are also shared by properly defined factorial wavelet correlations.
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
Wavelet approach to accelerator problems. 2: Metaplectic wavelets
Fedorova, A.; Zeitlin, M.; Parsa, Z.
1997-05-01
This is the second part of a series of talks in which the authors present applications of wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to the orbit method and by using construction from the geometric quantization theory they construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure and corresponding polarization. The key point is a consideration of semidirect product of Heisenberg group and metaplectic group as subgroup of automorphisms group of dual to symplectic space, which consists of elements acting by affine transformations.
NASA Astrophysics Data System (ADS)
Fadili, Jalal M.; Bullmore, Edward T.
2003-11-01
Wavelet-based methods for multiple hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging (fMRI) data is investigated. In this approach, we emphasize convergence between methods of wavelet thresholding or shrinkage and the problem of multiple hypothesis testing in both classical and Bayesian contexts. Specifically, our interest will be focused on ensuring a trade off between type I probability error control and power dissipation. We describe a technique for controlling the false discovery rate at an arbitrary level of type 1 error in testing multiple wavelet coefficients generated by a 2D discrete wavelet transform (DWT) of spatial maps of {fMRI} time series statistics. We also describe and apply recursive testing methods that can be used to define a threshold unique to each level and orientation of the 2D-DWT. Bayesian methods, incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image, are also tractable. These methods are comparatively evaluated by analysis of "null" images (acquired with the subject at rest), in which case the number of positive tests should be exactly as predicted under the hull hypothesis, and an experimental dataset acquired from 5 normal volunteers during an event-related finger movement task. We show that all three wavelet-based methods of multiple hypothesis testing have good type 1 error control (the FDR method being most conservative) and generate plausible brain activation maps.
Wavelet Representation of Contour Sets
Bertram, M; Laney, D E; Duchaineau, M A; Hansen, C D; Hamann, B; Joy, K I
2001-07-19
We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.
VHDL implementation of wavelet packet transforms using SIMULINK tools
NASA Astrophysics Data System (ADS)
Shirvaikar, Mukul; Bushnaq, Tariq
2008-02-01
The wavelet transform is currently being used in many engineering fields. The real-time implementation of the Discrete Wavelet Transform (DWT) is a current area of research as it is one of the most time consuming steps in the JPEG2000 standard. The standard implements two different wavelet transforms: irreversible and reversible Daubechies. The former is a lossy transform, whereas the latter is a lossless transform. Many current JPEG2000 implementations are software-based and not efficient enough to meet real-time deadlines. Field Programmable Gate Arrays (FPGAs) are revolutionizing image and signal processing. Many major FPGA vendors like Altera and Xilinx have recently developed SIMULINK tools to support their FPGAs. These tools are intended to provide a seamless path from system-level algorithm design to FPGA implementation. In this paper, we investigate FPGA implementation of 2-D lifting-based Daubechies 9/7 and Daubechies 5/3 transforms using a Matlab/Simulink tool that generates synthesizable VHSIC Hardware Description Language (VHDL) code. The goal is to study the feasibility of this approach for real time image processing by comparing the performance of the high-level toolbox with a handwritten VHDL implementation. The hardware platform used is an Altera DE2 board with a 50MHz Cyclone II FPGA chip and the Simulink tool chosen is DSPBuilder by Altera.
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.
Light field morphing using 2D features.
Wang, Lifeng; Lin, Stephen; Lee, Seungyong; Guo, Baining; Shum, Heung-Yeung
2005-01-01
We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field. PMID:15631126
2D materials for nanophotonic devices
NASA Astrophysics Data System (ADS)
Xu, Renjing; Yang, Jiong; Zhang, Shuang; Pei, Jiajie; Lu, Yuerui
2015-12-01
Two-dimensional (2D) materials have become very important building blocks for electronic, photonic, and phononic devices. The 2D material family has four key members, including the metallic graphene, transition metal dichalcogenide (TMD) layered semiconductors, semiconducting black phosphorous, and the insulating h-BN. Owing to the strong quantum confinements and defect-free surfaces, these atomically thin layers have offered us perfect platforms to investigate the interactions among photons, electrons and phonons. The unique interactions in these 2D materials are very important for both scientific research and application engineering. In this talk, I would like to briefly summarize and highlight the key findings, opportunities and challenges in this field. Next, I will introduce/highlight our recent achievements. We demonstrated atomically thin micro-lens and gratings using 2D MoS2, which is the thinnest optical component around the world. These devices are based on our discovery that the elastic light-matter interactions in highindex 2D materials is very strong. Also, I would like to introduce a new two-dimensional material phosphorene. Phosphorene has strongly anisotropic optical response, which creates 1D excitons in a 2D system. The strong confinement in phosphorene also enables the ultra-high trion (charged exciton) binding energies, which have been successfully measured in our experiments. Finally, I will briefly talk about the potential applications of 2D materials in energy harvesting.
Inertial solvation in femtosecond 2D spectra
NASA Astrophysics Data System (ADS)
Hybl, John; Albrecht Ferro, Allison; Farrow, Darcie; Jonas, David
2001-03-01
We have used 2D Fourier transform spectroscopy to investigate polar solvation. 2D spectroscopy can reveal molecular lineshapes beneath ensemble averaged spectra and freeze molecular motions to give an undistorted picture of the microscopic dynamics of polar solvation. The transition from "inhomogeneous" to "homogeneous" 2D spectra is governed by both vibrational relaxation and solvent motion. Therefore, the time dependence of the 2D spectrum directly reflects the total response of the solvent-solute system. IR144, a cyanine dye with a dipole moment change upon electronic excitation, was used to probe inertial solvation in methanol and propylene carbonate. Since the static Stokes' shift of IR144 in each of these solvents is similar, differences in the 2D spectra result from solvation dynamics. Initial results indicate that the larger propylene carbonate responds more slowly than methanol, but appear to be inconsistent with rotational estimates of the inertial response. To disentangle intra-molecular vibrations from solvent motion, the 2D spectra of IR144 will be compared to the time-dependent 2D spectra of the structurally related nonpolar cyanine dye HDITCP.
Internal Photoemission Spectroscopy of 2-D Materials
NASA Astrophysics Data System (ADS)
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
Tomographic inversion using L1-regularization of Wavelet Coefficients
NASA Astrophysics Data System (ADS)
Loris, I.; Nolet, G.; Daubechies, I.; Dahlen, T.
2006-12-01
Like most geophysical inverse problems, the inverse problem in seismic tomography is underdetermined, or at best offers a mix of over- and underdetermined parameters. One usually regularizes the inverse problem by minimizing the norm (|m|) or roughness of the model (|∇ m| or |∇2 m|) to obtain a solution that is void of unwarranted structural detail. The notion that we seek the 'simplest' model that is in agreement with a given data set is intuitively equivalent to the notion that the model should be describable with a small number of parameters. But clearly, limiting the model to a few Fourier coefficients, or large scale blocks, does not necessarily lead to a geophysically plausible solution. We investigate if a wavelet basis can serve as a basis with enough flexibility to represent the class of models we seek. We propose a regularization method based on the assumption that the model m is sparse in a wavelet basis, meaning that it can be faithfully represented by a small number of nonzero wavelet coefficients. This allows for models that vary smoothly without sacrificing the sharp boundaries by a smoothing operator to regularize the inversion. To regularize the inversion, we minimize I= ∥ d - Am ∥2 + 2 τ ∥ w ∥1, where w is a vector of wavelet coefficients (m=Ww), τ the damping parameter, d-Am the vector of data residuals and 1 and 2 denote the ℓ1 and ℓ2 norm, respectively. the system is solved using Landweber iteration: w(n+1)= Sτ [ WATd + (I - WATAWT)w(n)], where Sτ is a soft thresholding operator (Sτ(x)=0 for |x|<τ and x ± τ elsewhere). In synthetic tests on a 2D tomographic model we show that minimizing the ℓ1 norm of a wavelet decomposition of the model leads to tomographic images that are parsimonious in the sense that they represent both smooth and sharp features well without introducing significant blurring or artifacts. The ℓ1 norm performs significantly better than an ℓ2 regularization on either the model or its wavelet
The EM Method in a Probabilistic Wavelet-Based MRI Denoising.
Martin-Fernandez, Marcos; Villullas, Sergio
2015-01-01
Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images. PMID:26089959
Multispectral image compression technology based on dual-tree discrete wavelet transform
NASA Astrophysics Data System (ADS)
Fang, Zhijun; Luo, Guihua; Liu, Zhicheng; Gan, Yun; Lu, Yu
2009-10-01
The paper proposes a combination of DCT and the Dual-Tree Discrete Wavelet Transform (DDWT) to solve the problems in multi-spectral image data storage and transmission. The proposed method not only removes spectral redundancy by1D DCT, but also removes spatial redundancy by 2D Dual-Tree Discrete Wavelet Transform. Therefore, it achieves low distortion under the conditions of high compression and high-quality reconstruction of the multi-spectral image. Tested by DCT, Haar and DDWT, the results show that the proposed method eliminates the blocking effect of wavelet and has strong visual sense and smooth image, which means the superiors with DDWT has more prominent quality of reconstruction and less noise.
The EM Method in a Probabilistic Wavelet-Based MRI Denoising
2015-01-01
Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images. PMID:26089959
Wavelets based on Hermite cubic splines
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2016-06-01
In 2000, W. Dahmen et al. designed biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet bases with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions and propose a new wavelet which leads to improved Riesz constants. Wavelets have four vanishing wavelet moments.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
2D electronic materials for army applications
NASA Astrophysics Data System (ADS)
O'Regan, Terrance; Perconti, Philip
2015-05-01
The record electronic properties achieved in monolayer graphene and related 2D materials such as molybdenum disulfide and hexagonal boron nitride show promise for revolutionary high-speed and low-power electronic devices. Heterogeneous 2D-stacked materials may create enabling technology for future communication and computation applications to meet soldier requirements. For instance, transparent, flexible and even wearable systems may become feasible. With soldier and squad level electronic power demands increasing, the Army is committed to developing and harnessing graphene-like 2D materials for compact low size-weight-and-power-cost (SWAP-C) systems. This paper will review developments in 2D electronic materials at the Army Research Laboratory over the last five years and discuss directions for future army applications.
2-d Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
A Wavelet Perspective on the Allan Variance.
Percival, Donald B
2016-04-01
The origins of the Allan variance trace back 50 years ago to two seminal papers, one by Allan (1966) and the other by Barnes (1966). Since then, the Allan variance has played a leading role in the characterization of high-performance time and frequency standards. Wavelets first arose in the early 1980s in the geophysical literature, and the discrete wavelet transform (DWT) became prominent in the late 1980s in the signal processing literature. Flandrin (1992) briefly documented a connection between the Allan variance and a wavelet transform based upon the Haar wavelet. Percival and Guttorp (1994) noted that one popular estimator of the Allan variance-the maximal overlap estimator-can be interpreted in terms of a version of the DWT now widely referred to as the maximal overlap DWT (MODWT). In particular, when the MODWT is based on the Haar wavelet, the variance of the resulting wavelet coefficients-the wavelet variance-is identical to the Allan variance when the latter is multiplied by one-half. The theory behind the wavelet variance can thus deepen our understanding of the Allan variance. In this paper, we review basic wavelet variance theory with an emphasis on the Haar-based wavelet variance and its connection to the Allan variance. We then note that estimation theory for the wavelet variance offers a means of constructing asymptotically correct confidence intervals (CIs) for the Allan variance without reverting to the common practice of specifying a power-law noise type a priori. We also review recent work on specialized estimators of the wavelet variance that are of interest when some observations are missing (gappy data) or in the presence of contamination (rogue observations or outliers). It is a simple matter to adapt these estimators to become estimators of the Allan variance. Finally we note that wavelet variances based upon wavelets other than the Haar offer interesting generalizations of the Allan variance. PMID:26529757