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1
Toda, Hiroshi, Zhong Zhang, and Takashi Imamura. "Perfect-translation-invariant variable-density complex discrete wavelet transform." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (July 2014): 1460001. http://dx.doi.org/10.1142/s0219691314600017.
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The theorems giving the conditions for discrete wavelet transforms (DWTs) to achieve perfect translation invariance (PTI) have already been proven, and based on these theorems, the dual-tree complex DWT and the complex wavelet packet transform, achieving PTI, have already been proposed. However, there is not so much flexibility in their wavelet density. In the frequency domain, the wavelet density is fixed by octave filter banks, and in the time domain, each wavelet is arrayed on a fixed coordinate, and the wavelet packet density in the frequency domain can be only designed by dividing an octave frequency band equally in linear scale, and its density in the time domain is constrained by the division number of an octave frequency band. In this paper, a novel complex DWT is proposed to create variable wavelet density in the frequency and time domains, that is, an octave frequency band can be divided into N filter banks in logarithmic scale, where N is an integer larger than or equal to 3, and in the time domain, a distance between wavelets can be varied in each level, and its transform achieves PTI.
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TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (July 2013): 1360003. http://dx.doi.org/10.1142/s0219691313600035.
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The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.
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Zhang, Jie, Xuehua Chen, Wei Jiang, Yunfei Liu, and He Xu. "Estimation of the depth-domain seismic wavelet based on velocity substitution and a generalized seismic wavelet model." GEOPHYSICS 87, no. 2 (January 24, 2022): R213—R222. http://dx.doi.org/10.1190/geo2020-0745.1.
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Depth-domain seismic wavelet estimation is the essential foundation for depth-imaged data inversion, which is increasingly used for hydrocarbon reservoir characterization in geophysical prospecting. The seismic wavelet in the depth domain stretches with increasing medium velocity and compresses with decreasing medium velocity. The commonly used convolutional model cannot be directly used to estimate depth-domain seismic wavelets due to velocity-dependent wavelet variations. We have developed a separate parameter estimation method for estimating depth-domain seismic wavelets from poststack depth-domain seismic and well-log data. Our method is based on the velocity substitution and depth-domain generalized seismic wavelet model defined by the fractional derivative and reference wavenumber. Velocity substitution allows wavelet estimation with the convolutional model in the constant-velocity depth domain. The depth-domain generalized seismic wavelet model allows for a simple workflow that estimates the depth-domain wavelet by estimating two wavelet model parameters. In addition, this simple workflow does not need to perform searches for the optimal regularization parameter and wavelet length, which are time-consuming in least-squares (LS)-based methods. The limited numerical search ranges of the two wavelet model parameters can easily be calculated using the constant phase and peak wavenumber of the depth-domain seismic data. Our method is verified using synthetic and real seismic data and further compared with LS-based methods. The results indicate that our method is effective and stable even for data with a low signal-to-noise ratio.
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Ďuriš, Viliam, Vladimir I. Semenov, and Sergey G. Chumarov. "Wavelets and digital filters designed and synthesized in the time and frequency domains." Mathematical Biosciences and Engineering 19, no. 3 (2022): 3056–68. http://dx.doi.org/10.3934/mbe.2022141.
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<abstract> <p>The relevance of the problem under study is due to the fact that the comparison is made for wavelets constructed in the time and frequency domains. The wavelets constructed in the time domain include all discrete wavelets, as well as continuous wavelets based on derivatives of the Gaussian function. This article discusses the possibility of implementing algorithms for multiscale analysis of one-dimensional and two-dimensional signals with the above-mentioned wavelets and wavelets constructed in the frequency domain. In contrast to the discrete wavelet transform (Mallat algorithm), the authors propose a multiscale analysis of images with a multiplicity of less than two in the frequency domain, that is, the scale change factor is less than 2. Despite the fact that the multiplicity of the analysis is less than 2, the signal can be represented as successive approximations, as with the use of discrete wavelet transform. Reducing the multiplicity allows you to increase the depth of decomposition, thereby increasing the accuracy of signal analysis and synthesis. At the same time, the number of decomposition levels is an order of magnitude higher compared to traditional multi-scale analysis, which is achieved by progressive scanning of the image, that is, the image is processed not by rows and columns, but by progressive scanning as a whole. The use of the fast Fourier transform reduces the conversion time by four orders of magnitude compared to direct numerical integration, and due to this, the decomposition and reconstruction time does not increase compared to the time of multiscale analysis using discrete wavelets.</p> </abstract>
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Abuhamdia, Tariq, Saied Taheri, and John Burns. "Laplace wavelet transform theory and applications." Journal of Vibration and Control 24, no. 9 (May 11, 2017): 1600–1620. http://dx.doi.org/10.1177/1077546317707103.
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This study introduces the theory of the Laplace wavelet transform (LWT). The Laplace wavelets are a generalization of the second-order under damped linear time-invariant (SOULTI) wavelets to the complex domain. This generalization produces the mother wavelet function that has been used as the Laplace pseudo wavelet or the Laplace wavelet dictionary. The study shows that the Laplace wavelet can be used to transform signals to the time-scale or time-frequency domain and can be retrieved back. The properties of the new generalization are outlined, and the characteristics of the companion wavelet transform are defined. Moreover, some similarities between the Laplace wavelet transform and the Laplace transform arise, where a relation between the Laplace wavelet transform and the Laplace transform is derived. This relation can be beneficial in evaluating the wavelet transform. The new wavelet transform has phase and magnitude, and can also be evaluated for most elementary signals. The Laplace wavelets inherit many properties from the SOULTI wavelets, and the Laplace wavelet transform inherits many properties from both the SOULTI wavelet transform and the Laplace transform. In addition, the investigation shows that both the LWT and the SOULTI wavelet transform give the particular solutions of specific related differential equations, and the particular solution of these linear time-invariant differential equations can in general be written in terms of a wavelet transform. Finally, the properties of the Laplace wavelet are verified by applications to frequency varying signals and to vibrations of mechanical systems for modes decoupling, and the results are compared with the generalized Morse and Morlet wavelets in addition to the short time Fourier transform’s results.
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KING, EMILY J. "SMOOTH PARSEVAL FRAMES FOR L2(ℝ) AND GENERALIZATIONS TO L2(ℝd)." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 06 (November 2013): 1350047. http://dx.doi.org/10.1142/s0219691313500471.
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Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L2(ℝd) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝd, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of existence of Schwartz class functions which are Parseval frame wavelets and approximate Parseval frame wavelet set wavelets does not easily generalize to higher dimensions. However, a construction of wavelet sets in [Formula: see text] which may be smoothed is presented. Finally, it is shown that a commonly used class of functions cannot be the result of convolutional smoothing of a wavelet set wavelet.
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Bansal, Rishi, and Mike Matheney. "Wavelet distortion correction due to domain conversion." GEOPHYSICS 75, no. 6 (November 2010): V77—V87. http://dx.doi.org/10.1190/1.3494081.
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Converted-wave (PS) data, when converted to PP time, develop time- and location-varying compression of the seismic wavelet due to a variable subsurface [Formula: see text] [Formula: see text]. The time-dependent compression distorts the wavelet in a seismic trace. The lack of a consistent seismic wavelet in a domain-converted PS volume can eventually lead to an erroneous joint PP/PS inversion result. Depth-converted seismic data also have wavelet distortion due to velocity-dependent wavelet stretch. A high value of seismic velocity produces more stretch in a seismic wavelet than a low value. Variable wavelet stretch renders the depth data unsuitable for attribute analysis. A filtering scheme is proposed that corrects for distortion in seismic wavelets due to domain conversions (PS to PP time and time-to-depth) of seismic data in an amplitude-preserving manner. The method uses a Fourier scaling theorem to predict the seismic wavelet in the converted domain and calculates a shaping filter for each time/depth sample that corrects for the distortion in the wavelet. The filter is applied to the domain-converted data using the method of nonstationary filtering. We provide analytical expressions for the squeeze factor [Formula: see text] that is used to predict the wavelet in the converted domain. The squeeze factor [Formula: see text] for PS to PP time conversion is a function of the subsurface [Formula: see text] whereas for PP time-to-depth conversion [Formula: see text] is dependent on subsurface P-wave velocity. After filtering, the squeezed wavelets in domain-converted PS data appear to have resulted from a constant subsurface [Formula: see text], which we denote as [Formula: see text]. Similarly, the filtered depth-converted data appear to have resulted from a constant subsurface P-wave velocity [Formula: see text].
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Ďuriš, Viliam, Sergey G. Chumarov, and Vladimir I. Semenov. "Increasing the Speed of Multiscale Signal Analysis in the Frequency Domain." Electronics 12, no. 3 (February 2, 2023): 745. http://dx.doi.org/10.3390/electronics12030745.
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In the Mallat algorithm, calculations are performed in the time domain. To speed up the signal conversion at each level, the wavelet coefficients are sequentially halved. This paper presents an algorithm for increasing the speed of multiscale signal analysis using fast Fourier transform. In this algorithm, calculations are performed in the frequency domain, which is why the authors call this algorithm multiscale analysis in the frequency domain. For each level of decomposition, the wavelet coefficients are determined from the signal and can be calculated in parallel, which reduces the conversion time. In addition, the zoom factor can be less than two. The Mallat algorithm uses non-symmetric wavelets, and to increase the accuracy of the reconstruction, large-order wavelets are obtained, which increases the transformation time. On the contrary, in our algorithm, depending on the sample length, the wavelets are symmetric and the time of the inverse wavelet transform can be faster by 6–7 orders of magnitude compared to the direct numerical calculation of the convolution. At the same time, the quality of analysis and the accuracy of signal reconstruction increase because the wavelet transform is strictly orthogonal.
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Sun, Song Zhen, and Yi Guo. "Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering." Advanced Materials Research 1079-1080 (December 2014): 878–81. http://dx.doi.org/10.4028/www.scientific.net/amr.1079-1080.878.
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It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.
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Qin, Jun, and Pengfei Sun. "Applications and Comparison of Continuous Wavelet Transforms on Analysis of A-wave Impulse Noise." Archives of Acoustics 40, no. 4 (December 1, 2015): 503–12. http://dx.doi.org/10.1515/aoa-2015-0050.
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Abstract Noise induced hearing loss (NIHL) is a serious occupational related health problem worldwide. The A-wave impulse noise could cause severe hearing loss, and characteristics of such kind of impulse noise in the joint time-frequency (T-F) domain are critical for evaluation of auditory hazard level. This study focuses on the analysis of A-wave impulse noise in the T-F domain using continual wavelet transforms. Three different wavelets, referring to Morlet, Mexican hat, and Meyer wavelets, were investigated and compared based on theoretical analysis and applications to experimental generated A-wave impulse noise signals. The underlying theory of continuous wavelet transform was given and the temporal and spectral resolutions were theoretically analyzed. The main results showed that the Mexican hat wavelet demonstrated significant advantages over the Morlet and Meyer wavelets for the characterization and analysis of the A-wave impulse noise. The results of this study provide useful information for applying wavelet transform on signal processing of the A-wave impulse noise.
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Lundsgaard, Astrid K., Hanno Klemm, and Adam J. Cherrett. "Joint Bayesian wavelet and well-path estimation in the impedance domain." GEOPHYSICS 80, no. 2 (March 1, 2015): M15—M31. http://dx.doi.org/10.1190/geo2014-0378.1.
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We addressed the problem of the well-to-seismic tie as a Bayesian inversion for the wavelet and well path in the impedance domain. The result of the joint inversion is a set of wavelets for multiple angle stacks, and a corresponding well path. The wavelet optimally links the impedance data along the well to the seismic data along the optimized well path in the seismic time domain. Starting with prior distribution for wavelet and well path, the method calculates the posterior distribution of conditioning the prior distributions with the seismic and well-log data. This is done by iteratively inverting the seismic data with the current wavelet, to obtain an impedance cube around the well. In a second step, the seismic impedances are projected onto the well path. By minimizing the misfit between the inverted seismic impedances and the impedances derived from the well log, the wavelet and well path are optimized. Comparing the well and seismic data in the impedance domain enables the method to work on short and noisy well logs. Another advantage of this method is its ability to derive wavelets for multiple angle stacks and multiple well locations simultaneously. We tested the method on synthetic and real data examples. The algorithm performed well in the synthetic examples, in which we had control over the modeling wavelet, and the wavelets derived for a real data example showed consistently good seismic-to-well ties for six angle stacks and seven wells. The main algorithm we developed was aimed to linearize the problem. We compared the posterior distribution of the linearized result with a sampling-based result in a real data example and found good agreement.
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Zhou, Guang-Dong, You-Liang Ding, and Ai-Qun Li. "Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/870420.
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Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.
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Li, Yaoguo, and Douglas W. Oldenburg. "Rapid construction of equivalent sources using wavelets." GEOPHYSICS 75, no. 3 (May 2010): L51—L59. http://dx.doi.org/10.1190/1.3378764.
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We have developed a fast algorithm for generating an equivalent source by using fast wavelet transforms based on orthonormal, compactly supported wavelets. We apply a 2D wavelet transform to each row and column of the coefficient matrix and subsequently threshold the transformed matrix to generate a sparse representation in the wavelet domain. The algorithm then uses this sparse matrix to construct the the equivalent source directly in the wavelet domain. Performing an inverse wavelet transform then yields the equivalent source in the space domain. Using upward continuation of total-field magnetic data between uneven surfaces as examples, we have compared this approach with the direct solution using the dense matrix in the space domain. We have shown that the wavelet approach can reduce the CPU time by as many as two orders of magnitude.
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Wirasaet, Damrongsak, and Samuel Paolucci. "Adaptive Wavelet Method for Incompressible Flows in Complex Domains." Journal of Fluids Engineering 127, no. 4 (April 6, 2005): 656–65. http://dx.doi.org/10.1115/1.1949650.
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An adaptive wavelet-based method provides an alternative means to refine grids according to local demands of the physical solution. One of the prominent challenges of such a method is the application to problems defined on complex domains. In the case of incompressible flow, the application to problems with complicated domains is made possible by the use of the Navier-Stokes–Brinkman equations. These equations take into account solid obstacles by adding a penalized velocity term in the momentum equation. In this study, an adaptive wavelet collocation method, based on interpolating wavelets, is first applied to a benchmark problem defined on a simple domain to demonstrate the accuracy and efficiency of the method. Then the penalty technique is used to simulate flows over obstacles. The numerical results are compared to those obtained by other computational approaches as well as to experiments.
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Li, Pu, and Yuming Fang. "A Wavelet Interpolation Galerkin Method for the Simulation of MEMS Devices under the Effect of Squeeze Film Damping." Mathematical Problems in Engineering 2010 (2010): 1–25. http://dx.doi.org/10.1155/2010/586718.
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This paper presents a new wavelet interpolation Galerkin method for the numerical simulation of MEMS devices under the effect of squeeze film damping. Both trial and weight functions are a class of interpolating functions generated by autocorrelation of the usual compactly supported Daubechies scaling functions. To the best of our knowledge, this is the first time that wavelets have been used as basis functions for solving the PDEs of MEMS devices. As opposed to the previous wavelet-based methods that are all limited in one energy domain, the MEMS devices in the paper involve two coupled energy domains. Two typical electrically actuated micro devices with squeeze film damping effect are examined respectively to illustrate the new wavelet interpolation Galerkin method. Simulation results show that the results of the wavelet interpolation Galerkin method match the experimental data better than that of the finite difference method by about 10%.
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Zhdanov, Aleksei, Paul Constable, Sultan Mohammad Manjur, Anton Dolganov, Hugo F. Posada-Quintero, and Aleksander Lizunov. "OculusGraphy: Signal Analysis of the Electroretinogram in a Rabbit Model of Endophthalmitis Using Discrete and Continuous Wavelet Transforms." Bioengineering 10, no. 6 (June 11, 2023): 708. http://dx.doi.org/10.3390/bioengineering10060708.
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Background: The electroretinogram is a clinical test used to assess the function of the photoreceptors and retinal circuits of various cells in the eye, with the recorded waveform being the result of the summated response of neural generators across the retina. Methods: The present investigation involved an analysis of the electroretinogram waveform in both the time and time–frequency domains through the utilization of the discrete wavelet transform and continuous wavelet transform techniques. The primary aim of this study was to monitor and evaluate the effects of treatment in a New Zealand rabbit model of endophthalmitis via electroretinogram waveform analysis and to compare these with normal human electroretinograms. Results: The wavelet scalograms were analyzed using various mother wavelets, including the Daubechies, Ricker, Wavelet Biorthogonal 3.1 (bior3.1), Morlet, Haar, and Gaussian wavelets. Distinctive variances were identified in the wavelet scalograms between rabbit and human electroretinograms. The wavelet scalograms in the rabbit model of endophthalmitis showed recovery with treatment in parallel with the time-domain features. Conclusions: The study compared adult, child, and rabbit electroretinogram responses using DWT and CWT, finding that adult signals had higher power than child signals, and that rabbit signals showed differences in the a-wave and b-wave depending on the type of response tested, while the Haar wavelet was found to be superior in visualizing frequency components in electrophysiological signals for following the treatment of endophthalmitis and may give additional outcome measures for the management of retinal disease.
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Akimov, Pavel A., Alexander M. Belostotsky, Taymuraz B. Kaytukov, Marina L. Mozgaleva, and Mojtaba Aslami. "ABOUT SEVERAL NUMERICAL AND SEMIANALYTICAL METHODS OF LOCAL STRUCTURAL ANALYSIS." International Journal for Computational Civil and Structural Engineering 14, no. 4 (December 21, 2018): 59–69. http://dx.doi.org/10.22337/2587-9618-2018-14-4-59-69.
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Numerical or semianalytical solution of problems of structural mechanics with immense number of unknowns is time-consuming process. High-accuracy solution at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known domains. The choice of these domains is a priori data with respect to the structure being modelled. Designers usually choose domains with the so-called edge effect (with the risk of significant stresses that could lead to destruction of structures) and regions which are subject to specific operational requirements. Stress-strain state in such domains is important. Wavelets provide effective and popular tool for local structural analysis. Operational and variational formulations of problems of structural mechanics with the use of method of extended domain are presented. After discretization and obtaining of governing equations, problems are transformed to a multilevel space by multilevel wavelet transform. Discrete wavelet basis is used and corresponding direct and inverse algorithms of transformations are performed. Due to special algorithms of averaging, reduction of the problems is provided. Wavelet-based methods allows reducing the size of the problems and obtaining accurate results in selected domains simultaneously. These are rather efficient methods for evaluation of local phenomenon in structures.
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Brassarote, Gabriela De Oliveira Nascimento, Eniuce Menezes de Souza, and João Francisco Galera Monico. "Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation." TEMA (São Carlos) 16, no. 2 (September 7, 2015): 119. http://dx.doi.org/10.5540/tema.2015.016.02.0119.
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Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.
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NEUMANN, JULIA, and GABRIELE STEIDL. "DUAL-TREE COMPLEX WAVELET TRANSFORM IN THE FREQUENCY DOMAIN AND AN APPLICATION TO SIGNAL CLASSIFICATION." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 01 (March 2005): 43–65. http://dx.doi.org/10.1142/s0219691305000749.
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We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain where it can be formulated for standard wavelet filters without special filter design. We prove that the dual-tree filter bank construction leads to wavelets with vanishing negative frequency parts, present numerical examples illustrating the improvement of translation and rotation invariance for various standard wavelet filters and apply the method to the classification of signals.
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ZHANG, LI, WEIDA ZHOU, and LICHENG JIAO. "SUPPORT VECTOR MACHINES BASED ON THE ORTHOGONAL PROJECTION KERNEL OF FATHER WAVELET." International Journal of Computational Intelligence and Applications 05, no. 03 (September 2005): 283–303. http://dx.doi.org/10.1142/s1469026805001489.
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Recently the study on the theory of wavelets shows that the wavelets have not only the multi-resolution property both in frequency and time domain, but also the good approximation ability. SVMs based on the statistical learning theory are a kind of general and effective learning machines, and have described for us the nice application blueprint in machine learning domain. There exists a bottleneck problem, or the pre-selection of kernel parameter for SVMs. In this paper, the orthogonal projection kernels of father wavelet (OPFW kernels) are introduced into SVMs. In doing so SVMs based on the OPFW kernels can have good performance in both approximation and generalisation. Simultaneously the parameter pre-selection of wavelet kernels can be implemented by discrete wavelet transform. Experiments on regression estimation illustrate the approximation and generalisation ability of our method.
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Tratskas, P., and P. D. Spanos. "Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform." Journal of Applied Mechanics 70, no. 5 (September 1, 2003): 724–31. http://dx.doi.org/10.1115/1.1601252.
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The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.
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Zhou, Guang-Dong, You-Liang Ding, and Ai-Qun Li. "Evolutionary Spectra Estimation of Field Measurement Typhoon Processes Using Wavelets." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/945203.
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This paper presents a wavelet-based method for estimating evolutionary power spectral density (EPSD) of nonstationary stochastic oscillatory processes and its application to field measured typhoon processes. The EPSD, which is deduced in a closed form based on the definition of the EPSD and the algorithm of the continuous wavelet transform, can be formulated as a sum of squared moduli of the wavelet functions in time domain modulated by frequency-dependent coefficients that relate to the squared values of wavelet coefficients and two wavelet functions with different time shifts. A parametric study is conducted to examine the efficacy of the wavelet-based estimation method and the accuracy of different wavelets. The results indicate that all of the estimated EPSDs have acceptable accuracy in engineering application and the Morlet transform can provide desirable estimations in both time and frequency domains. Finally, the proposed method is adopted to investigate the time-frequency characteristics of the Typhoon Matsa measured in bridge site. The nonstationary energy distribution and stationary frequency component during the whole process are found. The work in this paper may promote an improved understanding of the nonstationary features of typhoon winds.
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Enesi, Indrit, Miranda Harizaj, and Betim Çiço. "Implementing Fusion Technique Using Biorthogonal Dwt to Increase the Number of Minutiae in Fingerprint Images." Journal of Sensors 2022 (May 24, 2022): 1–13. http://dx.doi.org/10.1155/2022/3502463.
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Biometric devices identify persons based on the minutiae extracted from fingerprint images. Image quality is very important in this process. Usually, fingerprint images have low quality and in many cases they are obtained in various positions. The paper focuses on increasing minutiae detected number by fusing two fingerprint images obtained in various positions. Biorthogonal wavelets have advantages compared to orthogonal wavelets. Fusion is performed in wavelet domain by implementing biorthogonal wavelet. Terminations and bifurcations are extracted from the original and fused images using licensed software Papillon 9.02 and manually extraction by an expert. Biorthogonal Wavelet transform is implemented in the image fusion process, yielding in the increased number of the minutiae compared to the original one. Different biorthogonal wavelets are experimented and various results are obtained. Finding the appropriate wavelet is important in the fusion process since it has a direct impact in the number of minutiae extracted. Based on the number of minutiae and MSE results, the appropriate wavelet to be used in the fusion process is defined.
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Rajeswari, R., and S. Balamurugan. "Image Super Resolution Enhancement Based on Interpolation of Discrete and Stationary Wavelet Domain." Asian Journal of Computer Science and Technology 1, no. 1 (May 5, 2012): 60–64. http://dx.doi.org/10.51983/ajcst-2012.1.1.1668.
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In this paper, we propose an image super resolution enhancement technique based on interpolation of the high frequency sub band images obtained by discrete wavelet transform (DWT) using different types of wavelets such as Daubechies 1. Daubechies 2 .., Daubechies 9 haar, and the input image. The edges are enhanced by introducing an intermediate stage by using stationary wavelet transform (SWT). We compare the results of different types of wavelets. DWT is applied in order to decompose an input image into different sub bands. Then the high frequency sub bands as well as the input image are interpolated. The estimated high frequency sub bands are being modified by using high frequency sub bands obtained through SWT then all these sub bands are combined to generate a new super-resolved image by using inverse DWT.
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Layla A. Ahmed and Monem Mohammed. "Extend Nearly Pseudo Quasi-2-Absorbing submodules(II)." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 2 (April 20, 2023): 420–29. http://dx.doi.org/10.30526/36.2.3060.
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Time series analysis is the statistical approach used to analyze a series of data. Time series is the most popular statistical method for forecasting, which is widely used in several statistical and economic applications. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. The wavelet transform method provides signal information in both the time domain and frequency domain. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Fibonacci coefficient polynomials, as well as a comparison between ARIMA and wavelet-ARIMA. The time series data for daily wind speed is used for this study. From the obtained results, the proposed wavelet-ARIMA is the most appropriate wavelet for wind speed. As compared to wavelets the proposed wavelet is the most appropriate wavelet for wind speed forecasting, it gives us less value of MAE and RMSE.
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Li, Shiwen, and Yunhe Liu. "Wavelet-Based Three-Dimensional Inversion for Geomagnetic Depth Sounding." Magnetochemistry 8, no. 12 (December 12, 2022): 187. http://dx.doi.org/10.3390/magnetochemistry8120187.
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The complexity of Earth’s structure poses a challenge to the multiscale detection capability of geophysics. In this paper, we present a new wavelet-based three-dimensional inversion method for geomagnetic depth sounding. This method is based on wavelet functions to transfer model parameters in the space domain into the wavelet domain. The model is represented by wavelet coefficients containing both large- and fine-scale information, enabling wavelet-based inversion to describe multiscale anomalies. L1-norm measurement is applied to measure the model roughness to accomplish the sparsity constraint in the wavelet domain. Meanwhile, a staggered-grid finite difference method in a spherical coordinate system is used to calculate the forward responses, and the limited-memory quasi-Newton method is applied to seek the solution of the inversion objective function. Inversion tests of synthetic data for multiscale models show that wavelet-based inversion is stable and has multiresolution. Although higher-order wavelets can lead to finer results, our tests present that a db6 wavelet is suitable for geomagnetic depth sounding inversion. The db6 inversion results of responses at 129 geomagnetic observatories around the world reveal a higher-resolution image of the mantle.
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Wachowiak, Mark P., Renata Wachowiak-Smolíková, Michel J. Johnson, Dean C. Hay, Kevin E. Power, and F. Michael Williams-Bell. "Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170250. http://dx.doi.org/10.1098/rsta.2017.0250.
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Theoretical and practical advances in time–frequency analysis, in general, and the continuous wavelet transform (CWT), in particular, have increased over the last two decades. Although the Morlet wavelet has been the default choice for wavelet analysis, a new family of analytic wavelets, known as generalized Morse wavelets, which subsume several other analytic wavelet families, have been increasingly employed due to their time and frequency localization benefits and their utility in isolating and extracting quantifiable features in the time–frequency domain. The current paper describes two practical applications of analysing the features obtained from the generalized Morse CWT: (i) electromyography, for isolating important features in muscle bursts during skating, and (ii) electrocardiography, for assessing heart rate variability, which is represented as the ridge of the main transform frequency band. These features are subsequently quantified to facilitate exploration of the underlying physiological processes from which the signals were generated. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.
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Xie, Haoyu, and Riki Honda. "Arbitrarily Oriented Phase Randomization of Design Ground Motions by Continuous Wavelets." Infrastructures 6, no. 10 (October 11, 2021): 144. http://dx.doi.org/10.3390/infrastructures6100144.
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For dynamic analysis in seismic design, selection of input ground motions is of huge importance. In the presented scheme, complex Continuous Wavelet Transform (CWT) is utilized to simulate stochastic ground motions from historical records of earthquakes with phase disturbance arbitrarily localized in time-frequency domain. The complex arguments of wavelet coefficients are determined as phase spectrum and an innovative formulation is constructed to improve computational efficiency of inverse wavelet transform with a pair of random complex arguments introduced and make more candidate wavelets available in the article. The proposed methodology is evaluated by numerical simulations on a two-degree-of-freedom system including spectral analysis and dynamic analysis with Shannon wavelet basis and Gabor wavelet basis. The result shows that the presented scheme enables time-frequency range of disturbance in time-frequency domain arbitrarily oriented and complex Shannon wavelet basis is verified as the optimal candidate mother wavelet for the procedure in case of frequency information maintenance with phase perturbation.
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Turkheimer, Federico E., Matthew Brett, Dimitris Visvikis, and Vincent J. Cunningham. "Multiresolution Analysis of Emission Tomography Images in the Wavelet Domain." Journal of Cerebral Blood Flow & Metabolism 19, no. 11 (November 1999): 1189–208. http://dx.doi.org/10.1097/00004647-199911000-00003.
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This article develops a theoretical framework for the use of the wavelet transform in the estimation of emission tomography images. The solution of the problem of estimation addresses the equivalent problems of optimal filtering, maximum compression, and statistical testing. In particular, new theory and algorithms are presented that allow current wavelet methodology to deal with the two main characteristics of nuclear medicine images: low signal-to-noise ratios and correlated noise. The technique is applied to synthetic images, phantom studies, and clinical images. Results show the ability of wavelets to model images and to estimate the signal generated by cameras of different resolutions in a wide variety of noise conditions. Moreover, the same methodology can be used for the multiscale analysis of statistical maps. The relationship of the wavelet approach to current hypothesis-testing methods is shown with an example and discussed. The wavelet transform is shown to be a valuable tool for the numerical treatment of images in nuclear medicine. It is envisaged that the methods described here may be a starting point for further developments in image reconstruction and image processing.
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Liu, Chenhua, and Anhong Wang. "State-Aware High-Order Diffusion Method for Edge Detection in the Wavelet Domain." Symmetry 15, no. 4 (March 25, 2023): 803. http://dx.doi.org/10.3390/sym15040803.
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This paper addresses how to use high-order diffusion to restore the wavelet coefficients in the wavelet domain. To avoid image distortion, wavelets with symmetry are used for image decomposition to obtain the wavelet coefficients of each sub-band. Due to the influence of noise, it is particularly important to obtain the wavelet coefficients, which can accurately reflect the image information. According to the characteristics of wavelet threshold shrinkage and the advantages of the high-order variational method in denoising, a wavelet coefficient restoration scheme is proposed. The theoretical basis of our proposed method is established through the analysis of wavelet threshold theory. To keep the original structure of wavelet coefficients unchanged, we introduce the concept of state quantity of wavelet coefficients and obtain the corresponding state quantity of wavelet coefficients using normalization. The denoising wavelet coefficient is obtained by performing a fourth-order anisotropic diffusion of the state quantities. This paper takes image edge feature extraction as the experimental content and image edges are detected by the module of the wavelet coefficients. The effectiveness of the proposed algorithm is objectively verified from three aspects: denoising effect, edge continuity, and accuracy. The experimental results show that the proposed algorithm can obtain continuous and precise image edges. The algorithm presented in this paper also applies to texture images. Compared with other algorithms, the edges image obtained by this scheme shows advantages in terms of noise removal and edge protection.
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Geng, Jianrong, Juan He, Hongxia Ye, and Bin Zhan. "A Clutter Suppression Method Based on LSTM Network for Ground Penetrating Radar." Applied Sciences 12, no. 13 (June 25, 2022): 6457. http://dx.doi.org/10.3390/app12136457.
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It is critical to estimate and eliminate the wavelets of ground penetrating radar (GPR), so as to optimally compensate the energy attenuation and phase distortion. This paper presents a new wavelet extraction method based on a two-layer Long Short-Term Memory (LSTM) network. It only uses several random A-scan echoes (i.e., single channel detection echo sequence) to accurately predict the wavelet of any scene. The layered detection scenes with objects buried in different region are set for the 3D Finite-Difference Time-Domain simulator to generate radar echoes as a dataset. Additionally, the simulation echoes of different scenes are used to test the performance of the neural network. Multiple experiments indicate that the trained network can directly predict the wavelets quickly and accurately, although the simulation environment becomes quite different. Moreover, the measured data collected by the Qingdao Radio Research Institute radar and the unmanned aerial vehicle ground penetrating radar are used for test. The predicted wavelets can perfectly offset the original data. Therefore, the presented LSTM network can effectively predict the wavelets and their tailing oscillations for different detection scenes. The LSTM network has obvious advantages compared with other wavelet extraction methods in practical engineering.
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JIANG, YINGCHUN, and YOUMING LIU. "INTERPOLATORY CURL-FREE WAVELETS AND APPLICATIONS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (September 2007): 843–58. http://dx.doi.org/10.1142/s0219691307002075.
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Divergence-free and curl-free vector wavelets have many applications for the analysis and numerical simulation of incompressible flows and certain electromagnetic phenomena. Because special domains are required in those applications, Bittner and Urban constructed interpolating divergence-free multi-wavelets based on cubic Hermite splines in 2005. In this paper, we construct interpolating curl-free multi-wavelets and give two wavelet estimates for a class of vector Besov spaces.
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Devi, Vaneeta, and M. L. Sharma. "Spectral Estimation of Noisy Seismogram using Time-Frequency Analyses." International Journal of Geotechnical Earthquake Engineering 7, no. 1 (January 2016): 19–32. http://dx.doi.org/10.4018/ijgee.2016010102.
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Time–Frequency analyses have the advantage of explaining the signal features in both time domain and frequency domain. This paper explores the performance of Time–Frequency analyses on noisy seismograms acquired from seismically active region in NW Himalayan. The Short Term Fourier Transform, Gabor Transform, Wavelet Transform and Wigner-Ville Distribution have been used in the present study to carry out Time-Frequency analyses. Parametric study has been carried out by varying basic parameters viz. sampling, window size and types. Wavelet analysis (Continuous Wavelet Transform) has been studied with different type of wavelets. The seismograms have been stacked in time-frequency domain using Gabor Transform and have been converted using Discrete Gabor Expansion techniques. The Spectrograms reveals better spectral estimation in time-frequency domain than Fourier Transform and hence recommended to estimate dominate frequency components, phase marking and timings of phase. The time of occurrence of frequency component corresponding to maximum energy burst can be identified on seismograms
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Deckmyn, Alex, and Loïk Berre. "A Wavelet Approach to Representing Background Error Covariances in a Limited-Area Model." Monthly Weather Review 133, no. 5 (May 1, 2005): 1279–94. http://dx.doi.org/10.1175/mwr2929.1.
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Abstract The use of orthogonal wavelets for the representation of background error covariances over a limited area is studied. Each wavelet function contains both information on position and information on scale: using a diagonal correlation matrix in wavelet space thus gives the possibility of representing the local variations of correlation scale. To this end, a generalized family of orthogonal Meyer wavelets that are not restricted to dyadic domains (i.e., powers of 2) is introduced. A three-bases approach is used, which allows one to take advantage of the respective properties of the spectral, wavelet, and gridpoint spaces. While the implied local anisotropies are relatively small, the local changes in the two-dimensional length scale are rather well represented.
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GRYLLIAS, KONSTANTINOS C., and IOANNIS ANTONIADIS. "A PEAK ENERGY CRITERION (P. E.) FOR THE SELECTION OF RESONANCE BANDS IN COMPLEX SHIFTED MORLET WAVELET (CSMW) BASED DEMODULATION OF DEFECTIVE ROLLING ELEMENT BEARINGS VIBRATION RESPONSE." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 04 (July 2009): 387–410. http://dx.doi.org/10.1142/s0219691309002982.
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Complex Shifted Morlet Wavelets (CSMW) present a number of advantages when used for the demodulation of the vibration response of defective rolling element bearings: (A) They present the optimally located window simultaneously in the time and in the frequency domains; (B) They allow for the maximal time-frequency resolution; (C) The magnitudes of the complex wavelet coefficients in the time domain lead directly to the required envelope; (D) They allow for the optimal selection of both the center frequency and the bandwidth of the requested filter. A Peak Energy criterion (P. E.) is proposed in this paper for the simultaneous automatic selection of both the center frequency and the bandwidth of the relevant wavelet window to be used. As shown in a number of application cases, this criterion presents a more effective behavior than other criteria used (Crest Factor, Kurtosis, Smoothness Index, Number of Peaks), since it combines the advantages of energy based criteria, with criteria characterizing the spikiness of the response.
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MEGHNEFI, F., F. BEREKSI REGUIG, and M. BRAHAMI. "ANALYSIS OF THE DOPPLER ULTRASOUND SIGNAL BY WAVELET PACKET TRANSFORM." Journal of Mechanics in Medicine and Biology 04, no. 03 (September 2004): 273–82. http://dx.doi.org/10.1142/s021951940400103x.
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The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the arteries in the spectro-temporal domain using the wavelet packet transform. The spectro-temporal representation is obtained by the decomposition of the Doppler signal in frequency sub-band, using filter banks associated with a well chosen wavelet. It is shown that the decomposition level depends on the stationarity of the Doppler signal, and the best profile of blood flow velocity in arteries is obtained according to an appropriate choice of wavelet type. Three types of wavelets have been tested on two Doppler signals previously recorded from the carotid and femoral arteries. The best representation is obtained when the frequency sub-bands of the filter bank associated with chosen wavelet are regularly distributed in the frequency domain and the level of decomposition is 7.
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Ramírez-Pacheco, Julio, Homero Toral-Cruz, Luis Rizo-Domínguez, and Joaquin Cortez-Gonzalez. "Generalized Wavelet Fisher’s Information of1/fαSignals." Advances in Mathematical Physics 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/210592.
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This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.
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GUO, PENGFEI, and ALWELL JULIUS OYET. "ON WAVELET METHODS FOR TESTING EQUALITY OF MEAN RESPONSE CURVES." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 03 (May 2009): 357–73. http://dx.doi.org/10.1142/s0219691309002969.
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In this article, we exploit the adaptive properties of wavelets to develop some procedures for testing the equality of nonlinear and nonparametric mean response curves which are assumed by an experimenter to be the underlying functions generating several groups of data with possibly hetereoscedastic errors. The essential feature of the techniques is the transformation of the problem from the domain of the input variable to the wavelet domain through an orthogonal discrete wavelet transformation or a multiresolution expansion. We shall see that this greatly simplifies the testing problem into either a wavelet thresholding problem or a linear wavelet regression problem. The size and power performances of the tests are reported and compared to some existing methods. The tests are also applied to data on dose response curves for vascular relaxation in the absence or presence of a nitric oxide inhibitor.
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Toda, Hiroshi, and Zhong Zhang. "Orthonormal basis of wavelets with customizable frequency bands." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 2016): 1650050. http://dx.doi.org/10.1142/s0219691316500508.
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We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.
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Behm, Michael, and Bharath Shekar. "Blind deconvolution of multichannel recordings by linearized inversion in the spectral domain." GEOPHYSICS 79, no. 2 (March 1, 2014): V33—V45. http://dx.doi.org/10.1190/geo2013-0170.1.
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In seismology, blind deconvolution aims to recover the source wavelet and the Green’s function, or parts of it (e.g., reflectivity series), from a recorded seismic trace. A multitude of algorithms exist that tackle this ill-posed problem by different approaches. Making assumptions on the phase spectra of the source wavelet and/or the statistical distribution of the reflectivity series is useful for single trace. The nature of closely spaced multichannel recordings enables a better estimation of a common source wavelet and thus increases the confidence of the results. This approach has been exploited in the past, although different types of assumptions are used for a variety of algorithms. We introduced a new method for simultaneous reconstruction of arbitrary source wavelets and local vertical reflectivity series from teleseismic earthquakes. Closely spaced receivers record vertically incident earthquake body waves and their surface-related multiples, which comprise the unknown reflectivity series. By assuming a common source wavelet for all receivers, the observation of several events resulted in a set of convolution equations relating the unknown source wavelets and unknown reflectivity series to the observed seismic trace. The overdetermined system of equations was linearized and solved by conventional inversion algorithms in the spectral domain. Synthetic tests indicated a better performance of the introduced method than conventional deconvolution in the presence of white noise, which is attributed to the constraint of a common model for all observations. Application to field data from a local deployment allowed imaging a basement reflector from teleseismic body waves, although the data were contaminated with strong coherent noise. From a practical point of view, the presented method is potentially well suited for local and regional large-scale imaging from multichannel passive seismic data.
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Prosser, R. "An adaptive algorithm for compressible reacting flows using interpolating wavelets." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 11 (November 1, 2007): 1397–410. http://dx.doi.org/10.1243/09544062jmes489.
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A new wavelet-based method for the simulation of reacting flows on adaptive meshes is presented. The method is based on the removal of grid points whose wavelet coefficients are small with reference to some user-specified threshold. Unlike some other collocation methods, the scheme simulates flow behaviour in the physical (i.e. not transformed) domain, and the wavelets, thus, provide the method by which the derivatives appearing in the transport equations are calculated. The wavelet transformis based on a subtraction algorithm, and circumvents the hanging node problem associated with other adaptive strategies. Interpolating wavelets are applied to a compressible one-dimensional laminar flame problem with time dependent boundary conditions. We find that the resolution of the chemistry distribution is comparatively straightforward. The same is not true of the pressure field, which demonstrates sensitivity to the imposed threshold level. Conclusions and directions for future work are presented based on these findings.
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Ghasemi-Ghalebahman, Ahmad, Mohammad-Reza Ashory, and Mohammad-Javad Kokabi. "A proper lifting scheme wavelet transform for vibration-based damage identification in composite laminates." Journal of Thermoplastic Composite Materials 31, no. 5 (July 6, 2017): 668–88. http://dx.doi.org/10.1177/0892705717718239.
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Damage detection using the wavelet transform was investigated and appropriate approaches to raising the method’s sensitivity level were proposed. In addition, the current study attempted to implement the impulse wavelet design algorithm in order to present appropriate wavelet function with respect to the characteristics of the signal. The initial wavelet function corresponding to the impulse response of composite plate was achieved using impulse wavelet algorithm in time domain. The function was optimized using lifting scheme method. To detect damages, an appropriate signal was selected through applying wavelet transform. To enhance damage identification, first, the edges’ effect of wavelet transform was removed, then a higher accuracy was observed by summing the wavelet coefficients in all scale factors for each mode shape and the wavelet coefficients for all mode shapes. The article also presents a quantitative measure to compare different wavelets.
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Yang, Yongqiang, Yunpeng Ma, and Lifeng Wang. "The Simultaneous Interpolation of Target Radar Cross Section in Both the Spatial and Frequency Domains by Means of Legendre Wavelets Model-Based Parameter Estimation." International Journal of Aerospace Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/543787.
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The understanding of the target radar cross section (RCS) is significant for target identification and for radar designing and optimization. In this paper, a numerical algorithm for calculating target RCS is presented which is based on Legendre wavelet model-based parameter estimation (LW-MBPE). The Padé rational function fitting model applied for MBPE in the frequency domain is enhanced to include spatial dependence on the numerator and denominator coefficients. This allows the function to interpolate target RCS in both the frequency and spatial domains simultaneously. The combination of Legendre wavelets guarantees the convergence of the algorithm. The method is convergent by increasing the sampling frequency and spatial points. Numerical results are provided to demonstrate the validity and applicability of the new technique.
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González-Concepción, C., M. C. Gil-Fariña, and C. Pestano-Gabino. "Using Wavelets to Understand the Relationship between Mortgages and Gross Domestic Product in Spain." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/917247.
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We use wavelet multiresolution decomposition and cross-wavelet analysis to reveal certain properties in financial data related to mortgages to households and gross domestic product data in Spain. Wavelet techniques possess many desirable properties, some of which are useful as a vehicle for analysing economic and financial data. In our case, wavelets are useful for drawing conclusions both in the time and frequency domains and for obtaining information on the different phases through which the study variables progress.
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Soleymani, Atefeh, Hashem Jahangir, Maria Rashidi, Farid Fazel Mojtahedi, Michael Bahrami, and Ahad Javanmardi. "Damage Identification in Reinforced Concrete Beams Using Wavelet Transform of Modal Excitation Responses." Buildings 13, no. 8 (July 31, 2023): 1955. http://dx.doi.org/10.3390/buildings13081955.
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This study focuses on identifying damage in reinforced concrete (RC) beams using time-domain modal testing and wavelet analysis. A numerical model of an RC beam was used to generate various damage scenarios with different severities and locations. Acceleration time histories were recorded for both damaged and undamaged structures. Two damage indices, DI_MW and DI_SW, derived from the wavelet analysis, were employed to determine the location and severity of the damage. The results showed that different wavelet families and specific mother wavelets had varying effectiveness in detecting damage. The Daubechies wavelet family (db2, db6, and db9) detected damage at the center and sides of the RC beams due to good time and frequency localization. The Biorthogonal wavelet family (bior2.8 and bior3.1) provided improved time–frequency resolution. The Symlets wavelet family (sym2 and sym7) offered a balanced trade-off between time and frequency localization. The Shannon wavelet family (shan1-0.5 and shan1-0.1) exhibited good time localization, while the Frequency B-Spline wavelet family (fbsp2-1-0.1) excelled in frequency localization. Certain combinations of mother wavelets, such as shan1-0.5 with the DI_SW index, were highly effective in detecting damage. The DI_SW index outperformed DI_MW across different numerical models. Selecting appropriate wavelet analysis techniques, particularly utilizing shan1-0.5 in the DI_SW, proved effective for detecting damage in RC beams.
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Cui, Yue Li, Zhi Gang Chen, and Ai Hua Chen. "Research and Progress of Image Compression Coding Based on Wavelet." Advanced Materials Research 403-408 (November 2011): 1352–55. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.1352.
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Image compression is a technology using as little as possible bits to represent the original image. As wavelet transform has local characteristics on the time and frequency domain, it makes up the deficiency of DCT. Moreover, its multi-resolution characteristics can easily associate with the human visual system (HVS). Besides, wavelet-based image compression is prone to combine with new image coding methods. It has become the research hotspots at present. This paper introduces wavelets theory and discusses the research status and progress of wavelet-based image compression then points out the main problems. Finally, the prospect in the future was presented.
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Kannadhasan, S., and R. Suresh. "EMD Algorithm for Robust Image Watermarking." Advanced Materials Research 984-985 (July 2014): 1255–60. http://dx.doi.org/10.4028/www.scientific.net/amr.984-985.1255.
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Watermarking is process of hiding digital information into another object/signal. To attain robustness information based on image data is transformed in multiple resolution using Wavelet based image watermarking methods. Embedding watermark bits in middle frequency sub images in the wavelet domain is done using Multiband Wavelet Transform (MWT). At this juncture an attempt is made to analyze robustness for different test images. To resist various attacks Empirical Mode Decomposition (EMD) is used. Performance evaluation of an Image watermarking includes robustness, imperceptibility, watermark capacity and security. Index Terms Image enhancement Empirical mode decomposition, Multiband wavelets transformation
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Saxena, Parul, and Vinay Saxena. "COMPARATIVE STUDY OF WHITE GAUSSIAN NOISE REDUCTION FOR DIFFERENT SIGNALS USING WAVELET." International Journal of Research -GRANTHAALAYAH 10, no. 7 (August 5, 2022): 112–23. http://dx.doi.org/10.29121/granthaalayah.v10.i7.2022.4711.
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The present work is an attempt to make a comparative study of the wavelet-based noise reduction algorithm. The algorithm has been developed and implemented in MATLAB GUI and then analyzed for different types of wavelets such as Coiflet, Daubechies, Symlet, and Biorthogonal with their different versions. This algorithm has been verified for different types of input signals from different domains. Various statistical aspects like Mean Absolute Error (MAE), Mean Squared Error (MSE), Signal to Noise Ratio (SNR), and Peak Signal to Noise Ratio (PSNR) are analyzed for this algorithm. It is observed that the developed algorithm for noise reduction using wavelet works very well for different types of wavelets.
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Jeon, Seonghye, Orietta Nicolis, and Brani Vidakovic. "Mammogram Diagnostics via 2-D Complex Wavelet-based Self-similarity Measures." São Paulo Journal of Mathematical Sciences 8, no. 2 (December 12, 2014): 265. http://dx.doi.org/10.11606/issn.2316-9028.v8i2p265-284.
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Breast cancer is the second leading cause of death in women in the United States. Mammography is currently the most eective method for detecting breast cancer early; however, radiological inter- pretation of mammogram images is a challenging task. Many medical images demonstrate a certain degree of self-similarity over a range of scales. This scaling can help us to describe and classify mammograms. In this work, we generalize the scale-mixing wavelet spectra to the complex wavelet domain. In this domain, we estimate Hurst parameter and image phase and use them as discriminatory descriptors to clas- sify mammographic images to benign and malignant. The proposed methodology is tested on a set of images from the University of South Florida Digital Database for Screening Mammography (DDSM). Keywords: Scaling; Complex Wavelets; Self-similarity; 2-D Wavelet Scale-Mixing Spectra.
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Lubis, Muhammad Zainuddin, Rasyid Alkhoir Lubis, and Ramadhan Ulil Albab Lubis. "The Two-Dimensional Wavelet Transform De-noising and Combining with Side Scan Sonar Image." Journal of Applied Geospatial Information 1, no. 01 (May 18, 2017): 1–4. http://dx.doi.org/10.30871/jagi.v1i01.307.
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This paper puts forward an image de-noising method based on 2D wavelet transform with the application of the method in seabed identification data collection system. Two-dimensional haar wavelets in image processing presents a unified framework for wavelet image compression and combining with side scan sonar image. Seabed identification target have 7 target detection in side scan sonar imagery result. The vibration signals were analyzed to perform fault diagnosis. The obtained signal was time-domain signal. The experiment result shows that the application of 2D wavelet transform image de-noising algorithm can achieve good subjective and objective image quality and help to collect high quality data and analyze the images for the data center with optimum effects, the features from time-domain signal were extracted. 3 vectors were formed which are v1, v2, v3. In Haar wavelet retained energy is 93.8 %, so from the results, it has been concluded that Haar wavelet transform shows the best results in terms of Energy from De-noised Image processing with side scan sonar imagery.