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Journal articles on the topic 'Wavelets (Mathematics) – Data processing'

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Published: 4 June 2021

Last updated: 3 February 2022

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1

Ahmadi, H., G. Dumont, F. Sassani, and R. Tafreshi. "Performance of Informative Wavelets for Classification and Diagnosis of Machine Faults." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 03 (2003): 275–89. http://dx.doi.org/10.1142/s0219691303000189.

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This paper deals with an application of wavelets for feature extraction and classification of machine faults in a real-world machine data analysis environment. We have utilized informative wavelet algorithm to generate wavelets and subsequent coefficients that are used as feature variables for classification and diagnosis of machine faults. Informative wavelets are classes of functions generated from a given analyzing wavelet in a wavelet packet decomposition structure in which for the selection of best wavelets, concepts from information theory, i.e. mutual information and entropy are utilize

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AMINGHAFARI, MINA, and JEAN-MICHEL POGGI. "FORECASTING TIME SERIES USING WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (2007): 709–24. http://dx.doi.org/10.1142/s0219691307002002.

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This paper deals with wavelets in time series, focusing on statistical forecasting purposes. Recent approaches involve wavelet decompositions in order to handle non-stationary time series in such context. A method, proposed by Renaud et al.,11 estimates directly the prediction equation by direct regression of the process on the Haar non-decimated wavelet coefficients depending on its past values. In this paper, this method is studied and extended in various directions. The new variants are used first for stationary data and after for stationary data contaminated by a deterministic trend.

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TANAKA, NOBUATSU. "A SIMPLE BUT EFFICIENT PRECONDITIONING FOR CONJUGATE GRADIENT POISSON SOLVER USING HAAR WAVELET." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (2006): 273–84. http://dx.doi.org/10.1142/s0219691306001233.

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This paper describes a wavelet-based preconditioning technique for conjugate gradient method for linear systems derived from the Poisson equation. The linear systems solved with a conventional iterative matrix solver resulted in a marked increase in computing time with respect to an increase in grid points. Use of our wavelet-based technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. In this study, one of the simplest wavelets, the Haar wavelet, is used for the purpose of developing a simple but efficient preconditioning algorithm. Simple

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ČASTOVÁ, NINA, DAVID HORÁK, and ZDENĚK KALÁB. "DESCRIPTION OF SEISMIC EVENTS USING WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (2006): 405–14. http://dx.doi.org/10.1142/s0219691306001336.

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This paper deals with engineering application of wavelet transform for processing of real seismological signals. Methodology for processing of these slight signals using wavelet transform is presented in this paper. Briefly, three basic aims are connected with this procedure:. 1. Selection of optimal wavelet and optimal wavelet basis B opt for selected data set based on minimal entropy: B opt = arg min B E(X,B). The best results were reached by symmetric complex wavelets with scaling coefficients SCD-6. 2. Wavelet packet decomposition and filtration of data using universal criterion of thresho

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DeVore, Ronald A., and Bradley J. Lucier. "Wavelets." Acta Numerica 1 (January 1992): 1–56. http://dx.doi.org/10.1017/s0962492900002233.

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The subject of ‘wavelets’ is expanding at such a tremendous rate that it is impossible to give, within these few pages, a complete introduction to all aspects of its theory. We hope, however, to allow the reader to become sufficiently acquainted with the subject to understand, in part, the enthusiasm of its proponents toward its potential application to various numerical problems. Furthermore, we hope that our exposition can guide the reader who wishes to make more serious excursions into the subject. Our viewpoint is biased by our experience in approximation theory and data compression; we wa

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PRABAKARAN, S., R. SAHU, and S. VERMA. "A WAVELET APPROACH FOR CLASSIFICATION OF MICROARRAY DATA." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 03 (2008): 375–89. http://dx.doi.org/10.1142/s0219691308002409.

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Microarray technologies facilitate the generation of vast amount of bio-signal or genomic signal data. The major challenge in processing these signals is the extraction of the global characteristics of the data due to their huge dimension and the complex relationship among various genes. Statistical methods are used in broad spectrum in this domain. But, various limitations like extensive preprocessing, noise sensitiveness, requirement of critical input parameters and prior knowledge about the microarray dataset emphasise the need for better exploratory techniques. Transform oriented signal pr

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MAITY, SANTI P., and MALAY K. KUNDU. "PERFORMANCE IMPROVEMENT IN SPREAD SPECTRUM IMAGE WATERMARKING USING WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 1–33. http://dx.doi.org/10.1142/s0219691311003931.

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This paper investigates the scope of wavelets for performance improvement in spread spectrum image watermarking. Performance of a digital image watermarking algorithm, in general, is determined by the visual invisibility of the hidden data (imperceptibility), reliability in the detection of the hidden information after various common and deliberate signal processing operations (robustness) applied on the watermarked signals and the amount of data to be hidden (payload) without affecting the imperceptibility and robustness properties. In this paper, we propose a few spread spectrum (SS) image w

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AZAD, SARITA, R. NARASIMHA, and S. K. SETT. "MULTIRESOLUTION ANALYSIS FOR SEPARATING CLOSELY SPACED FREQUENCIES WITH AN APPLICATION TO INDIAN MONSOON RAINFALL DATA." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (2007): 735–52. http://dx.doi.org/10.1142/s0219691307002026.

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In this paper we make use of the multiresolution properties of discrete wavelets, including their ability to remove interference, to reveal closely spaced spectral peaks. We propose a procedure which we first verify on two test signals, and then apply it to the time series of homogeneous Indian monsoon rainfall annual data. We show that, compared to empirical mode decomposition, discrete wavelet analysis is more effective in identifying closely spaced frequencies if used in combination with classical power spectral analysis of wavelet-based partially reconstructed time series. An effective cri

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JIANG, QINGTANG. "BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (2011): 773–812. http://dx.doi.org/10.1142/s0219691311004316.

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This paper discusses the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently, hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hexagonal data also have high symmetry which is pertinent to the symmetric structure of the hexagonal lattice. The high symmetry of filter banks and wavelets not only leads to simpler algorithms and effi

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Brysina, Iryna Victorivna, and Victor Olexandrovych Makarichev. "GENERALIZED ATOMIC WAVELETS." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (February 23, 2018): 23–31. http://dx.doi.org/10.32620/reks.2018.1.03.

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The problem of big data sets processing is considered. Efficiency of algorithms depends mainly on the appropriate mathematical tools. Now there exists a wide variety of different constructive tools for information analysis. Atomic functions are one of them. Theory of atomic functions was developed by V. A. Rvachev and members of his scientific school. A number of results, which prove that application of atomic functions is reasonable, were obtained. In particular, atomic functions are infinitely differentiable. This property is quite useful for smooth data processing (for example, color photos

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LEWALLE, JACQUES. "FIELD RECONSTRUCTION FROM SINGLE SCALE CONTINUOUS WAVELET COEFFICIENTS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (2009): 131–42. http://dx.doi.org/10.1142/s0219691309002738.

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The redundancy of continuous wavelet transforms implies that the wavelet coefficients are not independent of each other. This interdependence allows the reconstruction or approximation of the wavelet transform, and of the original field, from a subset of the wavelet coefficients. Contrasting with lines of modulus maxima, known to provide useful partition functions and some data compaction, the reconstruction from single-scale coefficients is derived for the Hermitian family of wavelets. The formula is exact in the continuum for d-dimensional fields, and its limitations under discretization are

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ROŞCA, DANIELA. "PIECEWISE CONSTANT WAVELETS ON TRIANGULATIONS OBTAINED BY 1-3 SPLITTING." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 02 (2008): 209–22. http://dx.doi.org/10.1142/s0219691308002318.

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We construct piecewise constant wavelets on a bounded planar triangulation, the refinement process consisting of dividing each triangle into three triangles having the same area. Thus, the wavelets depend on two parameters linked by a certain relation. We perform a compression and try to compare different norms of the compression error, when one wavelet coefficient is canceled. Finally, we show how this construction can be moved on to the two-dimensional sphere and sphere-like surfaces, avoiding the distortions around the poles, which occur in other approaches. As numerical example, we perform

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Araujo dos Santos, J. V., A. Katunin, and H. Lopes. "Vibration-Based Damage Identification Using Wavelet Transform and a Numerical Model of Shearography." International Journal of Structural Stability and Dynamics 19, no. 04 (2019): 1950038. http://dx.doi.org/10.1142/s021945541950038x.

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This paper presents a method for the identification of damage in plates based on the post-processing with wavelets of modal rotation fields. These modal rotation fields are obtained by use of a numerical model of shearography, which includes the simulation of noise in the data generated. The discrete wavelet transform was chosen because of its high sensitivity to perturbations in the modal rotations. Distinct damage scenarios, defined by regions where the thickness of a plate is reduced, are considered in this paper. A study on the differences in the natural frequencies and the changes in moda

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MAITY, SANTI P., CLAUDE DELPHA, and RÉMY BOYER. "WATERMARKING ON COMPRESSED DATA INTEGRATING CONVOLUTION CODING IN INTEGER WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 06 (2012): 1250051. http://dx.doi.org/10.1142/s0219691312500518.

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This paper explores the scope of integer wavelets in watermarking on compressed image with the aid of convolution coding as channel coding. Convolution coding is applied on compressed host data, instead of its direct application on watermark signal as used widely for robustness improvement in conventional system. Two-fold advantages, namely flexibility in watermarking through the creation of redundancy on the compressed data as well as protection of watermark information from additive white Gaussian noise (AWGN) attack are achieved. Integer wavelet is used to decompose the encoded compressed d

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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 (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 e

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ROŞCA, DANIELA. "WEIGHTED HAAR WAVELETS ON THE SPHERE." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 03 (2007): 501–11. http://dx.doi.org/10.1142/s0219691307001872.

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Starting from the one-dimensional Haar wavelets on the interval [0,1], we construct spherical Haar wavelets which are orthogonal with respect to a given scalar product. This scalar product induces a norm which is equivalent to the usual ‖ · ‖2 norm of L2(𝕊2). Thus, the Riesz stability in L2(𝕊2) is assured and we can use the algorithms of decomposition and reconstruction from the Haar wavelets in 2D. Another advantage is that we avoid the problems around the poles, which occur in other approaches. As example, we decompose a data set, showing the graphs of the approximations and details and thus

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Li, Fangyu, Rongchang Liu, Yihuai Lou, and Naihao Liu. "Revisit seismic attenuation attributes: Influences of the spectral balancing operation on seismic attenuation analysis." Interpretation 9, no. 3 (2021): T767—T779. http://dx.doi.org/10.1190/int-2020-0186.1.

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Seismic attenuation analysis is important for seismic processing and quantitative interpretation. Nevertheless, classic quality factor estimation methods make certain assumptions that may be invalid for a given geologic target and seismic volume. For this reason, seismic attenuation attribute analysis, which reduces some of the theoretical assumptions, can serve as a practical alternative in apparent attenuation characterization. Unfortunately, most of the published literature defines seismic attenuation attributes based on a specific source wavelet assumption, such as the Ricker wavelet, rath

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ENDO, HISASHI, SEIJI HAYANO, YOSHIFURU SAITO, ILIANA MARINOVA, and KIYOSHI HORII. "MODAL-WAVELET TRANSFORM AS A SMART VISUALIZATION TOOL." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (2006): 345–56. http://dx.doi.org/10.1142/s0219691306001294.

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A method of information processings based on the classical field theory is outlined to derive the modal-wavelet transform (MWT) as a wavelet-like orthonormal transform. The theoretical background and application of MWT are described. The bases of MWT are derived from modal analysis of the potential field equations. Namely, a principal idea of MWT is that a numerical data set is regarded as a set of the field potentials or source densities. A modal matrix, constituting characteristic vectors, derived from the discretized field equations enables us to carry out an orthonormal transform inasmuch

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Chui, Charles K., Yu-Ting Lin, and Hau-Tieng Wu. "Real-time dynamics acquisition from irregular samples — With application to anesthesia evaluation." Analysis and Applications 14, no. 04 (2016): 537–90. http://dx.doi.org/10.1142/s0219530515500165.

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Although most digital representations of information sources are obtained by uniform sampling of some continuous function representations, there are many important events for which only irregular data samples are available, including trading data of the financial market and various clinical data, such as the respiration signals hidden in ECG measurements. For such digital information sources, the only available effective smooth function interpolation scheme for digital-to-analog (D/A) conversion algorithms are mainly for offline applications. Hence, in order to adapt the powerful continuous-fu

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SIRCA, GENE F., and HOJJAT ADELI. "A NEURAL NETWORK-WAVELET MODEL FOR GENERATING ARTIFICIAL ACCELEROGRAMS." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 03 (2004): 217–35. http://dx.doi.org/10.1142/s0219691304000524.

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In earthquake-resistant design of structures, for certain structural configurations and conditions, it is necessary to use accelerograms for dynamic analysis. Accelerograms are also needed to simulate the effects of earthquakes on a building structure in the laboratory. A new method of generating artificial earthquake accelerograms is presented through adroit integration of neural networks and wavelets. A counterpropagation (CPN) neural network model is developed for generating artificial accelerograms from any given design spectrum such as the International Building Code (IBC) design spectrum

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PONT, ORIOL, ANTONIO TURIEL, and CONRAD J. PÉREZ-VICENTE. "ON OPTIMAL WAVELET BASES FOR THE REALIZATION OF MICROCANONICAL CASCADE PROCESSES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 35–61. http://dx.doi.org/10.1142/s0219691311003943.

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Multiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e. being able to decompose each variable as the product of larger scale contributions) is only achieved when signals are represented in an optimal wavelet basis. Finding such a basis is a data-demanding, highly-complex task. In this paper, we propose a formalism that allows

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JEMAI, OLFA, MOURAD ZAIED, CHOKRI BEN AMAR, and MOHAMED ADEL ALIMI. "PYRAMIDAL HYBRID APPROACH: WAVELET NETWORK WITH OLS ALGORITHM-BASED IMAGE CLASSIFICATION." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 111–30. http://dx.doi.org/10.1142/s0219691311003967.

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Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is pro

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FLORINDO, JOÃO BATISTA, MÁRIO DE CASTRO, and ODEMIR MARTINEZ BRUNO. "ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS." International Journal of Bifurcation and Chaos 20, no. 11 (2010): 3443–60. http://dx.doi.org/10.1142/s0218127410027805.

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This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand–Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment

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MATSUYAMA, SAWA, SHIHO MATSUYAMA, and YOSHIFURU SAITO. "DATA HANDLING METHODOLOGY FOR DISCRETE WAVELETS AND ITS APPLICATIONS TO THE DYNAMIC VECTOR FIELDS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (2006): 263–71. http://dx.doi.org/10.1142/s0219691306001221.

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A discrete wavelet transform is one of the effective methodologies for compressing the image data and extracting the major characteristics from various data, but it always requires a number of target data composed of a power of 2. To overcome this difficulty without losing any original data information, we propose here a novel approach based on the Fourier transform. The key idea is simple but effective because it keeps all of the frequency components comprising the target data exactly. The raw data is firstly transformed to the Fourier coefficients by Fourier transform. Then, the inverse Four

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Wiaux, Y., J. D. McEwen, and P. Vielva. "Complex Data Processing: Fast Wavelet Analysis on the Sphere." Journal of Fourier Analysis and Applications 13, no. 4 (2007): 477–93. http://dx.doi.org/10.1007/s00041-006-6917-9.

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JANSEN, MAARTEN. "REFINEMENT INDEPENDENT WAVELETS FOR USE IN ADAPTIVE MULTIRESOLUTION SCHEMES." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 04 (2008): 521–39. http://dx.doi.org/10.1142/s0219691308002471.

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This paper constructs a class of semi-orthogonal and bi-orthogonal wavelet transforms on possibly irregular point sets with the property that the scaling coefficients are independent from the order of refinement. That means that scaling coefficients at a given scale can be constructed with the configuration at that scale only. This property is of particular interest when the refinement operation is data dependent, leading to adaptive multiresolution analyses. Moreover, the proposed class of wavelet transforms are constructed using a sequence of just two lifting steps, one of which contains a l

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Chen, Shuo, Don Hong, and Yu Shyr. "Wavelet-based procedures for proteomic mass spectrometry data processing." Computational Statistics & Data Analysis 52, no. 1 (2007): 211–20. http://dx.doi.org/10.1016/j.csda.2007.02.022.

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Tygert, Mark, Joan Bruna, Soumith Chintala, Yann LeCun, Serkan Piantino, and Arthur Szlam. "A Mathematical Motivation for Complex-Valued Convolutional Networks." Neural Computation 28, no. 5 (2016): 815–25. http://dx.doi.org/10.1162/neco_a_00824.

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A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute valu

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Sajda, Paul, Andrew Laine, and Yehoshua Zeevi. "Multi-Resolution and Wavelet Representations for Identifying Signatures of Disease." Disease Markers 18, no. 5-6 (2002): 339–63. http://dx.doi.org/10.1155/2002/108741.

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Identifying physiological and anatomical signatures of disease in signals and images is one of the fundamental challenges in biomedical engineering. The challenge is most apparent given that such signatures must be identified in spite of tremendous inter and intra-subject variability and noise. Crucial for uncovering these signatures has been the development of methods that exploit general statistical properties of natural signals. The signal processing and applied mathematics communities have developed, in recent years, signal representations which take advantage of Gabor-type and wavelet-typ

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CAÑAMÓN, I., F. J. ELORZA, A. MANGIN, P. L. MARTÍN, and R. RODRÍGUEZ. "WAVELETS AND STATISTICAL TECHNIQUES FOR DATA ANALYSIS IN A MOCK-UP HIGH-LEVEL WASTE STORAGE EXPERIMENT." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 04 (2004): 351–70. http://dx.doi.org/10.1142/s0219691304000585.

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This work analyzes the physical processes occurring in the Mock-up test of the FEBEX I and II projects. FEBEX I and II is an European research project (1996–2004) led by ENRESA, that has financial support from the European Commission. This experiment is based in two large-scale heating tests ("in-situ" test and "Mock-up" test) simulating a radioactive waste repository, and tries to analyze the thermo-hydro-mechanical (THM) processes that could eventually happen in this kind of repositories.The main objectives of this study have been the following: to identify the physical processes occurring i

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Michel, Volker, and Frederik J. Simons. "A general approach to regularizing inverse problems with regional data using Slepian wavelets." Inverse Problems 33, no. 12 (2017): 125016. http://dx.doi.org/10.1088/1361-6420/aa9909.

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FREEDEN, W., and V. MICHEL. "WAVELET DEFORMATION ANALYSIS FOR SPHERICAL BODIES." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 04 (2005): 523–58. http://dx.doi.org/10.1142/s0219691305001007.

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In this paper, we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat. In what follows, we propose a local analysis based on tools (Navier scaling functions and wavelets) taki

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CIARLINI, PATRIZIA, GIUSEPPE COSTANZO, and MARIA LAURA LO CASCIO. "WAVELETS AND SPLINES FOR VERTICAL SCRATCH REMOVAL IN OLD MOVIE SEQUENCES." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (2006): 433–46. http://dx.doi.org/10.1142/s021969130600135x.

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In old movies, scratches are common damages that mostly result from a mechanical stress during the projection. A method for removing vertical scratches is proposed and suitable to be automatically applied to sequences of images. The method uses a wavelet decomposition of the original digital image, I, in order to separate the high frequency components and to elaborate corrupted data in the regular matrix, A, and in the vertical details matrix, V, only. For A, approximating functions are constructed in suitable spline spaces, which depend on the morphological quality of the image near the scrat

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Camerlingo, C., F. Zenone, G. M. Gaeta, R. Riccio, and M. Lepore. "Wavelet data processing of micro-Raman spectra of biological samples." Measurement Science and Technology 17, no. 2 (2006): 298–303. http://dx.doi.org/10.1088/0957-0233/17/2/010.

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Ishikawa, Yasuhiro, Hitoshi Horigome, Akihiko Kandori, Hiroshi Toda, and Zhong Zhang. "Noise reduction by perfect-translation-invariant complex discrete wavelet transforms for fetal electrocardiography and magnetocardiography." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (2014): 1460008. http://dx.doi.org/10.1142/s021969131460008x.

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Echocardiography is widely used for the diagnosis of fetal cardiac arrhythmias. However, this method does not detect configurational changes in the electrocardiogram (ECG) such as life-threatening changes in QRS and the prolongation of the QT interval. Fetal magnetocardiography (fMCG) and fetal electrocardiography (fECG) are valuable tools for the detection of electrophysiological cardiac signals although both have certain limitations. Such techniques must deal with excess internal noise such as maternal respiratory movements, fetal movements, muscle contraction and fetal body movement and ext

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KUNDU, MALAY K., and MAUSUMI ACHARYYA. "M-BAND WAVELETS: APPLICATION TO TEXTURE SEGMENTATION FOR REAL LIFE IMAGE ANALYSIS." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (2003): 115–49. http://dx.doi.org/10.1142/s0219691303000074.

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This paper describes two examples of real-life applications of texture segmentation using M-band wavelets. In the first part of the paper, an efficient and computationally fast method for segmenting text and graphics part of a document image based on textural cues is presented. It is logical to assume that the graphics part has different textural properties than the non-graphics (text) part. So, this is basically a two-class texture segmentation problem. The second part of the paper describes a segmentation scheme for another real-life data such as remotely sensed image. Different quasi-homoge

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KANG, SEONGGU, and SANGJUN LEE. "POLAR WAVELET TRANSFORM FOR TIME SERIES DATA." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 06 (2008): 869–81. http://dx.doi.org/10.1142/s0219691308002720.

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In this paper, we propose the novel wavelet transform, called the Polar wavelet, which can improve the search performance in large time series databases. In general, Harr wavelet has been popularly used to extract features from time series data. However, Harr wavelet shows the poor performance for locally distributed time series data which are clustered around certain values, since it uses the averages to reduce the dimensionality of data. Moreover, Harr wavelet has the limitation that it works best if the length of time series is 2n, and otherwise it approximates the left side of real signal

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Brandner, Paul A., James A. Venning, and Bryce W. Pearce. "Wavelet analysis techniques in cavitating flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20170242. http://dx.doi.org/10.1098/rsta.2017.0242.

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Cavitating and bubbly flows involve a host of physical phenomena and processes ranging from nucleation, surface and interfacial effects, mass transfer via diffusion and phase change to macroscopic flow physics involving bubble dynamics, turbulent flow interactions and two-phase compressible effects. The complex physics that result from these phenomena and their interactions make for flows that are difficult to investigate and analyse. From an experimental perspective, evolving sensing technology and data processing provide opportunities for gaining new insight and understanding of these comple

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KIMURA, MOTOAKI, MASAHIRO TAKEI, YOSHIFURU SAITO, and KIYOSHI HORII. "STUDY ON RELATIONSHIP BETWEEN CONDENSED PARTICLES AND STRUCTURE OF CONDENSATION JET USING 2D IMAGE AND DISCRETE WAVELETS MULTIRESOLUTION." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (2006): 227–38. http://dx.doi.org/10.1142/s021969130600118x.

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This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From

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ZHELUDEV, VALERY A., DAN D. KOSLOFF, and EUGENE Y. RAGOZA. "COMPRESSION OF SEGMENTED 3D SEISMIC DATA." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 03 (2004): 269–81. http://dx.doi.org/10.1142/s0219691304000536.

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We present a preliminary investigation of compression of segmented 3D seismic volumes for the rendering purposes. Promising results are obtained on the base of 3D discrete cosine transforms followed by the SPIHT coding scheme. An accelerated version of the algorithm combines 1D discrete cosine transform in vertical direction with the 2D wavelet transform of horizontal slices. In this case the SPIHT scheme is used for coding the mixed sets of cosine-wavelet coefficients.

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AVERBUCH, AMIR Z., VALERY A. ZHELUDEV, MOSHE GUTTMANN, and DAN D. KOSLOFF. "LCT-WAVELET BASED ALGORITHMS FOR DATA COMPRESSION." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 05 (2013): 1350032. http://dx.doi.org/10.1142/s021969131350032x.

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We present an algorithm that compresses two-dimensional data, which are piece-wise smooth in one direction and have oscillatory events in the other direction. Fine texture, seismic, hyper-spectral and fingerprints have this mixed structure. The transform part of the compression process is an algorithm that combines the application of the wavelet transform in one direction with the local cosine transform (LCT) in the other direction. This is why it is called hybrid compression. The quantization and the entropy coding parts in the compression process were taken from SPIHT codec but it can also b

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Liang, Yao, Xiaodong Ju, Anzong Li, Chuanwei Li, Zhiping Dai, and Li Ma. "The Process of High-Data-Rate Mud Pulse Signal in Logging While Drilling System." Mathematical Problems in Engineering 2020 (March 19, 2020): 1–11. http://dx.doi.org/10.1155/2020/3207087.

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We applied a mud pulse signal to transmit the downhole measured parameters in a Logging While Drilling (LWD) system. The high-data-rate mud pulse signal was almost completely overwhelmed by noise and difficult to be identified because of the narrow pulse width, impacts of the pump noise, and the reflected wave. The wavelet transform’s multiresolution is suitable for signal denoising. In this paper, during the denoising process of the wavelet transform, we used a series of evaluation parameters to select the optimal parameter combination for denoising a mud pulse signal. We verified the feasibi

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Yang, Lina, Yuan Yan Tang, Xiang Chu Feng, and Lu Sun. "Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing." Abstract and Applied Analysis 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/798080.

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Geometric (or shape) distortion may occur in the data acquisition phase in information systems, and it can be characterized by geometric transformation model. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation to remove the distortion for the geometric restoration. Consequently, finding a mathematical form to approximate the distorted image plays a key role in the restoration. A harmonic transformation cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation

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ARAI, KOHEI. "METHOD FOR DATA HIDING BASED ON LeGall 5/3 (COHEN-DAUBECHIES-FEAUVEAU: CDF 5/3) WAVELET WITH DATA COMPRESSION AND RANDOM SCANNING OF SECRET IMAGERY DATA." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (2013): 1360006. http://dx.doi.org/10.1142/s0219691313600060.

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Method for data hiding based on LeGall 5/3 of Cohen-Daubechies-Feauveau: CDF 5/3 wavelet with data compression and random scanning of secret imagery data together with steganography is proposed. Invisibility of secret imagery data is evaluated based on Peak Signal to Noise Ratio: PSNR with SIDBA standard image database. The experimental results show that PSNR of LeGall based wavelet utilized data hiding ranges from 43.82 to 46.9 while that of Daubechies based method ranges from 44.33 to 44.75 when the coded secret imagery data is inserted in the first 3 digits from Least Significant Bit: LSB o

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Wang, P., P. Yang, J. Arthur, and J. Y. H. Yang. "A dynamic wavelet-based algorithm for pre-processing tandem mass spectrometry data." Bioinformatics 26, no. 18 (2010): 2242–49. http://dx.doi.org/10.1093/bioinformatics/btq403.

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DUVAL, LAURENT, and CAROLINE CHAUX. "LAPPED TRANSFORMS AND HIDDEN MARKOV MODELS FOR SEISMIC DATA FILTERING." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 04 (2004): 455–76. http://dx.doi.org/10.1142/s0219691304000676.

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Seismic exploration provides information about the ground substructures. Seismic images are generally corrupted by several noise sources. Hence, efficient denoising procedures are required to improve the detection of essential geological information. Wavelet bases provide sparse representation for a wide class of signals and images. This property makes them good candidates for efficient filtering tools, allowing the separation of signal and noise coefficients. Recent works have improved their performance by modelling the intra- and inter-scale coefficient dependencies using hidden Markov model

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Zhou, Xiaohui. "Wavelet transform on regression trend curve and its application in financial data." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 05 (2020): 2050040. http://dx.doi.org/10.1142/s021969132050040x.

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In this paper, wavelet transform on a regression curve is investigated by using length-preserving projection and its application in financial data is also discussed. First, properties of wavelet filters on the regression trend curves are studied and two-scale equation of wavelet function is deduced on the regression trend curves. Second, the decomposition and reconstruction algorithm of discrete wavelet transform on regression trend curves is derived. Finally, two examples in financial data are given for discussion, based on decomposition and reconstruction algorithms on regression trend curve

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Xiong, Xiangtuan, Qiang Cheng, Yanfeng Kong, and Jin Wen. "A wavelet method for numerical fractional derivative with noisy data." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 05 (2016): 1650038. http://dx.doi.org/10.1142/s0219691316500387.

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Numerical fractional differentiation is a classical ill-posed problem in the sense that a small perturbation in the data can cause a large change in the fractional derivative. In this paper, we consider a wavelet regularization method for solving a reconstruction problem for numerical fractional derivative with noise. A Meyer wavelet projection regularization method is given, and the Hölder-type stability estimates under both apriori and aposteriori regularization parameter choice rules are obtained. Some numerical examples show that the method works well.

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Liu, Yi, Ji He Zhou, and An Yang. "Research of Flatting of Image Data of Human Movement." Applied Mechanics and Materials 457-458 (October 2013): 1232–35. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.1232.

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In order to insure the reliability of the biomechanics image analysis, the original image data should be in mathematical process, in which the noise data can be maximally removed while the real valid information can be reserved. This is the so called data smoothing. In recent years, few scholars conducted deep comparative studies in this area. Therefore, the present study tackles this rare issue, and fills in the gap of deep comparative studies involving different smoothing methods. This paper aims to test and compare these two different methods in their ability to process human movement image

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DONOHO, DAVID L., and XIAOMING HUO. "BEAMLAB AND REPRODUCIBLE RESEARCH." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 04 (2004): 391–414. http://dx.doi.org/10.1142/s0219691304000615.

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In the first 'Wavelets and Statistics' conference proceedings 1, our group published 'Wavelab and Reproducible Research', in which we advocated using the internet for publication of software and data so that research results could be duplicated by others. Much has happened in the last decade that bears on the notion of reproducibility, and we will review our experience. We will also describe a new software package BEAMLAB containing routines for multiscale geometric analysis, and describe some of its capabilities. BEAMLAB makes available, in one package, all the code to reproduce all the figur

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