Journal articles: 'Wavelets (Mathematics) – Data processing'

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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 (September 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 utilized. Training data are used to construct probability distributions required for the computation of the entropy and mutual information. In our data analysis, we have used machine data acquired from a single cylinder engine under a series of induced faults in a test environment. The objective of the experiment was to evaluate the performance of the informative wavelet algorithm for the accuracy of classification results using a real-world machine data and to examine to what extent the results were influenced by different analyzing wavelets chosen for data analysis. Accuracy of classification results as related to the correlation structure of the coefficients is also discussed in the paper.

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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 (September 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 (June 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 wavelets having low data communication property such as the Haar wavelet are expected to be suitable for the purpose of improving computing performance. In this study, we also pay attention to the basic characteristics of the Haar-wavelet-based preconditioning method for a Poisson equation solver.

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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 (September 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 thresholding of the form [Formula: see text], where σ is minimal variance of the sum of packet decomposition of chosen level. 3. Cluster analysis of decomposed data. All programs were elaborated using program MATLAB 5.

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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 warn the reader that there are other viewpoints that are either not represented here or discussed only briefly. For example, orthogonal wavelets were developed primarily in the context of signal processing, an application upon which we touch only indirectly. However, there are several good expositions (e.g. Daubechies (1990) and Rioul and Vetterli (1991)) of this application. A discussion of wavelet decompositions in the context of Littlewood-Paley theory can be found in the monograph of Frazieret al. (1991). We shall also not attempt to give a complete discussion of the history of wavelets. Historical accounts can be found in the book of Meyer (1990) and the introduction of the article of Daubechies (1990). We shall try to give sufficient historical commentary in the course of our presentation to provide some feeling for the subject's development.

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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 (May 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 processing techniques are successful in many data processing techniques like image and video processing. But, the use of wavelets in analyzing the microarray bio-signals is not sufficiently probed. The aim of this paper is to propose a wavelet power spectrum based technique for dimensionality reduction through gene selection and classification problem of gene microarray data. The proposed method was administered on such datasets and the results are encouraging. The present method is robust to noise since no preprocessing has been applied. Also, it does not require any critical input parameters or any prior knowledge about the data which is required in many existing methods.

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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 (January 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 watermarking schemes using discrete wavelet transform (DWT), biorthogonal DWT and M-band wavelets coupled with various modulation, multiplexing and signaling techniques. The performance of the watermarking methods are also reported along with the relative merits and demerits.

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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 (September 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 criterion based on better localization of specific frequency components and accurate estimation of their amplitudes is used to select an appropriate wavelet. It is shown here that the discrete Meyer wavelet has the best frequency properties among the wavelet families considered (Haar, Daubechies, Coiflet and Symlet). In rainfall data, the present analysis reveals two additional spectral peaks besides the fifteen found by classical spectral analysis. Moreover, these two new peaks have been found to be statistically significant, although a detailed discussion of testing for significance is being presented elsewhere.

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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 (September 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 efficient computations, it also has the potential application for the texture segmentation of hexagonal data. While in the field of computer-aided geometric design (CAGD), when the filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms for regular vertices have high symmetry, which make it possible to design the corresponding multiresolution algorithms for extraordinary vertices. In this paper we study the construction of six-fold axial symmetric biorthogonal filter banks and the associated wavelets, with both the dyadic and [Formula: see text]-refinements. The constructed filter banks have the desirable symmetry for hexagonal data processing. By associating the outputs (after one-level multiresolution decomposition) appropriately with the nodes of the regular triangular mesh with which the input data is associated (sampled), we represent multiresolution analysis and synthesis algorithms as templates. The six-fold axial symmetric filter banks constructed in this paper result in algorithm templates with desirable symmetry for triangle surface processing.

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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). Also, these functions have a local support, which allows to decrease complexity of numerical algorithms. Besides, it was shown that spaces of atomic functions have good approximation properties, which can reduce the error of computations. Hence, application of atomic functions is perspective. There are different ways to use atomic functions and their generalizations in practice. One such approach is a construction and application of wavelet-like structures. In this paper, generalized atomic wavelets are constructed using generalized Fup-functions and formulas for their evaluation are obtained. Also, the main properties of generalized atomic wavelets are presented. In addition, it is shown that these wavelets are smooth functions with a local support and have good approximation properties. Furthermore, the set of generalized atomic wavelets is a wide class of functions with flexible parameters that can be chosen according to specific needs. This means that the constructive analysis tool, which is introduced in this paper, gives researches and developers of algorithms flexible possibilities of adapting to the specifics of various problems. In addition, the problem of representation of data using generalized atomic wavelets is considered. Generalized atomic wavelets expansion of data is introduced. Such an expansion is a sum of trend or principal value function and several functions that describe the corresponding frequencies. The remainder term, which is an error of approximation of data by generalized atomic wavelets, is small. To estimate its value the inequalities from the previous papers of V. A. Rvachev, V. O. Makarichev and I. V. Brysina can be used

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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 (January 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 illustrated.

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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 (March 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 a compression of some spherical data and calculate some norms of the compression error for different compression rates. The main advantage is the orthogonality and sparsity of the decomposition and reconstruction matrices.

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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 (April 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 modal rotation fields due to the damage is carried out. The order of the B-spline wavelets used in the post-processing of the modal rotation fields is discussed. The damage detectability in terms of its intensity, the selected mode, and the type of rotation field and wavelet coefficient is also studied. Finally, a scheme for the damage detectability enhancement, in particular for multiple damage scenarios, is proposed.

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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 (November 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 data that leads to lossless processing and creation of correlation among the host samples due to its mathematical structure. Watermark information is then embedded using dither modulation (DM)-based quantization index modulation (QIM). The relative gain in imperceptibility and robustness performance are reported for direct watermark embedding on entropy decoded host, using repetition code, convolution code, and finally the combined use of channel codes and integer wavelets. Simulation results show that 6.24 dB (9.50 dB) improvement in document-to-watermark ratio (DWR) at watermark power 12.73 dB (16.81 dB) and 15 dB gain in noise power for watermark decoding at bit error rate (BER) of 10-2 are achieved, respectively over direct watermarking on entropy decoded data.

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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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ROŞCA, DANIELA. "WEIGHTED HAAR WAVELETS ON THE SPHERE." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 03 (May 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 the capability to detect the singularities (contours). The method described here can be also used for constructing spherical wavelets starting from wavelets on an interval.

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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 (June 30, 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, rather than wavelets that exhibit the relatively flat spectrum produced by modern data processing workflows. One of the most common processing steps is to spectrally balance the data either explicitly in the frequency domain or implicitly through wavelet shaping deconvolution. If the poststack seismic data have gone through spectral balancing/whitening to improve their seismic resolution, the wavelet would exhibit a flat spectrum instead of a Ricker or Gaussian shape. We have addressed the influence of spectral balancing on seismic attenuation analysis. Our mathematical analysis shows that attenuation attributes are still effective for poststack seismic data after certain types of spectral balancing. More importantly, this analysis explains why seismic attenuation attributes work for real seismic applications with common seismic processing procedures. Synthetic and field data examples validate our conclusions.

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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 (June 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 as the same way as those of conventional discrete wavelets. MWT is based on this data modeling to provide multiresolution analysis in an efficient manner. Three-dimensional MWT demonstrates a classification of a weather satellite infrared animation into background and cloud-moving frame images.

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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 (April 27, 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-function mathematical approaches for real-time applications, it is necessary to introduce an effective D/A conversion scheme as well as to modify the desired continuous-function mathematical method for online implementation. The powerful signal processing tool to be discussed in this paper is the synchrosqueezed continuous wavelet transform (SST), which requires computation of the continuous wavelet transform (CWT), as well as its derivative, of the analog signal of interest. An important application of this transform is to extract information, such as the underlying dynamics, hidden in the signal representation. The first objective of this paper is to introduce a unified approach to remove the two main obstacles for adapting the SST approach to irregular data samples in order to allow online computation. Firstly, for D/A conversion, a real-time algorithm, based on spline functions of arbitrarily desired order, is proposed to interpolate the irregular data samples, while preserving all polynomials of the same spline order, with assured maximum order of approximation. Secondly, for real-time dynamic information extraction from an oscillatory signal via SST, a family of vanishing-moment and minimum-supported spline-wavelets (to be called VM wavelets) are introduced for online computation of the CWT and its derivative. The second objective of this paper is to apply the proposed real-time algorithm and VM wavelets to clinical applications, particularly to the study of the “anesthetic depth” of a patient during surgery, with emphasis on analyzing two dynamic quantities: the “instantaneous frequencies” and the “non-rhythmic to rhythmic ratios” of the patient’s respiration, based on a one-lead electrocardiogram (ECG) signal. Indeed, the “R-peaks” of the ECG signal, which constitute a waveform landmark for clinical evaluation, are non-uniform samples of the respiratory signal. It is envisioned that the proposed algorithm and VM wavelets should enable real-time monitoring of “anesthetic depth”, during surgery, from the respiration signal via ECG measurement.

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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 (September 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. Using the IBC design spectrum as network input means an accelerogram may be generated for any geographic location regardless of whether earthquake records exist for that particular location or not. In order to improve the efficiency of the model, the CPN network is modified with the addition of the wavelet transform as a data compression tool to create a new CPN-wavelet network. The proposed CPN-wavelet model is trained using 20 sets of accelerograms and tested with additional five sets of accelerograms available from the U.S. Geological Survey. Given the limited set of training data, the result is quite remarkable.

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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 (January 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 to find the optimal wavelet of a signal in an efficient, little data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. We show the validity of our approach constrained to given families of wavelets, though it can be generalized for a continuous unconstrained search scheme.

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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 (January 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 proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

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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 (November 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 using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

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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 (June 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 Fourier transform makes it possible to the number of data comprising a power of 2. We have applied this interpolation for the wind vector image data, and we have tried to compress the data by the multiresolution analysis by using the three-dimensional discrete wavelet transform. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.

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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 (April 11, 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 (July 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 linear interpolating prediction operator. This operator easily allows extensions towards directional offsets from predictions, leading to an edge-adaptive nonlinear multiscale decomposition.

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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 (September 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 (May 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 values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

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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-type functions that localize signal energy in a joint time-frequency and/or space-frequency domain. These techniques can be expressed as multi-resolution transformations, of which perhaps the best known is the wavelet transform. In this paper we review wavelets, and other related multi-resolution transforms, within the context of identifying signatures for disease. These transforms construct a general representation of signals which can be used in detection, diagnosis and treatment monitoring. We present several examples where these transforms are applied to biomedical signal and imaging processing. These include computer-aided diagnosis in mammography, real-time mosaicking of ophthalmic slit-lamp imagery, characterization of heart disease via ultrasound, predicting epileptic seizures and signature analysis of the electroencephalogram, and reconstruction of positron emission tomography data.

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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 (December 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 in the Mock-up experiment and to characterize them quantitatively; to understand the nature and consequences of several incidents happening in the Mock-up during the heating phase; and, finally, to analyze the data reliability of the sensors measurements and to predict possible failures.The analysis techniques used in this work are both statistical (time series correlation and spectral analysis, wavelets analysis, matching pursuit analysis) and non-statistical (spatial distribution analysis of data). These methods aim to establish the existing relationships between several data series registered in the experiment, corresponding to the measured parameters, and to characterize on time and frequency the non-stationary response of the series. A better understanding of the main THM processes affecting the engineered barriers used for the isolation of the radioactive waste is then available with the results obtained from those analyses.

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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 (November 30, 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 (December 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) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively.

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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 (September 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 scratch. Monochromatic old images and images with simulated scratches have been considered to validate the method.

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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 (January 4, 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 (July 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 external noise (e.g., electromagnetic waves). Heart rate variability (HRV) is a well-known phenomenon with fluctuation in the time interval between heartbeats. The lack of translation invariance is a serious defect in the conventional wavelet transforms (discrete wavelet transform (DWT)). Fluctuation of the impulse response at each energy level is observed in the multi-resolution analysis (MRA). Configurational changes in the ECG waveforms are frequently observed after noise reduction by the conventional wavelet transforms. Both the lack of translation invariance of conventional wavelet transforms and HRV cause deformation of the ECG waveforms. We describe here the CDWTs with perfect translation invariance (PTI). Compared with conventional wavelets, PTI of the fECG and fMCG resulted in only minor configurational changes in the ECG waveforms. This technique yields persistently stable ECG waveforms, including P wave and QRS complex. First, an independent component analysis (ICA) was applied to fECG or fMCG data to remove noise. We provide an example to show that the morphological change in QRS complex is barely affected when PTI is applied to normal fECG. Examples of fetal arrhythmias, such as ventricular trigeminy, ventricular bigeminy and premature atrial contraction are demonstrated using this technique. The results lead us to the conclusion that ICA and noise reduction in fECG and fMCG by PTI are promising methods for the diagnosis of fetal arrhythmia.

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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 (March 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-homogeneous regions in the image can be treated to have different texture properties. Based on this assumption the multi-class texture segmentation scheme is applied for this purpose.

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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 (November 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 by substituting the right side with 0 elements to make the length of time series to 2n, which consequently, distortion of a signal occurs. The Polar wavelet does not only suggest the solution of the low distinction between time sequences of similar averages in Harr wavelet transform, but also improves the search performance as the length of time series is increased. Actually, several kinds of data such as rainfall are locally distributed and have the similar averages, so Harr wavelet which transforms data using their averages has shortcomings, naturally. To solve this problem, the Polar wavelet uses the polar coordinates which are not affected from averages and can improve the search performance especially in locally distributed time series databases. In addition, we show that the Polar wavelet guarantees no false dismissals. The effectiveness of the Polar wavelet is evaluated empirically on real weather data and the syntactic data, reporting the significant improvements in reducing the search space.

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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 (July 9, 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 complex flows, and the continuous wavelet transform (CWT) is a powerful tool to aid in their elucidation. Five case studies are presented involving many of these phenomena in which the CWT was key to data analysis and interpretation. A diverse set of experiments are presented involving a range of physical and temporal scales and experimental techniques. Bubble turbulent break-up is investigated using hydroacoustics, bubble dynamics and high-speed imaging; microbubbles are sized using light scattering and ultrasonic sensing, and large-scale coherent shedding driven by various mechanisms are analysed using simultaneous high-speed imaging and physical measurement techniques. The experimental set-up, aspect of cavitation being addressed, how the wavelets were applied, their advantages over other techniques and key findings are presented for each case study. This paper is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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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 (June 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 the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

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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 (September 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 (September 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 be taken from any multiresolution based codec such as EZW. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. When oscillating events are present in different directions as in fingerprints or when the image comprises of a fine texture, a 2D LCT with coefficients reordering is applied. These algorithms outperform algorithms that are solely based on the the application of 2D wavelet transforms to each direction with either SPIHT or EZW coding including JPEG2000 compression standard. The proposed algorithms retain fine oscillating events including texture even at a low bitrate. Its compression capabilities are also demonstrated on multimedia images that have a fine texture. The wavelet part in the mixed transform of the hybrid algorithm utilizes the Butterworth wavelet transforms library that outperforms the 9/7 biorthogonal wavelet transform.

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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 feasibility of the wavelet transform denoising algorithm by analysing and processing an operational high-data-rate mud pulse signal. The decoding algorithm was available by applying self-correlation and bit synchronization. The application results through a field application showed that the processing algorithm was suitable for the high-data-rate mud pulse signal’s process.

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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 (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the geometric restoration. In this paper, a novel wavelet-based method is presented, which consists of three phases. In phase 1, the partial differential equation is converted into boundary integral equation and representation by an indirect method. In phase 2, the boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. In phase 3, the plane integral equation and representation are then solved by a method we call wavelet collocation. The performance of our method is evaluated by numerical experiments.

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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 (July 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 of the original image. Data compression ratio for the secret imagery data ranges from 1.3 to 19.4 which depends on the complexity of the secret imagery data. Meanwhile, PSNR of data hidden image ranges from 46.83 to 47.41. Consequently, the proposed data hiding method is permissive because PSNR is over 40 dB results in satisfaction on invisibility of the secret imagery data in the data hidden image.

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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 (July 13, 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 (December 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 models, since image features tend to cluster and persist in the wavelet domain. This work focuses on the use of lapped transforms associated with hidden Markov modelling. Lapped transforms are traditionally viewed as block-transforms, composed of M pass-band filters. Seismic data present oscillatory patterns and lapped transforms oscillatory bases have demonstrated good performances for seismic data compression. A dyadic like representation of lapped transform coefficient is possible, allowing a wavelet-like modelling of coefficients dependencies. We show that the proposed filtering algorithm often outperforms the wavelet performance both objectively (in terms of SNR) and subjectively: lapped transform better preserve the oscillatory features present in seismic data at low to moderate noise levels.

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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 (June 24, 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 curves. Some new research interpretations are presented in dealing with financial data such as “volatility on regression growth trend”, “error on regression growth trend”, and so on.

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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 (August 24, 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 images. The result is readied by applying theoretical analysis and conducting experiments. The present study relies on various mathematics principles of interpolation and filter methods, the comparison between the merits and demerits, range of applications and effects of different interpolation and filter combinations. The present study then adopts experimental method to validate the hypothesis and reach our conclusion. We obtain the conclusion that it is better to use low-pass filtering to remove the high-frequency noise data, a method which is used by most scholars. However, the data of IIR is closer to the original value and has a better effect, when processing smoothly change data. Henceforth, new process method from other areas can be tentatively introduced to improve the precision of data processing, such as wavelet analysis method, integrated use of multistage filtering analysis and so on.

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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 (December 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 figures in our recently published articles on beamlets, curvelets and ridgelets. The interested reader can inspect the source code to see what algorithms were used, and how parameters were set to produce the figures, and will then be able to modify the source codes to produce variations of our results. Some new examples of numerical studies based on BEAMLAB are provided here.

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

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