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Journal articles on the topic 'Multiresolution wavelet analyses'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Gao, Jing Li, and Shi Hui Cheng. "The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials." Advanced Materials Research 684 (April 2013): 663–66. http://dx.doi.org/10.4028/www.scientific.net/amr.684.663.

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Frame theory has become a popular subject in scientific research during the past twenty years. In our study we use generalized multiresolution analyses in with dilation factor 4. We describe, in terms of the underlying multiresolution structure, all generalized multiresolution analyses Parseval frame wavelets all semi-orthogonal Parseval frame wavelets in . We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonica

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2

Lim, Jae Kun. "Gramian analysis of multivariate frame multiresolution analyses." Bulletin of the Australian Mathematical Society 66, no. 2 (2002): 291–300. http://dx.doi.org/10.1017/s0004972700040132.

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We perform a Gramian analysis of a frame multiresolution analysis to give a condition for it to admit a minimal wavelet set and to show that the frame bounds of the natural generator for the wavelet space of a degenerate frame multiresolution analysis shrink.

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Bhat, Mohd Younus. "Dual wavelets associated with nonuniform MRA." Tamkang Journal of Mathematics 50, no. 2 (2018): 119–32. http://dx.doi.org/10.5556/j.tkjm.50.2019.2646.

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A generalization of Mallats classical multiresolution analysis, based on thetheory of spectral pairs, was considered in two articles by Gabardo and Nashed. In thissetting, the associated translation set is no longer a discrete subgroup of R but a spectrumassociated with a certain one-dimensional spectral pair and the associated dilation is aneven positive integer related to the given spectral pair. In this paper, we construct dualwavelets which are associated with Nonuniform Multiresolution Analysis. We show thatif the translates of the scaling functions of two multiresolution analyses are bio

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4

San Antolín, A. "On Parseval Wavelet Frames via Multiresolution Analyses in." Canadian Mathematical Bulletin 63, no. 1 (2019): 157–72. http://dx.doi.org/10.4153/s0008439519000341.

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AbstractWe give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Oblique Extension Principle with the assumption that the origin is a point of approximate continuity of the Fourier transform of the involved refinable functions. Our results are written for reducing subspaces.

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Behera, Biswaranjan. "Wavelet packets associated with nonuniform multiresolution analyses." Journal of Mathematical Analysis and Applications 328, no. 2 (2007): 1237–46. http://dx.doi.org/10.1016/j.jmaa.2006.06.068.

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6

Jawerth, Björn, and Wim Sweldens. "An Overview of Wavelet Based Multiresolution Analyses." SIAM Review 36, no. 3 (1994): 377–412. http://dx.doi.org/10.1137/1036095.

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7

KING, EMILY J. "SMOOTH PARSEVAL FRAMES FOR L2(ℝ) AND GENERALIZATIONS TO L2(ℝd)". International Journal of Wavelets, Multiresolution and Information Processing 11, № 06 (2013): 1350047. http://dx.doi.org/10.1142/s0219691313500471.

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Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L2(ℝd) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝd, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of exist

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Jouini, Abdellatif, and Khalifa Trimèche. "Biorthogonal multiresolution analyses and decompositions of Sobolev spaces." International Journal of Mathematics and Mathematical Sciences 28, no. 9 (2001): 517–34. http://dx.doi.org/10.1155/s0161171201010936.

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The object of this paper is to construct extension operators in the Sobolev spacesHk(]−∞,0])andHk([0,+∞[)(k≥0). Then we use these extensions to get biorthogonal wavelet bases inHk(ℝ). We also give a construction inL2([−1,1])to see how to obtain boundaries functions.

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9

ANTOLÍN, A. SAN, and R. A. ZALIK. "A FAMILY OF NONSEPARABLE SMOOTH COMPACTLY SUPPORTED WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 02 (2013): 1350014. http://dx.doi.org/10.1142/s0219691313500148.

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We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L2(ℝd), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dimensions. Both the refinable functions and the wavelets can be made as smooth as desired. Estimates for the supports of these scaling functions and wavelets, are given.

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10

Kui, Zhiqing, Jean Baccou, and Jacques Liandrat. "On the construction of multiresolution analyses associated to general subdivision schemes." Mathematics of Computation 90, no. 331 (2021): 2185–208. http://dx.doi.org/10.1090/mcom/3646.

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Subdivision schemes are widely used in numerical mathematics such as signal/image approximation, analysis and control of data or numerical analysis. However, to develop their full power, subdivision schemes should be incorporated into a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a function, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated to a subdivision scheme are a decimation scheme and detail operators. Their construction is not straightforward as soon as the subdivision scheme is non-inter

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11

ABDEL KAREEM, WALEED, TAMER NABIL, SEIICHERIO IZAWA, and YU FUKUNISHI. "MULTIRESOLUTION AND NONLINEAR DIFFUSION FILTERING OF HOMOGENEOUS ISOTROPIC TURBULENCE." International Journal of Computational Methods 11, no. 01 (2013): 1350054. http://dx.doi.org/10.1142/s0219876213500540.

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The multiresolution (Gabor and wavelet transforms) and nonlinear diffusion filtering (NDF) methods are investigated to extract the coherent and incoherent parts of a forced homogeneous isotropic turbulent field. The aim of this paper is to apply two different analyses to decompose the turbulent field into organized coherent and random incoherent parts. The first analysis filtering process (Gabor and wavelet transforms) is based on the frequency domain; however the second NDF filtering analysis is implemented in the spatial domain. The turbulent field is generated using the Lattice Boltzmann me

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McLACHLAN, NEIL, DINESH KANT KUMAR, and JOHN BECKER. "WAVELET CLASSIFICATION OF INDOOR ENVIRONMENTAL SOUND SOURCES." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 01 (2006): 81–96. http://dx.doi.org/10.1142/s0219691306001105.

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Computational auditory scene analysis (CASA) has been attracting growing interest since the publication of Bregman's text on human auditory scene analysis, and is expected to find many applications in data retrieval, autonomous robots, security and environmental analysis. This paper reports on the use of Fourier transforms and wavelet transforms to produce spectral data of sounds from different sources for classification by neural networks. It was found that the multiresolution time-frequency analyses of wavelet transforms dramatically improved classification accuracy when statistical descript

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13

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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Shokouhi, Parisa, Nenad Gucunski, Ali Maher, and Sameh M. Zaghloul. "Wavelet-Based Multiresolution Analysis of Pavement Profiles as a Diagnostic Tool." Transportation Research Record: Journal of the Transportation Research Board 1940, no. 1 (2005): 79–88. http://dx.doi.org/10.1177/0361198105194000110.

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Discrete wavelet transform (DWT) was proposed as a new diagnostic tool for locating various frequency-related features of profiles, such as repeated waves and short-lived surface distress, that affect ride quality. The shortcomings of power spectrum density (PSD) analysis in evaluating the distribution of energy of a profile between various frequency band-widths were pointed out. The theoretical background and the basics of the DWT decomposition algorithm are discussed. Advantages of DWT analysis over PSD analysis in detection of short-lived features of the profile are illustrated by an exampl

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15

Nowak, Jennifer A., Anthony Ocon, Indu Taneja, Marvin S. Medow, and Julian M. Stewart. "Multiresolution wavelet analysis of time-dependent physiological responses in syncopal youths." American Journal of Physiology-Heart and Circulatory Physiology 296, no. 1 (2009): H171—H179. http://dx.doi.org/10.1152/ajpheart.00963.2008.

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Our prior studies indicated that postural fainting relates to thoracic hypovolemia. A supranormal increase in initial vascular resistance was sustained by increased peripheral resistance until late during head-up tilt (HUT), whereas splanchnic resistance, cardiac output, and blood pressure (BP) decreased throughout HUT. Our aim in the present study was to investigate the alterations of baroreflex activity that occur in synchrony with the beat-to-beat time-dependent changes in heart rate (HR), BP, and total peripheral resistance (TPR). We proposed that changes of low-frequency Mayer waves refle

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16

Peng, Lifang, Kefu Chen, and Ning Li. "Predicting Stock Movements: Using Multiresolution Wavelet Reconstruction and Deep Learning in Neural Networks." Information 12, no. 10 (2021): 388. http://dx.doi.org/10.3390/info12100388.

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Stock movement prediction is important in the financial world because investors want to observe trends in stock prices before making investment decisions. However, given the non-linear non-stationary financial time series characteristics of stock prices, this remains an extremely challenging task. A wavelet is a mathematical function used to divide a given function or continuous-time signal into different scale components. Wavelet analysis has good time-frequency local characteristics and good zooming capability for non-stationary random signals. However, the application of the wavelet theory

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Rathinasamy, Maheswaran, and Rakesh Khosa. "Multiscale nonlinear model for monthly streamflow forecasting: a wavelet-based approach." Journal of Hydroinformatics 14, no. 2 (2011): 424–42. http://dx.doi.org/10.2166/hydro.2011.130.

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The dynamics of the streamflow in rivers involve nonlinear and multiscale phenomena. An attempt is made to develop nonlinear models combining wavelet decomposition with Volterra models. This paper describes a methodology to develop one-month-ahead forecasts of streamflow using multiscale nonlinear models. The method uses the concept of multiresolution decomposition using wavelets in order to represent the underlying integrated streamflow dynamics and this information, across scales, is then linked together using the first- and second-order Volterra kernels. The model is applied to 30 river dat

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18

Labat, D., R. Ababou, and A. Mangin. "Rainfall–runoff relations for karstic springs. Part II: continuous wavelet and discrete orthogonal multiresolution analyses." Journal of Hydrology 238, no. 3-4 (2000): 149–78. http://dx.doi.org/10.1016/s0022-1694(00)00322-x.

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Liu, Xiaojing, G. R. Liu, Jizeng Wang, and Youhe Zhou. "A wavelet multiresolution interpolation Galerkin method with effective treatments for discontinuity for crack growth analyses." Engineering Fracture Mechanics 225 (February 2020): 106836. http://dx.doi.org/10.1016/j.engfracmech.2019.106836.

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Jian, Zhao, Sun Meiling, Jia Jian, Huang Luxi, Han Fan, and Liu Shan. "Image Watermark Based on Extended Shearlet and Insertion Using the Largest Information Entropy on Horizontal Cone." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/450819.

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Extended discrete shearlet provides a directional multiresolution decomposition. It has been mathematically shown that extended discrete shearlet is a more efficient representation for the signals containing distributed discontinuities such as edges, compared to discrete wavelet. Multiresolution analyses such as curvelet and ridgelet share similar properties, yet their directional representations are significantly different from that of extended discrete shearlet. Taking advantage of the unique properties of directional representation of extended discrete shearlet, we develop an image watermar

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Liu, Weixin, Yujia Wang, Baoji Yin, Xing Liu, and Mingjun Zhang. "Thruster fault identification based on fractal feature and multiresolution wavelet decomposition for autonomous underwater vehicle." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 13 (2016): 2528–39. http://dx.doi.org/10.1177/0954406216632280.

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There exist some problems when the fractal feature method is applied to identify thruster faults for autonomous underwater vehicles (AUVs). Sometimes it could not identify the thruster fault, or the identification error is large, even the identification results are not consistent for the repeated experiments. The paper analyzes the reasons resulting in these above problems according to the experiments on AUV prototype with thruster faults. On the basis of these analyses, in order to overcome the above deficiency, an improved fractal feature integrated with wavelet decomposition identification

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HSU, WEI-YEN. "CONTINUOUS EEG SIGNAL ANALYSIS FOR ASYNCHRONOUS BCI APPLICATION." International Journal of Neural Systems 21, no. 04 (2011): 335–50. http://dx.doi.org/10.1142/s0129065711002870.

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In this study, we propose a two-stage recognition system for continuous analysis of electroencephalogram (EEG) signals. An independent component analysis (ICA) and correlation coefficient are used to automatically eliminate the electrooculography (EOG) artifacts. Based on the continuous wavelet transform (CWT) and Student's two-sample t-statistics, active segment selection then detects the location of active segment in the time-frequency domain. Next, multiresolution fractal feature vectors (MFFVs) are extracted with the proposed modified fractal dimension from wavelet data. Finally, the suppo

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SHAH, FIRDOUS AHMAD. "CONSTRUCTION OF WAVELET PACKETS ON p-ADIC FIELD." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (2009): 553–65. http://dx.doi.org/10.1142/s0219691309003082.

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Wavelet packets are subsets of a multiresolution analysis and retain many of the orthogonality, smoothness and localization properties of their parent wavelets. In this paper, we study the construction of p-wavelet packets associated with multiresolution p-analysis defined by Farkov for L2(ℝ+). The collection of all dilations and translations of the wavelet packets defines the general wavelet packets and is an overcomplete system.

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Sharma, Vikram, and P. Manchanda. "WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE." Asian-European Journal of Mathematics 06, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s1793557113500071.

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Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10

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Gao, Hong Wei, and Li Ping Ding. "Existence and Designment of Filter Banks of Biorthogonal Vector-Valued Wavelets with Three-Scale Constant Factor." Key Engineering Materials 439-440 (June 2010): 938–43. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.938.

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In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for constructing a class of biorthogonal compactly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

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SHEN, JUN, WEI SHEN, and DANFEI SHEN. "ON GEOMETRIC AND ORTHOGONAL MOMENTS." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 07 (2000): 875–94. http://dx.doi.org/10.1142/s0218001400000581.

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Moments are widely used in pattern recognition, image processing, computer vision and multiresolution analysis. To clarify and to guide the use of different types of moments, we present in this paper a study on the different moments and compare their behavior. After an introduction to geometric, Legendre, Hermite and Gaussian–Hermite moments and their calculation, we analyze at first their behavior in spatial domain. Our analysis shows orthogonal moment base functions of different orders having different number of zero-crossings and very different shapes, therefore they can better separate ima

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Chen, Qing Jiang, and Jian Tang Zhao. "Constructional Approaches on Vector-Valued Wavelets with Multi-Scale Dilation Factor." Key Engineering Materials 460-461 (January 2011): 323–28. http://dx.doi.org/10.4028/www.scientific.net/kem.460-461.323.

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In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc- -ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived

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SHUKLA, NIRAJ K. "NON-MSF A-WAVELETS FROM A-WAVELET SETS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (2013): 1350002. http://dx.doi.org/10.1142/s0219691313500021.

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Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W, we conclude that the non-MSF A-wavelet and the A-wavelet set through which it is constructed possess the same nature as far as the multiresolution analysis is concerned. Some examples of non-MSF d-wavelets and

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LEVAN, NHAN, and CARLOS S. KUBRUSLY. "TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 03 (2004): 237–48. http://dx.doi.org/10.1142/s0219691304000494.

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A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ2(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2m. This is achieved by means of "el

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Wang, Guo Xin, and De Lin Hua. "The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support." Advanced Materials Research 219-220 (March 2011): 496–99. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.496.

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The frame theory has been one of powerful tools for researching into wavelets. In this article, the notion of orthogonal nonseparable quarternary wavelet wraps, which is the generalizati- -on of orthogonal univariate wavelet wraps, is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A liable approach for constructing two-directional orthogonal wavelet wraps is developed. The orthogonality property of quarternary wavelet wraps is discussed. Three orthogonality formulas concerning these wavelet wraps are estabished. A constructive

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Yu, Bao Min. "On Existence of Matrix-Valued Wavelets." Advanced Materials Research 282-283 (July 2011): 153–56. http://dx.doi.org/10.4028/www.scientific.net/amr.282-283.153.

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Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, we investigate the existence of matrix-valued wavelet associated with a matrix-valued multireslution analysis. By using operator polar decomposition, we provide a new proof for the existence of matrix-valued wavelets. We prove that, like in the scalar case, every matrix-valued multiresolution analysis guarantees the existence of an orthogonal matrix-valued wavelet.

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Yang, Wei Qing. "Study of High Dimensional Orthogonal Vector-Valued Wavelet with Scale 4." Advanced Materials Research 790 (September 2013): 665–68. http://dx.doi.org/10.4028/www.scientific.net/amr.790.665.

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In this paper, we introduce the definition of vector-valued multiresolution analysis with scale 4 and orthogonal vector-valued wavelet with scale 4 is gived. The properties of compactly supported orthogonal vector-valued wavelets with scale 4 are proved.

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Yu, Yu Min, and Zong Sheng Sheng. "Constructive Algorithm to Two-Directional Biorthogonal Shortly Supported Wavelets with Poly-Scale Dilation Factor." Advanced Materials Research 171-172 (December 2010): 113–16. http://dx.doi.org/10.4028/www.scientific.net/amr.171-172.113.

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In this work, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelet packets is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a class of biorthogonal shortly supported vector-valued wavelet functions is presented by using

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Zhao, Jian Tang. "Designment Algorithm on Orthogonal Two-Directional Vector-Valued Wavelets with Three-Scale Dilation Factor." Advanced Materials Research 430-432 (January 2012): 1203–6. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.1203.

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In this work, the notion of orthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional orthogonal wavelet wraps is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a sort of orthogonal shortly supported two-directional vector-valued wavelet functions is

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Fu, Shengyu, B. Muralikrishnan, and J. Raja. "Engineering Surface Analysis With Different Wavelet Bases." Journal of Manufacturing Science and Engineering 125, no. 4 (2003): 844–52. http://dx.doi.org/10.1115/1.1616947.

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Traditional surface texture analysis involves filtering surface profiles into different wavelength bands commonly referred to as roughness, waviness and form. The primary motivation in filtering surface profiles is to map each band to the manufacturing process that generated the part and the intended functional performance of the component. Current trends in manufacturing are towards tighter tolerances and higher performance standards that require close monitoring of the process. Thus, there is a need for finer bandwidths for process mapping and functional correlation. Wavelets are becoming in

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Caso, Gregory, and C. C. Jay Kuo. "Multiresolution Analysis of Fractal Image Compression." Fractals 05, supp01 (1997): 215–29. http://dx.doi.org/10.1142/s0218348x97000772.

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In this research, we perform a multiresolution analysis of the mappings used in fractal image compression. We derive the transform-domain structure of the mappings and demonstrate a close connection between fractal image compression and wavelet transform coding using the Haar basis. We show that under certain conditions, the mappings correspond to a hierarchy of affine mappings between the subbands of the transformed image. Our analysis provides new insights into the mechanism underlying fractal image compression, leads to a new non-iterative transform-domain decoding algorithm, and suggests a

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Feng, Jin Shun, and Qing Jiang Chen. "A Study of a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials." Advanced Materials Research 889-890 (February 2014): 1270–74. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.1270.

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The existence of compactly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal shortly supported vector-valued scaling functions is researched. We introduce a class of two-directional vector-valued four-dimensional wavelet wraps according to a dilation matrix, which are generalizations of univariate wavelet wraps. Three orthogonality formulas regarding the wavelet wraps are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet wraps. The sufficient condition for the existence of four-dimensional wavelet wraps is e

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González-Concepción, C., M. C. Gil-Fariña, and C. Pestano-Gabino. "Using Wavelets to Understand the Relationship between Mortgages and Gross Domestic Product in Spain." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/917247.

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We use wavelet multiresolution decomposition and cross-wavelet analysis to reveal certain properties in financial data related to mortgages to households and gross domestic product data in Spain. Wavelet techniques possess many desirable properties, some of which are useful as a vehicle for analysing economic and financial data. In our case, wavelets are useful for drawing conclusions both in the time and frequency domains and for obtaining information on the different phases through which the study variables progress.

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EHLER, MARTIN. "COMPACTLY SUPPORTED MULTIVARIATE, PAIRS OF DUAL WAVELET FRAMES OBTAINED BY CONVOLUTION." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 02 (2008): 183–208. http://dx.doi.org/10.1142/s0219691308002306.

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In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable functions, i.e. the refinable function has minimal mask size with respect to smoothness and approximation order of its generated multiresolution analysis. The wavelet system has maximal approximation orde

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Bunrit, Supaporn, Nittaya Kerdprasop, and Kittisak Kerdprasop. "Multiresolution Analysis Based on Wavelet Transform for Commodity Prices Time Series Forecasting." International Journal of Machine Learning and Computing 8, no. 2 (2018): 175–80. http://dx.doi.org/10.18178/ijmlc.2018.8.2.683.

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Olphert, Sean, and Stephen C. Power. "Higher Rank Wavelets." Canadian Journal of Mathematics 63, no. 3 (2011): 689–720. http://dx.doi.org/10.4153/cjm-2011-012-1.

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Abstract A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in L2(ℝd). While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct Latin square wavelets as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the a

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BANAKAR, AHMAD, MOHAMMAD FAZLE AZEEM, and VINOD KUMAR. "COMPARATIVE STUDY OF WAVELET BASED NEURAL NETWORK AND NEURO-FUZZY SYSTEMS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (2007): 879–906. http://dx.doi.org/10.1142/s0219691307002099.

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Based on the wavelet transform theory and its well emerging properties of universal approximation and multiresolution analysis, the new notion of the wavelet network is proposed as an alternative to feed forward neural networks and neuro-fuzzy for approximating arbitrary nonlinear functions. Earlier, two types of neuron models, namely, Wavelet Synapse (WS) neuron and Wavelet Activation (WA) functions neuron have been introduced. Derived from these two neuron models with different non-orthogonal wavelet functions, neural network and neuro-fuzzy systems are presented. Comparative study of wavele

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SASTRY, CHALLA S., and P. C. DAS. "WAVELET BASED MULTILEVEL BACKPROJECTION ALGORITHM FOR PARALLEL AND FAN BEAM SCANNING GEOMETRIES." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (2006): 523–45. http://dx.doi.org/10.1142/s0219691306001427.

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In the present work, a new multilevel backprojection procedure for both parallel and fan beam geometries based on 1D MRA wavelet is derived and analyzed. It is based on the characterization property of orthonormal wavelets via their autocorrelation functions. The algorithm does not involve any wavelet-based decomposition in the normal sense, yet it uses a multiresolution formula as a crucial element in a CBP type procedure valid for both the parallel and complex fan beam geometries. The algorithm can be used for wavelet based image analysis.

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Han, Ke Zhong. "An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support." Advanced Materials Research 461 (February 2012): 835–39. http://dx.doi.org/10.4028/www.scientific.net/amr.461.835.

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Wavelet analysis is nowadays a widely used tool in applied mathe-matics. The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years.. The notion of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with multi-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An

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Turkheimer, Federico E., Matthew Brett, Dimitris Visvikis, and Vincent J. Cunningham. "Multiresolution Analysis of Emission Tomography Images in the Wavelet Domain." Journal of Cerebral Blood Flow & Metabolism 19, no. 11 (1999): 1189–208. http://dx.doi.org/10.1097/00004647-199911000-00003.

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This article develops a theoretical framework for the use of the wavelet transform in the estimation of emission tomography images. The solution of the problem of estimation addresses the equivalent problems of optimal filtering, maximum compression, and statistical testing. In particular, new theory and algorithms are presented that allow current wavelet methodology to deal with the two main characteristics of nuclear medicine images: low signal-to-noise ratios and correlated noise. The technique is applied to synthetic images, phantom studies, and clinical images. Results show the ability of

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Shi, Jun, Xiaoping Liu, and Naitong Zhang. "Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform." Signal, Image and Video Processing 9, no. 1 (2013): 211–20. http://dx.doi.org/10.1007/s11760-013-0498-2.

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Lv, Yan Hui, and Jin Shun Feng. "Designment and Traits of Quarternary Multiwavelets and Applications in Solid-State Physics and Materials Science." Advanced Materials Research 485 (February 2012): 189–92. http://dx.doi.org/10.4028/www.scientific.net/amr.485.189.

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Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. New physics emerge because of the diverse new material properties which need to be explained. In this work, the notion of vector-valued multiresolution analysis and biorthogonal binary multi- tiwavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for constructing a c

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Brassarote, Gabriela De Oliveira Nascimento, Eniuce Menezes de Souza, and João Francisco Galera Monico. "Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation." TEMA (São Carlos) 16, no. 2 (2015): 119. http://dx.doi.org/10.5540/tema.2015.016.02.0119.

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Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the

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VAMPA, VICTORIA, MARÍA T. MARTÍN, and EDUARDO SERRANO. "A NEW REFINEMENT WAVELET–GALERKIN METHOD IN A SPLINE LOCAL MULTIRESOLUTION ANALYSIS SCHEME FOR BOUNDARY VALUE PROBLEMS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 02 (2013): 1350015. http://dx.doi.org/10.1142/s021969131350015x.

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In this work, a new Wavelet–Galerkin method for boundary value problems is presented. It improves the approximation in terms of scaling functions obtained through a collocation scheme combined with variational equations. A B-spline multiresolution structure on the interval is designed in order to refine the solution recursively and efficiently using wavelets. Numerical examples are given to verify good convergence properties of the proposed method.

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Akimov, Pavel A., and Mojtaba Aslami. "Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam." Applied Mechanics and Materials 580-583 (July 2014): 2924–27. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2924.

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This paper is devoted to correct and efficient method of local static analysis of Bernoulli beam on elastic foundation. First of all, problem discretized by finite difference method, and then transformed to a localized one by using the Haar wavelets. Finally, imposing an optimal reduction in wavelet coefficients, the localized, reduced results can be obtained. It becomes clear after comparison with analytical solutions, that the localization of the problem by multiresolution wavelet approach gives exact solution in desired regions of beam even in high level of reduction in wavelet coefficients

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