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Journal articles on the topic 'MULTIWAVELET'

Author: Grafiati

Published: 11 September 2023

Last updated: 25 July 2025

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1

Shouzhi, Yang. "Biorthogonal interpolatory multiscaling functions and corresponding multiwavelets." ANZIAM Journal 49, no. 1 (2007): 85–97. http://dx.doi.org/10.1017/s1446181100012694.

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A method for constructing a pair of biorthogonal interpolatory multiscaling functions is given and an explicit formula for constructing the corresponding biorthogonal multiwavelets is obtained. A multiwavelet sampling theorem is also established. In addition, we improve the stability of the biorthogonal interpolatory multiwavelet frame by the linear combination of a pair of biorthogonal interpolatory multiwavelets. Finally, we give an example illustrating how to use our method to construct biorthogonal interpolatory multiscaling functions and corresponding multiwavelets.

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2

Huang, Yongdong, Qiufu Li, and Ming Li. "Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor." Mathematical Problems in Engineering 2012 (2012): 1–37. http://dx.doi.org/10.1155/2012/640789.

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In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finall

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3

Kromka, Jozef, Antónia Jusková, and Ján Šaliga. "ECG Sparsity Evaluation on a Multiwavelet Basis." Acta Electrotechnica et Informatica 23, no. 4 (2023): 17–23. http://dx.doi.org/10.2478/aei-2023-0018.

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Abstract In this paper, an evaluation of the multiwavelet basis’ capability to represent the ECG signal sparsely was performed. The paper includes the mathematical formulation of sparsity, a brief introduction to the multiwavelet transform, as well as details about the simulation setup used for evaluation. Throughout the paper, various multiwavelets were investigated. The reported results show that the BAT and DB multiwavelets performed well, thus they could be used in the ECG signal sparsification. The investigation also focused on the ECG signals displaying deformations associated with illne

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Taha, Saleem, and Walid Mahmood. "New techniques for Daubechies wavelets and multiwavelets implementation using quantum computing." Facta universitatis - series: Electronics and Energetics 26, no. 2 (2013): 145–56. http://dx.doi.org/10.2298/fuee1302145t.

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In this paper, new techniques to implement the Daubechies wavelets and multiwavelets are presented using quantum computing synthesis structures. Also, a new quantum implementation of inverse Daubechies multiwavelet transform is proposed. The permutation matrices, particular unitary matrices, play a pivotal role. The particular set of permutation matrices arising in quantum wavelet and multiwavelet transforms is considered, and efficient quantum circuits that implement them are developed. This allows the design of efficient and complete quantum circuits for the quantum wavelet and multiwavelet

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5

NGUYEN, PHAN. "BIORTHOGONAL MULTIWAVELETS RELATED BY DIFFERENTIATION." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 02 (2014): 1450021. http://dx.doi.org/10.1142/s0219691314500210.

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We provide a procedure for constructing biorthogonal multiwavelets from a family of biorthogonal multiscaling functions compactly supported on [-1,1]. The scaling vectors and the associated multiwavelets are piecewise continuously differentiable, symmetrical and possess approximation order three. The construction of scaling vectors is accomplished using quadratic fractal interpolation functions. The filters corresponding to scaling vectors possess certain properties which enable us to construct a new pair of biorthogonal scaling vectors and associated multiwavelets with different regularity an

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Saini, Manish Kumar, and Rajiv Kapoor. "Power Quality Events Classification Using MWT and MLP." Advanced Materials Research 403-408 (November 2011): 4266–71. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4266.

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The work presented uses multiwavelet because of its inherent property to resolve the signal better than all single wavelets. Multiwavelets are based on more than one scaling function. The proposed methodology utilizes an enhanced resolving capability of multiwavelet to recognize power system disturbances. The disturbance classification schema is performed with multiwavelet neural network (MWNN). It performs a feature extraction and a classification algorithm composed of a multiwavelet feature extractor based on norm entropy and a classifier based on a multi-layer perceptron. The performance of

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7

Mahmoud, Waleed Ameen, Ali Ibrahim Abbas, and Nuha Abdul Sahib Alwan. "FACE IDENTIFICATION USING BACK-PROPAGATION ADAPTIVE MULTIWAVENET." Journal of Engineering 18, no. 03 (2023): 392–402. http://dx.doi.org/10.31026/j.eng.2012.03.12.

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Face Identification is an important research topic in the field of computer vision and pattern recognition and has become a very active research area in recent decades. Recently multiwavelet-based neural networks (multiwavenets) have been used for function approximation and recognition, but to our best knowledge it has not been used for face Identification. This paper presents a novel approach for the Identification of human faces using Back-Propagation Adaptive Multiwavenet. The proposed multiwavenet has a structure similar to a multilayer perceptron (MLP) neural network with three layers, bu

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8

BACCHELLI, SILVIA, and SERENA PAPI. "A NOTE ON A MATRIX APPROACH TO MULTIWAVELET APPLICATIONS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (2006): 509–22. http://dx.doi.org/10.1142/s0219691306001415.

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In recent years, many papers have been devoted to the topic of balanced multiwavelets, namely, multiwavelet bases which are especially designed to avoid the prefiltering step in the implementation of the multiwavelet transform. In this work, we give a simple algebraic proof of how scalar wavelets can be reinterpreted as the most natural balanced multiwavelets, which maintain the good properties of the wavelet bases they come from. We then show how these new bases can be successfully used to apply matrix thresholding for the denoising of images corrupted by Gaussian noise. In fact, this new app

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9

Lang, W. Christopher. "Fractal multiwavelets related to the cantor dyadic group." International Journal of Mathematics and Mathematical Sciences 21, no. 2 (1998): 307–14. http://dx.doi.org/10.1155/s0161171298000428.

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Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double-knot spline spaceS1,2.

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10

Hnativ, Lev. "Orthonormalized basic of fractal stepped multiwavelets – a new multiwavelet technology for signal and image processing." Physico-mathematical modelling and informational technologies, no. 32 (July 7, 2021): 91–95. http://dx.doi.org/10.15407/fmmit2021.32.091.

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A new class of fractal step functions with linear and nonlinear changes in values is described, and on their basis a recurrent method for constructing functions of a new class of fractal step multiwavelets (FSMW) of various shapes with linear and nonlinear changes in values is developed. A method and an algorithm for constructing a whole family of basic FSMW systems have been developed. An algorithm for calculating the coefficients of a discrete multiwavelet transform based on a multiwavelet packet without performing convolution and decimated sampling operations, in contrast to the classical m

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11

Saini, Manish Kumar, Rajiv Kapoor, and Bharat Bhushan Sharma. "PQ Event Classification Using Fuzzy Classifier." Advanced Materials Research 403-408 (November 2011): 3854–58. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.3854.

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The work presented here uses multiwavelet because of its inherent property to resolve the signal better than all single wavelets. Multiwavelets are based on more than one scaling function. The proposed methodology utilizes an enhanced resolving capability of multiwavelet to recognize power quality events. PQ events classification scheme is performed using multiwavelet transform for feature extraction and fuzzy classifier for classification. In proposed algorithm,statistical features (.i.e. mean, standard deviation, variation etc.) and energy of the signal at different decomposition levels have

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12

Krivoshein, Aleksandr. "Multivariate Symmetric Interpolating Dual Multiwavelet Frames." Symmetry 14, no. 7 (2022): 1425. http://dx.doi.org/10.3390/sym14071425.

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The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix ext

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13

Zhu, Fengjuan, Yongdong Huang, Xiao Feng, and Qiufu Li. "Minimum-Energy Multiwavelet Frame on the Interval[0,1]." Mathematical Problems in Engineering 2015 (2015): 1–19. http://dx.doi.org/10.1155/2015/262637.

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Drawing inspiration from the idea of combining multiwavelets on the interval with frame theory organically, we study minimum-energy multiwavelet frame on the interval[0,1](MEMWFI). Firstly, left boundary multiscaling functions, right boundary multiscaling functions, and the definition of MEMWFI are put forward, and the equivalent characterizations of MEMWFI are given. Then, two algorithms of constructing MEMWFI are proposed. Finally, the decomposition formula, reconstruction formulas, and numerical examples are given.

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14

Hnativ, Lev. "Discrete fractal step multiwavelets and multiwavelet packets – a new multiwavelet technology for image processing and coding." Physico-Mathematical Modelling and Informational Technologies, no. 36 (July 1, 2023): 53–57. http://dx.doi.org/10.15407/fmmit2023.36.053.

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15

Li, Youfa, Shouzhi Yang, Yanfeng Shen, and Gengrong Zhang. "High Balanced Biorthogonal Multiwavelets with Symmetry." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/154269.

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Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisy

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16

Martin, M. B., and A. E. Bell. "New image compression techniques using multiwavelets and multiwavelet packets." IEEE Transactions on Image Processing 10, no. 4 (2001): 500–510. http://dx.doi.org/10.1109/83.913585.

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17

D.M.Garge and Dr.V.N.Bapat. "Feature Extraction using Balanced Multiwavelets for Classification of Microcalcification Clusters with application in breast cancer diagnostic." International Journal of BioSciences and Technology (IJBST) ISSN: 0974-3987 4, no. 5 (2011): 29–35. https://doi.org/10.5281/zenodo.1438759.

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<strong>Abstract:</strong> This paper presents an approach for early breast cancer diagnostic by employing newer member of multiwavelet family: Balanced Multiwavelets. Detection and classification of microcalcification cluster is based on subband image decomposition. Detection of microcalcification is achieved by decomposing the mammogram and then reconstructing it from from the subbands containing only high frequency components. For this type of approach, we have applied different type of balanced multiwavelets for feature extraction. We used these results as an input to classification system

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18

Mathew, Manju, A. B. Premkumar, and A. S. Madhukumar. "Spectrum-Efficient Cognitive Radio Transceiver Using Multiwavelet Filters." ISRN Communications and Networking 2012 (August 16, 2012): 1–13. http://dx.doi.org/10.5402/2012/607825.

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Cognitive radio (CR) transceiver that can offer adequate data rate and multiuser support for future wireless networks is a promising technology for reliable and spectrum-efficient mobile communication. Orthogonal frequency division multiplexing (OFDM) and scalar wavelet based schemes have been proposed as physical layer techniques for CR. This paper proposes multiwavelet packet-based multicarrier multiple-access scheme as an equally promising candidate for multi-user CR networks and using existing orthonormal multiwavelets, the performance of the proposed system is evaluated. It is shown that

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19

Zhou, Xiaohui. "On the Study of Multiwavelet Deconvolution Density Estimators." Mathematical Problems in Engineering 2020 (April 21, 2020): 1–10. http://dx.doi.org/10.1155/2020/4259373.

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In this paper, multiwavelet deconvolution density estimators are presented by a linear multiwavelet expansion and a nonlinear multiwavelet expansion, respectively. Moreover, the unbiased estimation is shown, and asymptotic normality is discussed for the multiwavelet deconvolution density estimators. Finally, a numerical example is given for our discussion.

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20

Zhanwei, Liu, Hu Guoen, and Wu Guochang. "Orthogonal Multiwavelet Frames inL2Rd." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/846852.

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We characterize the orthogonal frames and orthogonal multiwavelet frames inL2Rdwith matrix dilations of the form(Df)(x)=detAf(Ax), whereAis an arbitrary expandingd×dmatrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.

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21

KIM, WONKOO, and CHING-CHUNG LI. "ON PRECONDITIONING MULTIWAVELET SYSTEMS FOR IMAGE COMPRESSION." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (2003): 51–74. http://dx.doi.org/10.1142/s0219691303000049.

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This paper presents a study on applications of multiwavelet analysis to image compression. The biorthogonality and perfect reconstruction conditions are applied to multiwavelet filters. As a multiwavelet filter bank has multiple channels of inputs, the data structure of inputs to the multiwavelet system should be taken into consideration in multiwavelet decomposition and reconstruction algorithms. We investigate the data initialization problem by considering prefilters and postfilters that may give more efficient representations of the decomposed data. The interpolation postfilter and prefilte

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22

Masood, Dania, and Pooja Singh. "Nonuniform N-multiwavelet sets and multiwavelet induced isomorphisms." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 01 (2015): 1550004. http://dx.doi.org/10.1142/s0219691315500046.

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In this paper, we introduce the notion of a nonuniform N-multiwavelet set and provide a characterization for it. Besides, we describe the counterpart of wavelet induced isomorphism for a dyadic multiwavelet set as well as for a nonuniform N-multiwavelet set of order L.

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23

HUANG, CHIN-PAN, and CHING-CHUNG LI. "SECURE AND PROGRESSIVE IMAGE TRANSMISSION THROUGH SHADOWS GENERATED BY MULTIWAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 06 (2008): 907–31. http://dx.doi.org/10.1142/s0219691308002677.

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In this paper, multiwavelet transform is used in the context of image sharing employing the SPIHT-generated bit stream with the modified Shamir's (r, m) threshold scheme over the Galois field. This provides multiwavelet-based embedded shadow images for progressive transmission and reconstruction. Both integer multiwavelet transform and balanced multiwavelet transform are considered in the method. It is secure and fault-tolerant, and gives small shadow size and excellent rate-distortion performance. Experimental results and sample applications are given to demonstrate the characteristics of thi

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24

Zhang, Xiao-Bing, Yun-Hui Li, and Xiao-Meng Cui. "Active Power Measurement Based on Multiwavelet Transforms." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/905108.

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This paper discusses a new method for calculating active power in the multiwavelet domain. When the voltage and current waveforms are analyzed using multiwavelet, the active power can be calculated by simply adding the products of the multiwavelet coefficients without having to reconstruct the signals back to the time domain first and then using the traditional integration. From the simulation result, we can see that the results using multiwavelet are better than the ones using wavelet and Fourier Transforms no matter which prefilter is used.

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25

Zhang, Xin Cheng. "Symmetric Multiwavelet Frames with General Lattice." Advanced Materials Research 709 (June 2013): 650–53. http://dx.doi.org/10.4028/www.scientific.net/amr.709.650.

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The multiwavelet has more desired properties than any single wavelet, such as short support, symmetry, and smoothness. In this paper, symmetric multiwavelet frames with general lattice and with any symmetric points are constructed from multiwavelet frames given. The existing result is generalized to the case of general lattice.

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Kováč, Ondrej, and Ján Mihalík. "Banks of filters for implementation of DMWT of an image." Journal of Electrical Engineering 70, no. 6 (2019): 429–42. http://dx.doi.org/10.2478/jee-2019-0076.

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Abstract We describee some possible options for implementation of the Discrete multiwavelet transform (DMWT) of an image by using filter banks. DMWT can be implemented by two channel bank of vector filters which are made by cross-connected scalar filters. The properties of DGHM, CL, BiHermite and SA4 multiwavelets are here analyzed, and compression analysis for output normalization of DMWT is performed. A procedure is design of equivalent replacing of 2 channel multifilters bank by 4 channel bank of single scalar filters. Finally, we deal with a possible reduction and combinations of subbands

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Shiva, Mittal, A. S. Atlouba Nadya, and Paul Ajit. "Nonuniform Multiwavelet Packets associated with Nonuniform Multiresolution Analysis with Multiplicity D." Journal of Progressive Research in Mathematics 3, no. 3 (2015): 192–202. https://doi.org/10.5281/zenodo.3980646.

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In this paper we construct nonuniform multiwavelet packets associated with the nonuniform multiresolution analysis (NUMRA) with multiplicity D based on the theory of one dimensional spectral pairs, which is a generalization of NUMRA introduced by Gabardo and Nashed. Further, we obtained an orthonormal basis for 𝐿<sup>2</sup>(ℝ) from the collection of dilation and transilation of nonuniform multiwavelet packets as a generalization of nonuniform multiwavelet packets, that generalizes a result of Behera on wavelet packets associated with NUMRA.

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JUNG, TAE KWON. "MULTIWAVELETS AND APPLICATIONS TO IMAGE DENOISING WITH EFFECTIVE ITERATION METHOD." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (2009): 535–51. http://dx.doi.org/10.1142/s0219691309003070.

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The multiscaling function of Alpert multiwavelet system and Chui–Lian multiwavelet system consist of one symmetric and one antisymmetric scaling functions. In its single level decomposition, only one of 16 subband blocks may be considered as a core part because the antisymmetric scaling function may play the high pass filter. We complete the Alpert multiwavelet system by determining the high pass filter using the algorithm of paraunitary extension principle. Taking the advantage of the symmetric/antisymmetric (SA) feature of Alpert and Chui–Lian multiscaling functions, our iteration (SA iterat

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29

Archibald, Rick, Katherine J. Evans, John Drake, and James B. White. "Multiwavelet Discontinuous Galerkin-Accelerated Exact Linear Part (ELP) Method for the Shallow-Water Equations on the Cubed Sphere." Monthly Weather Review 139, no. 2 (2011): 457–73. http://dx.doi.org/10.1175/2010mwr3271.1.

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Abstract In this paper a new approach is presented to increase the time-step size for an explicit discontinuous Galerkin numerical method. The attributes of this approach are demonstrated on standard tests for the shallow-water equations on the sphere. The addition of multiwavelets to the discontinuous Galerkin method, which has the benefit of being scalable, flexible, and conservative, provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions. This paper explains how combining a multiwavelet discontinuous Gale

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Miller, J. T., and Ching-Chung Li. "Adaptive multiwavelet initialization." IEEE Transactions on Signal Processing 46, no. 12 (1998): 3282–91. http://dx.doi.org/10.1109/78.735303.

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31

Yang, Xinxing, and Licheng Jiao. "Adaptive multiwavelet prefilter." Electronics Letters 35, no. 1 (1999): 11. http://dx.doi.org/10.1049/el:19990001.

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32

Locke, Judson B., and Adrian M. Peter. "Multiwavelet density estimation." Applied Mathematics and Computation 219, no. 11 (2013): 6002–15. http://dx.doi.org/10.1016/j.amc.2012.11.099.

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Han, Bin, Soon-Geol Kwon, and Sang Soo Park. "Riesz multiwavelet bases." Applied and Computational Harmonic Analysis 20, no. 2 (2006): 161–83. http://dx.doi.org/10.1016/j.acha.2005.10.002.

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Huang, Yun Sheng, and Xin Cheng Zhang. "Symmetric Multiwavelet Frames with General Composite Dilation in Higher Dimensions." Applied Mechanics and Materials 275-277 (January 2013): 2669–72. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.2669.

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Frames play an important role in signal processing, image processing, data compression and sampling theory. In this paper, symmetric multiwavelet frames with general composite dilation and with any symmetric points are constructed from composite dilation multiwavelet frames given. At last, an example is provided to prove the theory.

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Jensen, Stig Rune, Jonas Jusélius, Antoine Durdek, Tor Flå, Peter Wind, and Luca Frediani. "Linear scaling Coulomb interaction in the multiwavelet basis, a parallel implementation." International Journal of Modeling, Simulation, and Scientific Computing 05, supp01 (2014): 1441003. http://dx.doi.org/10.1142/s1793962314410037.

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We present a parallel and linear scaling implementation of the calculation of the electrostatic potential arising from an arbitrary charge distribution. Our approach is making use of the multi-resolution basis of multiwavelets. The potential is obtained as the direct solution of the Poisson equation in its Green's function integral form. In the multiwavelet basis, the formally non local integral operator decays rapidly to negligible values away from the main diagonal, yielding an effectively banded structure where the bandwidth is only dictated by the requested accuracy. This sparse operator s

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Kovac, Ondrej, Jan Mihalik, and Iveta Gladisova. "Convolution implementation with a novel approach of DGHM multiwavelet image transform." Journal of Electrical Engineering 68, no. 6 (2017): 455–62. http://dx.doi.org/10.1515/jee-2017-0080.

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AbstractThe purpose of this paper is to develop convolution implementation of DGHM (Donovan, Geronimo, Harding, Massopust) multiwavelet image transform using a new approach of ordering wavelet coefficients at the second and higher levels. Firstly, the method of implementation of one-dimensional discrete multiwavelet transform (1D DMWT) for DGHM multiwavelet using discrete convolution and scalar filters is presented. Then, convolution implementation of DGHM multiwavelet image transform by application of 1D DMWT for two dimensions (2D) in a separable way is proposed. Next, the second level of 2D

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Jing, Mingli, Hua Huang, Wuling Liu, and Chun Qi. "A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/163758.

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An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and th

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38

Poppeliers, C. "Multiwavelet Seismic-Wave Gradiometry." Bulletin of the Seismological Society of America 101, no. 5 (2011): 2108–21. http://dx.doi.org/10.1785/0120100226.

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Haldar, Debasis, and Divya Singh. "p-Adic Multiwavelet Sets." p-Adic Numbers, Ultrametric Analysis and Applications 11, no. 3 (2019): 192–204. http://dx.doi.org/10.1134/s2070046619030026.

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40

Sembiring, Jaka, Alireza S. Sabzevary, and Kageo Akizuki. "STOCHASTIC PROCESS ON MULTIWAVELET." IFAC Proceedings Volumes 35, no. 1 (2002): 211–15. http://dx.doi.org/10.3182/20020721-6-es-1901.00446.

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41

Bacchelli, S., and S. Papi. "Statistically based multiwavelet denoising." Journal of Computational and Applied Mathematics 210, no. 1-2 (2007): 47–55. http://dx.doi.org/10.1016/j.cam.2006.10.091.

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Deshmukh, P. R., and A. A. Ghatol. "Multiwavelet and Image Compression." IETE Journal of Research 48, no. 3-4 (2002): 217–20. http://dx.doi.org/10.1080/03772063.2002.11416279.

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Serdean, C. V., M. K. Ibrahim, A. Moemeni, and M. M. Al-Akaidi. "Wavelet and multiwavelet watermarking." IET Image Processing 1, no. 2 (2007): 223. http://dx.doi.org/10.1049/iet-ipr:20060214.

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Lin, Luchun, Baoping Shi, and Ping An. "Multiwavelet prestack Kirchhoff migration." GEOPHYSICS 81, no. 3 (2016): S79—S85. http://dx.doi.org/10.1190/geo2015-0140.1.

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The problems of stretching and aliasing usually occur in prestack Kirchhoff migration. A multiwavelet-based approach is proposed to provide an alternative approach to resolve these problems. Two steps are involved in the multiwavelet-based algorithm: The first step is the decomposition of the seismic traces with a series of wavelets of different dominant frequencies. This step is based on the principle of basis pursuit and is enhanced for more accurate and sparse decomposition by adding an adaptive subdictionary that is associated with the minima and maxima of a seismic trace. The second step

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Kwon, Soon-Geol. "Two-direction multiwavelet moments." Applied Mathematics and Computation 219, no. 8 (2012): 3530–40. http://dx.doi.org/10.1016/j.amc.2012.09.034.

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Sun, Lei, and Gang Li. "Generalized orthogonal multiwavelet packets." Chaos, Solitons & Fractals 42, no. 4 (2009): 2420–24. http://dx.doi.org/10.1016/j.chaos.2009.03.111.

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Guo, Wei, Jiayi Jiang, and Lihong Qiao. "Parametrization of balanced multiwavelet." Analysis in Theory and Applications 26, no. 4 (2010): 383–400. http://dx.doi.org/10.1007/s10496-010-0383-6.

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Sun, Hao, Ke Li, Huaqing Wang, Peng Chen, and Yi Cao. "Intelligent Mechanical Fault Diagnosis Based on Multiwavelet Adaptive Threshold Denoising and MPSO." Mathematical Problems in Engineering 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/142795.

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The condition diagnosis of rotating machinery depends largely on the feature analysis of vibration signals measured for the condition diagnosis. However, the signals measured from rotating machinery usually are nonstationary and nonlinear and contain noise. The useful fault features are hidden in the heavy background noise. In this paper, a novel fault diagnosis method for rotating machinery based on multiwavelet adaptive threshold denoising and mutation particle swarm optimization (MPSO) is proposed. Geronimo, Hardin, and Massopust (GHM) multiwavelet is employed for extracting weak fault feat

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Yuan, Jing, Chenjun Wei, Bo Zou, et al. "A Comparative Study on Multiwavelet Construction Methods and Customized Multiwavelet Library for Mechanical Fault Detection." Shock and Vibration 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/963528.

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Inner product transform principle reveals that the basis functions most relevant or similar to the fault features are pivotal to the meaningful fault detection. Customized multiwavelet methods and practices have continued to improve over the recent years, focused on two-scale similarity transform (TST), lifting transform (LT), and lifting scheme (LS). Due to the respective advantages and disadvantages, a comparative study on the multiwavelet construction methods by TST, symmetric and dissymmetric LT, and LS is discussed in the paper, covering the differences of construction theories, the synth

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Zhanwei, Liu, Hu Guoen, and Wu Guochang. "Regular and Irregular Sampling Theorem for Multiwavelet Subspaces." Mathematical Problems in Engineering 2010 (2010): 1–18. http://dx.doi.org/10.1155/2010/757039.

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We study the sampling theorem for frames in multiwavelet subspaces. Firstly, a sufficient condition under which the regular sampling theorem holds is established. Then, notice that irregular sampling is also useful in practice; we consider the general cases of the irregular sampling and establish a general irregular sampling theorem for multiwavelet subspaces. Finally, using this generalized irregular sampling theorem, we obtain an estimate for the perturbations of regular sampling in shift-invariant spaces.

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