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Journal articles on the topic 'MULTIWAVELET'

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Author: Grafiati

Published: 11 September 2023

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1

Shouzhi, Yang. "Biorthogonal interpolatory multiscaling functions and corresponding multiwavelets." ANZIAM Journal 49, no. 1 (July 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. Finally, we give several numerical examples based on B-spline functions.

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3

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 transforms.

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4

NGUYEN, PHAN. "BIORTHOGONAL MULTIWAVELETS RELATED BY DIFFERENTIATION." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 02 (March 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 and approximation order, related to the old ones by differentiation. The old and new biorthogonal multiwavelet systems give rise to compactly supported biorthogonal multiwavelet basis for the space of divergence-free vector fields on the upper half plane with the Navier boundary condition.

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5

Mahmoud, Waleed Ameen, Ali Ibrahim Abbas, and Nuha Abdul Sahib Alwan. "FACE IDENTIFICATION USING BACK-PROPAGATION ADAPTIVE MULTIWAVENET." Journal of Engineering 18, no. 03 (July 21, 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, but the activation function of hidden layer is replaced with multiscaling functions. In experiments performed on the ORL face database it achieved a recognition rate of 97.75% in the presence of facial expression, lighting and pose variations. Results are compared with its wavelet-based counterpart where it obtained a recognition rate of 10.4%. The proposed multiwavenet demonstrated very good recognition rate in the presence of variations in facial expression, lighting and pose and outperformed its wavelet-based counterpart.

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6

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 this classifier is evaluated by using total 1000 PQ disturbance signals which are generated the based model. The classification performance of different PQ disturbance using proposed algorithm is tested. The rate of average correct classification is about 99.65% for the different PQ disturbance signals and noisy disturbances.

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7

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 (September 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 approach discovers a balanced matrix nature in Daubechies bases, hence obtaining better numerical results with respect to those achieved via scalar thresholding. In particular, this reinterpretation of scalar wavelets as balanced multiwavelets allows us to successfully use the thresholding filters, previously introduced in the scalar case, in a matrix setting.

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8

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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9

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 method, is presented. A method and algorithm for fast multiwavelet transform of low computational complexity has been developed, which, in comparison with the well-known classical Mall's algorithm, is 70 times less in multiplicative complexity, and 20 times less in additive complexity.

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10

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 been considered as feature vectors. The performance of fuzzy classifier has been evaluated by using total 1000 PQ disturbance signals which are generated using the based model. The classification performance of different PQ events using proposed algorithm has been tested. The rate of average correct classification is about 99.95% for the different PQ disturbance signals and noisy disturbances.

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11

Krivoshein, Aleksandr. "Multivariate Symmetric Interpolating Dual Multiwavelet Frames." Symmetry 14, no. 7 (July 11, 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 extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented.

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12

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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13

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 antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.

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14

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

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15

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 the error performance of the proposed system under frequency and phase offset conditions is comparable with existing schemes.

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16

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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17

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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18

Masood, Dania, and Pooja Singh. "Nonuniform N-multiwavelet sets and multiwavelet induced isomorphisms." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 01 (January 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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19

KIM, WONKOO, and CHING-CHUNG LI. "ON PRECONDITIONING MULTIWAVELET SYSTEMS FOR IMAGE COMPRESSION." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (March 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 prefilter are formulated, which are capable to provide a better approximate image at each coarser resolution level. A design process is given to obtain both filters having compact supports, if exist. Image compression performances of three multiwavelet systems are studied in comparison to those of single wavelet systems.

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20

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 (November 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 this method.

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21

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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22

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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23

Kováč, Ondrej, and Ján Mihalík. "Banks of filters for implementation of DMWT of an image." Journal of Electrical Engineering 70, no. 6 (December 1, 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 and suggest their use.

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24

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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25

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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26

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

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27

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

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28

JUNG, TAE KWON. "MULTIWAVELETS AND APPLICATIONS TO IMAGE DENOISING WITH EFFECTIVE ITERATION METHOD." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (September 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 iteration) of multiwavelet decomposition continues to the core part (1/16 of subbands) for the image denoising problem while the traditional iteration applies to the one fourth of 16 subbands as core parts. The numerical results demonstrate that our method of symmetric/antisymmetric iteration exhibits performance superior to the traditional ways.

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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 (February 1, 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 Galerkin method with exact-linear-part time evolution schemes, which can remain stable for implicit-sized time steps, can help increase the time-step size for shallow-water equations on the sphere.

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30

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 (October 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 structure has been exploited to achieve linear scaling and parallel algorithms. Parallelization has been achieved both through the shared memory (OpenMP) and the message passing interface (MPI) paradigm. Our implementation has been tested by computing the electrostatic potential of the electronic density of long-chain alkanes and diamond fragments showing (sub)linear scaling with the system size and efficent parallelization.

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31

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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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 (November 1, 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 DMWT is performed in three possible ways. The novelty of the proposed implementation is in reordering of L subband wavelet coefficients at the first level into one subimage. The results are evaluated as the energy ratios between the transformed images in L subband at the second level and the input original image. According to the experimental results, the developed implementation of 2D DMWT is approximately 5% more effective in energy compression than the ones most commonly mentioned in the literature. This paper shows a possibility of convolution implementation of 2D DMWT with higher energy compression.

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33

Poppeliers, C. "Multiwavelet Seismic-Wave Gradiometry." Bulletin of the Seismological Society of America 101, no. 5 (September 26, 2011): 2108–21. http://dx.doi.org/10.1785/0120100226.

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34

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

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35

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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36

Bacchelli, S., and S. Papi. "Statistically based multiwavelet denoising." Journal of Computational and Applied Mathematics 210, no. 1-2 (December 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 (May 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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39

Lin, Luchun, Baoping Shi, and Ping An. "Multiwavelet prestack Kirchhoff migration." GEOPHYSICS 81, no. 3 (May 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 is wavelet migration based on the Kirchhoff formulation using a novel approach. The outer iteration is the wavelets of the input seismic traces, which ensures that an input wavelet is only used once in the entire migration process. This enables output of multiple migrated images of different wavelets of dominant frequency ranges, elimination of noisy images, and composition of images for specific interpretation and reservoir characterization purposes with very little extra computational cost. The stretching and aliasing problems are naturally resolved because interpolation on the seismic trace is not required in the migration. We tested the algorithm using a synthetic model with a dipping layer and a 2D real seismic section. We compared our results with results obtained by conventional Kirchhoff migration.

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40

Kwon, Soon-Geol. "Two-direction multiwavelet moments." Applied Mathematics and Computation 219, no. 8 (December 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 (November 2009): 2420–24. http://dx.doi.org/10.1016/j.chaos.2009.03.111.

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42

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

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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 the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.

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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 features under background noise, and the method of adaptively selecting appropriate threshold for multiwavelet with energy ratio of multiwavelet coefficient is presented. The six nondimensional symptom parameters (SPs) in the frequency domain are defined to reflect the features of the vibration signals measured in each state. Detection index (DI) using statistical theory has been also defined to evaluate the sensitiveness of SP for condition diagnosis. MPSO algorithm with adaptive inertia weight adjustment and particle mutation is proposed for condition identification. MPSO algorithm effectively solves local optimum and premature convergence problems of conventional particle swarm optimization (PSO) algorithm. It can provide a more accurate estimate on fault diagnosis. Practical examples of fault diagnosis for rolling element bearings are given to verify the effectiveness of the proposed method.

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Wang, Ning, Shuangkui Ge, Baobin Li, and Lizhong Peng. "Multiple description image compression based on multiwavelets." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 01 (January 2019): 1850063. http://dx.doi.org/10.1142/s0219691318500637.

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Multiple description coding (MDC) is one of the source coding techniques to alleviate the problems of packet loss in the network. The decoder estimates the lost signals from received ones, based on the certain statistical correlation between descriptions. However, this correlation also leads to compression redundancy at the same time. Therefore, how to make efficient use of the introduced correlation has great importance in practical MDC approaches. In this paper, we propose a multiple description image coding scenario based on balanced multiwavelets. Two simple and effective methods to reconstruct the original image from partial descriptions are suggested. Furthermore, optimization criterion corresponding to this multiwavelet based system is provided. According to this criterion, we can choose appropriate multifilter banks to satisfy different demands. Experimental results show that the optimized multifilter banks in a simulated transform coding environment perform very well.

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Yuan, Jing, Chenjun Wei, Bo Zou, Jun Zhu, Ying Wei, Yanyang Zi, and Yu Zhou. "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 synthetic analyses of construction strategies, and the comparison of waveform characteristics along with their applicable occasions. Comprehensively utilizing the capabilities of the construction methods, a novel customized multiwavelet library is established for the accurate fault detection. The proposed method is applied to incipient fault detection of rolling bearing for electric locomotive to verify the effectiveness and feasibility.

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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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LU, JIANMING, LING WANG, YEQIU LI, and TAKASHI YAHAGI. "NOISE REMOVAL FOR MEDICAL X-RAY IMAGES IN MULTIWAVELET DOMAIN." International Journal of Image and Graphics 08, no. 01 (January 2008): 25–46. http://dx.doi.org/10.1142/s0219467808002952.

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When a signal is embedded in an additive Gaussian noise, its estimation is often done by finding a wavelet basis that concentrates the signal energy over few coefficients and by thresholding the noisy coefficients. However, in many practical problems such as medical X-ray image, astronomical and low-light images, the recorded data is not modeled by Gaussian noise but as the realization of a Poisson process. Multiwavelet is a new development to the body of wavelet theory. Multiwavelet simultaneously offers orthogonality, symmetry and short support which are not possible in scalar 2-channel wavelet systems. After reviewing this recently developed theory, a new theory and algorithm for denoising medical X-ray images using multiwavelet multiple resolution analysis (MRA) are presented and investigated in this paper. The proposed covariance shrink (CS) method is used to threshold wavelet coefficients. The form of thresholds is carefully formulated which is the key to more excellent results obtained in the extensive numerical simulations of medical image denoising compared to conventional methods.

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Zou, Qing Yun, and Qian Cao. "Balanced Biorthogonal Multiwavelet with Symmetric/Antisymmetric Filter Banks." Applied Mechanics and Materials 568-570 (June 2014): 185–88. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.185.

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A class of the balanced biorthogonal multiwavelets was constructed by defining a specific matrix filter structure, in which the multifilter banks of multiwavelets have had the desired symmetry. Here, the multifilter banks have possess symmetric/antisymmetric, which resembled filters of scalar wavelet and have in favor of application, notwithstanding the multiwavelets constructed in this paper have lost the linear phase, so they have formed a new type of multiwavelets undoubtedly.

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Jarczewska, K., W. Glabisz, and W. Zielichowski-Haber. "Multiwavelets and multiwavelet packets of Legendre functions in the direct method for solving variational problems." Archives of Civil and Mechanical Engineering 15, no. 1 (January 2015): 1–10. http://dx.doi.org/10.1016/j.acme.2014.04.008.

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