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Applications of multiresolution analysis in Besov-Q type spaces and Triebel-Lizorkin-Q type spaces

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Frontiers of Mathematics in China 2022年第3期17卷 373-435页

作者： Pengtao LI Wenchang SUN School of Mathematics and Statistics Qingdao UniversityQingdao 266071China School of Mathematical Sciences Nankai UniversityTianjin 300000China

In this survey,we give a neat summary of the applications of the multi-resolution analysis to the studies of Besov-Q type spaces B_(p,q)^(γ1,γ2) (R^(n))and Triebel-Lizorkin-Q type spaces B_(p,q)^(γ1,γ2) (R^(n)).We will state briefly the recent progress on the wavelet characterizations,the boundedness of Calderon-Zygmund operators,the boundary value problem of B_(p,q)^(γ1,γ2) (R^(n)) and F_(p,q)^(γ1,γ2) (R^(n)).We also present the recent developments on the well-posedness of fluid equations with small data in B_(p,q)^(γ1,γ2) (R^(n))and F_(p,q)^(γ1,γ2) (R^(n)).

关键词： multiresolution analysis regular wavelet Besov-Q type spaces Triebel-Lizorkin-Q type spaces

Cascade algorithm and multiresolution analysis on the Heisenberg group

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Progress in Natural Science:Materials International 2005年第7期15卷 602-608页

作者： LIU Heping, LIU Yu, PENG Lizhong and CHU Xiaoyong (LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China) LMAM School of Mathematical Sciences Peking University Beijing 100871 China

In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogo-nal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa . Similar results are also proved for biorthogo-nal multiresolution analysis.

关键词： Heisenberg group cascade algorithm multiresolution analysis refinable functions.

A Construction of multiresolution analysis on Interval

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Acta Mathematica Sinica,English Series 2007年第4期23卷 705-710页

作者： Di Rong CHEN Dao Hong XIANG Department of Mathematics and LMIB Beijing University of Areonautics and Astronautics Beijing 100083 P. R. China

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.

关键词： multiresolution analysis Refinable function Approximation order Subdivision operator

Statistical multiresolution analysis in amplitude- frequency domain

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Science in China(Series F) 2004年第4期47卷 518-526页

作者： SUNHong GUANBao HenriMaitre SchoolofElectronicInformation WuhanUniversityLIESMARSWuhan430072China DepartementdeTSI EcoleNationnaleSuperieuredesTelecommunication75013ParisFranceCorrespondenceshouldbeaddressedtoSunHong

A concept of statistical multiresolution analysis in amplitude-frequency domain is proposed, which is to employ the wavelet transform on the statistical character of a signal in amplitude domain. In terms of the theorem of generalized ergodicity, an algorithm to estimate the transform coefficients based on the amplitude statistical multiresolution analysis (AMA) is presented. The principle of applying the AMA to Synthetic Aperture Radar (SAR) image processing is described, and the good experimental results imply that the AMA is an efficient tool for processing of speckled signals modeled by the multiplicative noise.

关键词： statistical signal analysis multiresolution analysis SAR image processing discrete-amplitude signal processing.

multiresolution analysis of functions in Cantor set

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Progress in Natural Science:Materials International 1998年第2期 122-126页

作者：熊小芸 Beijing 100029 China) Chinese Academy of Sciences Institute of Atmospheric Physics State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry

Wavelet transform is a great breakthrough in harmonic analysis of Fourier transform analysis, and it replaces the basis function e±iwtwith wavelet basis function ψa,b=((t-b)/a)) possessing finite or compact support, which ensures the good timefrequency localization of the transform. However, the Fourier analysis has clear physical sense; that is, a signal is represented by

关键词： wavelet multiresolution analysis Cantor set Hilbert space infinite nest sequence.

Wavelet-fractional Fourier transforms

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Chinese Physics B 2008年第1期17卷 170-179页

作者：袁琳 College of Mathematics Physics and Information Zhejiang Normal University

This paper extends the definition of fractional Fourier transform （FRFT） proposed by Namias V by using other orthonormal bases for L^2（R） instead of Hermite-Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.

关键词： multiresolution analysis fractional Fourier transform wavelets-fractional Fourier transform

Multimodality Medical Image Fusion Based on Pixel Significance with Edge-Preserving Processing for Clinical Applications

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Computers, Materials & Continua 2024年第3期78卷 4317-4342页

作者： Bhawna Goyal Ayush Dogra Dawa Chyophel Lepcha Rajesh Singh Hemant Sharma Ahmed Alkhayyat Manob Jyoti Saikia Department of ECE and UCRD Chandigarh UniversityMohaliPunjab140413India Chitkara University Institute of Engineering and Technology Chitkara UniversityPunjab140401India Department of ECE Uttaranchal Institute of TechnologyUttaranchal UniversityDehradun248007India IES College of Technology IES UniversityBhopal462044India College of Technical Engineering The Islamic UniversityNajaf54001Iraq Department of Electrical Engineering University of North FloridaJacksonvilleFL32224USA

Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical *** fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many ***,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing *** solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion ***,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing *** outputs of CBF are then subtracted from the original images to obtain detailed *** further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural *** regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate *** outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the *** addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical *** standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion *** results from th

关键词： Image fusion fractal data analysis biomedical diseases research multiresolution analysis numerical analysis

h-ADAPTIVITY analysis BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

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Applied Mathematics and Mechanics(English Edition) 2005年第8期26卷 1064-1071页

作者： ZHANG Zhi-qian（张智谦） ZHOU Jin-xiong（周进雄） WANG Xue-ming（王学明） ZHANG Yan-fen（张艳芬） ZHANG Ling（张陵） School of Civil Engineering and Mechanics Xi＇an Jiaotong University Xi＇ an 710049 P. R. China

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

关键词： meshfree method reproducing kernel particle method multiresolution analysis adaptive analysis

Wavelets and Wavelet Packets Related to a Class of Dilation Matrices

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Acta Mathematica Sinica,English Series 2004年第5期20卷 879-892页

作者： QiaoFangLIAN DepartmentofMathematics BeijingJiaotongUniversityBeijing100044P.R.China

The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix,which is not easy in most *** and Micchelli gave a solution to the problem in the case where the dilation matrix is 21 and the dimension does not exceed *** this paper,by the method of unitary extension of a matrix,we obtain the construction of wavelets and wavelet packets related to a class of dilation matrices.

关键词： multiresolution analysis Full set Wavelet Wavelet packet