Applied and Computational Harmonic Analysis最新文献_第3页

Two subspace methods for frequency sparse graph signals 频率稀疏图信号的两种子空间方法

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-10-02 DOI: 10.1016/j.acha.2024.101711

Tarek Emmrich, Martina Juhnke, Stefan Kunis

引用次数: 0

Approximation theory of wavelet frame based image restoration 基于小波帧的图像修复近似理论

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-09-27 DOI: 10.1016/j.acha.2024.101712

Jian-Feng Cai , Jae Kyu Choi , Jianbin Yang

引用次数: 0

Donoho-Logan large sieve principles for the wavelet transform 小波变换的 Donoho-Logan 大筛原理

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-09-26 DOI: 10.1016/j.acha.2024.101709

Luís Daniel Abreu , Michael Speckbacher

引用次数: 0

Data-driven optimal shrinkage of singular values under high-dimensional noise with separable covariance structure with application 具有可分离协方差结构的高维噪声下奇异值的数据驱动优化收缩及其应用

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-09-12 DOI: 10.1016/j.acha.2024.101698

Pei-Chun Su , Hau-Tieng Wu

{"title":"Data-driven optimal shrinkage of singular values under high-dimensional noise with separable covariance structure with application","authors":"Pei-Chun Su , Hau-Tieng Wu","doi":"10.1016/j.acha.2024.101698","DOIUrl":"10.1016/j.acha.2024.101698","url":null,"abstract":"<div>We develop a data-driven optimal shrinkage algorithm, named extended OptShrink (eOptShrink), for matrix denoising with high-dimensional noise and a separable covariance structure. This noise is colored and dependent across samples. The algorithm leverages the asymptotic behavior of singular values and vectors of the noisy data's random matrix. Our theory includes the sticking property of non-outlier singular values, delocalization of weak signal singular vectors, and the spectral behavior of outlier singular values and vectors. We introduce three estimators: a novel rank estimator, an estimator for the spectral distribution of the pure noise matrix, and the optimal shrinker eOptShrink. Notably, eOptShrink does not require estimating the noise's separable covariance structure. We provide a theoretical guarantee for these estimators with a convergence rate. Through numerical simulations and comparisons with state-of-the-art optimal shrinkage algorithms, we demonstrate eOptShrink's application in extracting maternal and fetal electrocardiograms from single-channel trans-abdominal maternal electrocardiograms.</div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"74 ","pages":"Article 101698"},"PeriodicalIF":2.6,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Construction of pairwise orthogonal Parseval frames generated by filters on LCA groups 构建由 LCA 组滤波器生成的成对正交 Parseval 框架

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-09-07 DOI: 10.1016/j.acha.2024.101708

Navneet Redhu , Anupam Gumber , Niraj K. Shukla

{"title":"Construction of pairwise orthogonal Parseval frames generated by filters on LCA groups","authors":"Navneet Redhu , Anupam Gumber , Niraj K. Shukla","doi":"10.1016/j.acha.2024.101708","DOIUrl":"10.1016/j.acha.2024.101708","url":null,"abstract":"<div>The generalized translation invariant (GTI) systems unify the discrete frame theory of generalized shift-invariant systems with its continuous version, such as wavelets, shearlets, Gabor transforms, and others. This article provides sufficient conditions to construct pairwise orthogonal Parseval GTI frames in <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math> satisfying the local integrability condition (LIC) and having the Calderón sum one, where G is a second countable locally compact abelian group. The pairwise orthogonality plays a crucial role in multiple access communications, hiding data, synthesizing superframes and frames, etc. Further, we provide a result for constructing N numbers of GTI Parseval frames, which are pairwise orthogonal. Consequently, we obtain an explicit construction of pairwise orthogonal Parseval frames in <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math> and <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math>, using B-splines as a generating function. In the end, the results are particularly discussed for wavelet systems.</div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"74 ","pages":"Article 101708"},"PeriodicalIF":2.6,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust sparse recovery with sparse Bernoulli matrices via expanders 通过扩展器利用稀疏伯努利矩阵进行稳健的稀疏恢复

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-08-20 DOI: 10.1016/j.acha.2024.101697

Pedro Abdalla

{"title":"Robust sparse recovery with sparse Bernoulli matrices via expanders","authors":"Pedro Abdalla","doi":"10.1016/j.acha.2024.101697","DOIUrl":"10.1016/j.acha.2024.101697","url":null,"abstract":"<div>Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, Bernoulli (p) matrices formed by independent identically distributed (i.i.d.) Bernoulli (p) random variables are of practical relevance in the context of noise-blind recovery in nonnegative compressed sensing.In this work, we investigate the robust nullspace property of Bernoulli (p) matrices. Previous results in the literature establish that such matrices can accurately recover n-dimensional s-sparse vectors with <math><mi>m</mi><mo>=</mo><mi>O</mi><mrow><mo>(</mo><mfrac><mrow><mi>s</mi></mrow><mrow><mi>c</mi><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mfrac><mi>log</mi><mo>⁡</mo><mfrac><mrow><mi>e</mi><mi>n</mi></mrow><mrow><mi>s</mi></mrow></mfrac><mo>)</mo></mrow></math> measurements, where <math><mi>c</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>≤</mo><mi>p</mi></math> is a constant dependent only on the parameter p. These results suggest that in the sparse regime, as p approaches zero, the (sparse) Bernoulli (p) matrix requires significantly more measurements than the minimal necessary, as achieved by standard isotropic subgaussian designs. However, we show that this is not the case.Our main result characterizes, for a wide range of sparsity levels s, the smallest p for which sparse recovery can be achieved with the minimal number of measurements. We also provide matching lower bounds to establish the optimality of our results and explore connections with the theory of invertibility of discrete random matrices and integer compressed sensing.</div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"73 ","pages":"Article 101697"},"PeriodicalIF":2.6,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1063520324000745/pdfft?md5=da55acefd115269f8b0ce4f5a4a72295&pid=1-s2.0-S1063520324000745-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The G-invariant graph Laplacian part II: Diffusion maps G不变图拉普拉奇第二部分：扩散映射

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-08-12 DOI: 10.1016/j.acha.2024.101695

Eitan Rosen , Xiuyuan Cheng , Yoel Shkolnisky

引用次数: 0

On the concentration of Gaussian Cayley matrices 论高斯凯利矩阵的集中性

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-08-06 DOI: 10.1016/j.acha.2024.101694

Afonso S. Bandeira , Dmitriy Kunisky , Dustin G. Mixon , Xinmeng Zeng

引用次数: 0

A lower bound for the Balan–Jiang matrix problem 巴兰姜矩阵问题的下限

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-08-06 DOI: 10.1016/j.acha.2024.101696

Afonso S. Bandeira , Dustin G. Mixon , Stefan Steinerberger

引用次数: 0

Needlets liberated 释放针头

IF 2.6 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-08-02 DOI: 10.1016/j.acha.2024.101693

Johann S. Brauchart , Peter J. Grabner , Ian H. Sloan , Robert S. Womersley

{"title":"Needlets liberated","authors":"Johann S. Brauchart , Peter J. Grabner , Ian H. Sloan , Robert S. Womersley","doi":"10.1016/j.acha.2024.101693","DOIUrl":"10.1016/j.acha.2024.101693","url":null,"abstract":"<div>Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet construction makes use of integration rules that are exact for polynomials up to a given degree. The aim of the present paper is to relax the exactness of the integration rules by replacing them with QMC designs as introduced by Brauchart, Saff, Sloan, and Womersley (2014). Such integration rules (generalised here by allowing non-equal cubature weights) provide the same asymptotic order of convergence as exact rules for Sobolev spaces <math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></math>, but are easier to obtain numerically. With such rules we construct “generalised needlets”. The paper provides an error analysis that allows the replacement of the original needlets by generalised needlets, and more generally, analyses a hybrid scheme in which the needlets for the lower levels are of the traditional kind, whereas the new generalised needlets are used for some number of higher levels. Numerical experiments complete the paper.</div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"73 ","pages":"Article 101693"},"PeriodicalIF":2.6,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1063520324000708/pdfft?md5=9a180ff7ceb60a51f1d46ba86c076b69&pid=1-s2.0-S1063520324000708-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0