Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

被引：0
作者：
Isaac Z. Pesenson
Meyer Z. Pesenson
机构：
[1] Temple University,Department of Mathematics
[2] California Institute of Technology,Spitzer Science Center
来源：
Journal of Fourier Analysis and Applications | 2010年 / 16卷
关键词：
Combinatorial Laplace operator; Poincare and Plancherel-Polya inequalities; Paley-Wiener spaces; Best approximations; Sparse approximations; Schrödinger Semigroup; Modulus of continuity; Hilbert frames; 42C99; 05C99; 94A20; 94A12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schrödinger’s group of operators generated by combinatorial Laplace operator. Then we construct a sampling theory by proving Poincare and Plancherel-Polya-type inequalities for functions on graphs. These results lead to a theory of sparse approximations on graphs and have potential applications to filtering, denoising, data dimension reduction, image processing, image compression, computer graphics, visualization and learning theory.
引用
收藏
页码：921 / 942
页数：21
相关论文
共 24 条
[1]  
Bremer J.C.(2006)Diffusion wavelet packets Appl. Comput. Harmon. Anal. 21 95-112
[2]  
Coifman R.R.(2006)Diffusion wavelets Appl. Comput. Harmon. Anal. 21 53-94
[3]  
Maggioni M.(1952)A class of nonharmonic Fourier series Trans. AMS 72 341-366
[4]  
Szlam A.D.(1993)A discrete theory of irregular sampling Linear Algebra Its Appl. 193 129-150
[5]  
Coifman R.R.(2008)Diffusion polynomial frames on metric measure spaces Appl. Comput. Harmon. Anal. 24 329-353
[6]  
Maggioni M.(2002)Discrete analogues in harmonic analysis: spherical averages Ann. Math. (2) 155 189-208
[7]  
Duffin R.(2007)Laplace spectra as fingerprints for image recognition Comput.-Aided Des. 39 460-476
[8]  
Schaeffer A.(2000)A sampling theorem on homogeneous manifolds Trans. AMS 352 4257-4270
[9]  
Gröchenig K.(2001)Sampling of Band limited vectors J. Fourier Anal. Appl. 7 93-100
[10]  
Maggioni M.(2008)Sampling in Paley-Wiener spaces on combinatorial graphs Trans. Am. Math. Soc. 360 5603-5627
123