Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

被引：53
|
作者：
Pesenson, Isaac Z. [1 ]
Pesenson, Meyer Z. [2 ]
机构：
[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA
[2] CALTECH, Spitzer Sci Ctr, Pasadena, CA 91125 USA
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2010年 / 16卷 / 06期
关键词：
Combinatorial Laplace operator; Poincare and Plancherel-Polya inequalities; Paley-Wiener spaces; Best approximations; Sparse approximations; Schrodinger Semigroup; Modulus of continuity; Hilbert frames; THEOREM;
D O I：
10.1007/s00041-009-9116-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schrodinger'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.
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页码：921 / 942
页数：22
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