Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

Details Sampling, Filtering and Sparse Approximations on Combinatorial Graphs Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

2011-11-25

arxiv.org/abs/1111.5899v1

J Fourier Anal Appl, 2010. DOI 10.1007/s00041-009-9116-7

Computer Science

Information Theory

Scientific paper

In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\"odinger'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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