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Published December 2010 | public
Journal Article

Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

Abstract

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.

Additional Information

© 2010 Springer Science+Business Media, LLC. eceived: 21 January 2009. Published online: 28 January 2010. Communicated by Michael W. Frazier. I.Z. Pesenson was supported in part by the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019. M.Z. Pesenson was supported in part by the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019. Authors would like to thank the anonymous referee for useful and constructive suggestions.

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023