Random Sampling of Sparse Trigonometric Polynomials, II. Orthogonal Matching Pursuit versus Basis Pursuit

Authors:
Stefan Kunis;Holger Rauhut
Affiliations:
Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Str. 39, 09107, Chemnitz, Germany;University of Vienna, NuHAG, Faculty of Mathematics, Nordbergstr. 15, 1090, Wien, Austria
Venue:
Foundations of Computational Mathematics
Year:
2008

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Abstract

We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, we provide theoretical results on the success probability of reconstruction via Thresholding and OMP for both a continuous and a discrete probability model for the sampling points. We present numerical experiments, which indicate that usually Basis Pursuit is significantly slower than greedy algorithms, while the recovery rates are very similar.