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

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. Key Words: random sampling, trigonometric polynomials, Orthogonal Matching Pursuit, Basis Pursuit, Thresholding, sparse recovery, random matrices, fast Fourier transform, nonequispaced fast Fourier transform AMS Subject classification: 94A20, 42A05, 15A52, 90C05, 90C25

• Type: Journal
• Year: 2008
• Where: FOCM
• Authors: Stefan Kunis, Holger Rauhut
• Keywords: Basis Pursuit, FOCM 2008, Orthogonal Matching Pursuit, Trigonometric Polynomials