2006/09/22 by Holger Rauhut, Rauhut, Holger · 1 citation
Computer Science · Engineering · #15A52 #42A05 #90C25 #94A20 #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.math/0609630
openalex publication_date 2006/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal Matching Pursuit (OMP). In the present article it is shown that recovery by a BP variant is stable under perturbation of the samples values by noise. A similar partial result for OMP is provided. For BP in addition, the stability result is extended to (non-sparse) trigonometric polynomials that can be well-approximated by sparse ones. The theoretical findings are illustrated by numerical experiments.