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Stability results for random sampling of sparse trigonometric polynomials

Holger Rauhut
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Abstract

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.

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Holger Rauhut. 2006-09-22. Stability results for random sampling of sparse trigonometric polynomials. https://arxiv.org/abs/math/0609630

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