Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 54, Issue 12, Pages 5661-5670Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2008.2006382
Keywords
Basis pursuit (BP); compressed sensing; fast Fourier transform (FFT); nonequispaced fast Fourier transform (NFFT); orthogonal matching pursuit (OMP); random sampling; stability under noise; trigonometric polynomials
Funding
- European Union [MEIF-CT-2006-022811]
- The European Union's Potential Programme
- [HPRN-CT-2002-00285]
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Recently, it has been observed that a sparse trigonometric polynomial, i.e., having only a small number of nonzero coefficients, can be reconstructed exactly from a small number of random samples using basis pursuit (BP) or orthogonal matching pursuit (OMP). In this paper, it is shown that recovery by a BP variant is stable tinder 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 (nonsparse) trigonometric polynomials that can he well approximated by sparse ones. The theoretical findings are illustrated by numerical experiments.
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