Nonconvex Compressed Sensing and Error Correction
- 1 January 2007
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3 (15206149) , III-889-III-892
- https://doi.org/10.1109/icassp.2007.366823
Abstract
The theory of compressed sensing has shown that sparse signals can be reconstructed exactly from remarkably few measurements. In this paper we consider a nonconvex extension, where the lscr11 norm of the basis pursuit algorithm is replaced with the lscrp norm, for p < 1. In the context of sparse error correction, we perform numerical experiments that show that for a fixed number of measurements, errors of larger support can be corrected in the nonconvex case. We also provide a theoretical justification for why this should be so.Keywords
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