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Cite Details

Rayan Saab, Rick Chartrand and Özgür Yilmaz, "Stable sparse approximations via nonconvex optimization", in 33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008

Abstract

We present theoretical results pertaining to the ability of p minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candès, Romberg and Tao to the p < 1 case. Our results indicate that depending on the restricted isometry constants and the noise level, p minimization with certain values of p < 1 provides better theoretical guarantees in terms of stability and robustness than 1 minimization does. This is especially true when the restricted isometry constants are relatively large.

BibTeX Entry

@inproceedings{saab-2008-stable,
author = {Rayan Saab and Rick Chartrand and \"{O}zg\"{u}r Yilmaz},
title = {Stable sparse approximations via nonconvex optimization},
year = {2008},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/saab-2008-stable.pdf},
booktitle = {33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}
}