Title | Stable sparse approximations via nonconvex optimization |
Publication Type | Conference Paper |
Year of Publication | 2008 |
Authors | Saab, R., R. Chartrand, and O. Yilmaz |
Conference Name | Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on |
Pagination | 3885 -3888 |
Date Published | mar. |
Keywords | compressible signals, lscrp minimization, minimisation, noise level, nonconvex optimization, numerical stability, restricted isometry constants, robustness, signal processing, stable sparse approximations |
Abstract | We present theoretical results pertaining to the ability of lscrp minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candes, Romberg and Tao (2005) to the p lt; 1 case. Our results indicate that depending on the restricted isometry constants (see, e.g., Candes and Tao (2006; 2005)) and the noise level, lscrp minimization with certain values of p lt; 1 provides better theoretical guarantees in terms of stability and robustness than lscr1 minimization does. This is especially true when the restricted isometry constants are relatively large. |
URL | http://dx.doi.org/10.1109/ICASSP.2008.4518502 |
DOI | 10.1109/ICASSP.2008.4518502 |