TY - JOUR
T1 - RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT
AU - Giryes, Raja
AU - Elad, Michael
N1 - Funding Information:
Manuscript received January 18, 2011; revised July 08, 2011 and October 09, 2011; accepted October 12, 2011. Date of publication November 07, 2011; date of current version February 10, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Philippe Ciblat. This research was supported by the European Community FP7-FET program, SMALL project, under grant agreement 225913. The work of R. Giryes is supported in part by the Azrieli Foundation through an Azrieli Fellowship.
PY - 2012/3
Y1 - 2012/3
N2 - This correspondence presents an average case denoising performance analysis for SP, CoSaMP, and IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that it is corrupted by an additive random zero-mean white Gaussian noise and has a K-sparse representation with respect to a known dictionary bf D. The proposed analysis is based on the RIP, establishing a near-oracle performance guarantee for each of these algorithms. Beyond bounds for the reconstruction error that hold with high probability, in this work we also provide a bound for the average error.
AB - This correspondence presents an average case denoising performance analysis for SP, CoSaMP, and IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that it is corrupted by an additive random zero-mean white Gaussian noise and has a K-sparse representation with respect to a known dictionary bf D. The proposed analysis is based on the RIP, establishing a near-oracle performance guarantee for each of these algorithms. Beyond bounds for the reconstruction error that hold with high probability, in this work we also provide a bound for the average error.
KW - Additive white noise
KW - Gaussian noise
KW - compressed sensing
KW - signal denoising
KW - signal reconstruction
KW - signal representations
UR - http://www.scopus.com/inward/record.url?scp=84857213851&partnerID=8YFLogxK
U2 - 10.1109/TSP.2011.2174985
DO - 10.1109/TSP.2011.2174985
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AN - SCOPUS:84857213851
VL - 60
SP - 1465
EP - 1468
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 3
M1 - 6071013
ER -