RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT

Raja Giryes; Michael Elad

doi:10.1109/TSP.2011.2174985

RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT

Raja Giryes^*, Michael Elad

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	6071013
Pages (from-to)	1465-1468
Number of pages	4
Journal	IEEE Transactions on Signal Processing
Volume	60
Issue number	3
DOIs	https://doi.org/10.1109/TSP.2011.2174985
State	Published - Mar 2012
Externally published	Yes

Keywords

Additive white noise
Gaussian noise
compressed sensing
signal denoising
signal reconstruction
signal representations

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10.1109/TSP.2011.2174985

Cite this

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title = "RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT",

abstract = "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.",

keywords = "Additive white noise, Gaussian noise, compressed sensing, signal denoising, signal reconstruction, signal representations",

author = "Raja Giryes and Michael Elad",

note = "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.",

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month = mar,

doi = "10.1109/TSP.2011.2174985",

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volume = "60",

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KW - Additive white noise

KW - Gaussian noise

KW - compressed sensing

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KW - signal reconstruction

KW - signal representations

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RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT

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Keywords

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