RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT

Author

Giryes, Raja ; Elad, Michael

Author_Institution

Dept. of Comput. Sci., Technion - Israel Inst. of Technol., Haifa, Israel

Volume

60

Issue

3

fYear

2012

fDate

3/1/2012 12:00:00 AM

Firstpage

1465

Lastpage

1468

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 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

AWGN; probability; signal denoising; signal reconstruction; signal representation; CoSaMP algorithm; IHT algorithm; RIP-based near-oracle performance; SP algorithm; additive random zero-mean white Gaussian noise; average error; denoising performance analysis; dictionary D; k-sparse representation; noisy signal recovery; probability; reconstruction error; Algorithm design and analysis; Approximation methods; Dictionaries; Gaussian noise; Matching pursuit algorithms; Vectors; Additive white noise; Gaussian noise; compressed sensing; signal denoising; signal reconstruction; signal representations;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2011.2174985

Filename

6071013