Journal of Applied Mathematics

Noise Folding in Completely Perturbed Compressed Sensing

Limin Zhou, Xinxin Niu, and Jing Yuan

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Abstract

This paper first presents a new generally perturbed compressed sensing (CS) model y=(A+E)(x+u)+e, which incorporated a general nonzero perturbation E into sensing matrix A and a noise u into signal x simultaneously based on the standard CS model y=Ax+e and is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property (RIP) and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noise e, signal noise u, and perturbation E involved.

Article information

Source
J. Appl. Math., Volume 2016 (2016), Article ID 5094239, 13 pages.

Dates
Received: 10 November 2015
Accepted: 18 February 2016
First available in Project Euclid: 13 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.jam/1460554510

Digital Object Identifier
doi:10.1155/2016/5094239

Mathematical Reviews number (MathSciNet)
MR3484236

Citation

Zhou, Limin; Niu, Xinxin; Yuan, Jing. Noise Folding in Completely Perturbed Compressed Sensing. J. Appl. Math. 2016 (2016), Article ID 5094239, 13 pages. doi:10.1155/2016/5094239. https://projecteuclid.org/euclid.jam/1460554510


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