## Journal of Applied Mathematics

### Noise Folding in Completely Perturbed Compressed Sensing

#### 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 ($\mathrm{R}\mathrm{I}\mathrm{P}$) 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
Accepted: 18 February 2016
First available in Project Euclid: 13 April 2016

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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