Noise Folding in Completely Perturbed Compressed Sensing

Noise Folding in Completely Perturbed Compressed Sensing

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 pertu...

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Main Authors: Limin Zhou, Xinxin Niu, Jing Yuan
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2016/5094239
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spelling doaj-81fd3a1c1f5545afa5bc55362270459f2020-11-24T23:16:16ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/50942395094239Noise Folding in Completely Perturbed Compressed SensingLimin Zhou0Xinxin Niu1Jing Yuan2Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaInformation Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaInformation Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaThis 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.http://dx.doi.org/10.1155/2016/5094239
collection DOAJ
language English
format Article
sources DOAJ
author Limin Zhou
Xinxin Niu
Jing Yuan
spellingShingle Limin Zhou
Xinxin Niu
Jing Yuan
Noise Folding in Completely Perturbed Compressed Sensing
Journal of Applied Mathematics
author_facet Limin Zhou
Xinxin Niu
Jing Yuan
author_sort Limin Zhou
title Noise Folding in Completely Perturbed Compressed Sensing
title_short Noise Folding in Completely Perturbed Compressed Sensing
title_full Noise Folding in Completely Perturbed Compressed Sensing
title_fullStr Noise Folding in Completely Perturbed Compressed Sensing
title_full_unstemmed Noise Folding in Completely Perturbed Compressed Sensing
title_sort noise folding in completely perturbed compressed sensing
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2016-01-01
description 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.
url http://dx.doi.org/10.1155/2016/5094239
work_keys_str_mv AT liminzhou noisefoldingincompletelyperturbedcompressedsensing
AT xinxinniu noisefoldingincompletelyperturbedcompressedsensing
AT jingyuan noisefoldingincompletelyperturbedcompressedsensing
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