@article{Zhang:2018:10.1109/TSP.2018.2806345,
author = {Zhang, P and Gan, L and Ling, C and Sun, S},
doi = {10.1109/TSP.2018.2806345},
journal = {IEEE Transactions on Signal Processing},
pages = {2086--2097},
title = {Uniform recovery bounds for structured random matrices in corrupted compressed sensing},
url = {http://dx.doi.org/10.1109/TSP.2018.2806345},
volume = {66},
year = {2018}
}

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TY  - JOUR
AB  - We study the problem of recovering an s-sparse signal x ∈ C n from corrupted measurements y = Ax + z + w, where z ∈ C m is a k-sparse corruption vector whose nonzero entries may be arbitrarily large and w ∈ C m is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix, and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. μ(U) ~ 1/√m), we prove that with high probability, one can recover an s-sparse signal exactly and stably by l 1 minimization programs even if the measurements are corrupted by a sparse vector, provided m = O(s log 2 s log 2 n) and the sparsity level k of the corruption is a constant fraction of the total number of measurements. The second class considers a randomly subsampled orthonormal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.
AU  - Zhang,P
AU  - Gan,L
AU  - Ling,C
AU  - Sun,S
DO  - 10.1109/TSP.2018.2806345
EP  - 2097
PY  - 2018///
SN  - 1053-587X
SP  - 2086
TI  - Uniform recovery bounds for structured random matrices in corrupted compressed sensing
T2  - IEEE Transactions on Signal Processing
UR  - http://dx.doi.org/10.1109/TSP.2018.2806345
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000427194000006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/62165
VL  - 66
ER  - 

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