DocumentCode :
81023
Title :
Efficient Algorithms for Robust Recovery of Images From Compressed Data
Author :
Duc-Son Pham ; Venkatesh, Svetha
Author_Institution :
Dept. of Comput., Curtin Univ., Perth, WA, Australia
Volume :
22
Issue :
12
fYear :
2013
fDate :
Dec. 2013
Firstpage :
4724
Lastpage :
4737
Abstract :
Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended to cope with the case where corruption to the CS data is modeled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS into a single framework to suppress outliers in the CS recovery. To solve the newly formulated robust CS problem, a scheme that iteratively solves a number of CS problems-the solutions from which provably converge to the true robust CS solution-is suggested. This scheme is, however, rather inefficient as it has to use existing CS solvers as a proxy. To overcome limitations with the original robust CS algorithm, we propose in this paper more computationally efficient algorithms by following latest advances in large-scale convex optimization for nonsmooth regularization. Furthermore, we also extend the robust CS formulation to various settings, including additional affine constraints, l1-norm loss function, mix-norm regularization, and multitasking, so as to further improve robust CS and derive simple but effective algorithms to solve these extensions. We demonstrate that the new algorithms provide much better computational advantage over the original robust CS method on the original robust CS formulation, and effectively solve more sophisticated extensions where the original methods simply cannot. We demonstrate the usefulness of the extensions on several imaging tasks.
Keywords :
data compression; image coding; image sampling; statistical analysis; affine constraints; compressed data; compressed sensing; compressible data recovery; image robust recovery; impulsive noise; l1-norm loss function; large-scale convex optimization; mix-norm regularization; multitasking; nonsmooth regularization; robust CS algorithm; robust statistics; subNyquist sampling; Approximation algorithms; Approximation methods; Compressed sensing; Convergence; Noise; Optimization; Robustness; $ell_{1}$ regularization; ADMM; FISTA; IRLS; Robust compressed sensing; optimization algorithms;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2013.2277821
Filename :
6578162
Link To Document :
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