Efficient algorithms for robust recovery of images from compressed data

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 modelled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS...

Full description

Bibliographic Details
Main Authors: Pham, DucSon, Venkatesh, S.
Format: Journal Article
Published: IEEE 2013
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/17178
_version_ 1848749391890874368
author Pham, DucSon
Venkatesh, S.
author_facet Pham, DucSon
Venkatesh, S.
author_sort Pham, DucSon
building Curtin Institutional Repository
collection Online Access
description 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 modelled 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.
first_indexed 2025-11-14T07:20:12Z
format Journal Article
id curtin-20.500.11937-17178
institution Curtin University Malaysia
institution_category Local University
last_indexed 2025-11-14T07:20:12Z
publishDate 2013
publisher IEEE
recordtype eprints
repository_type Digital Repository
spelling curtin-20.500.11937-171782017-09-13T15:41:23Z Efficient algorithms for robust recovery of images from compressed data Pham, DucSon Venkatesh, S. compressed sensing optimization approximation algorithms 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 modelled 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. 2013 Journal Article http://hdl.handle.net/20.500.11937/17178 10.1109/TIP.2013.2277821 IEEE fulltext
spellingShingle compressed sensing
optimization
approximation algorithms
Pham, DucSon
Venkatesh, S.
Efficient algorithms for robust recovery of images from compressed data
title Efficient algorithms for robust recovery of images from compressed data
title_full Efficient algorithms for robust recovery of images from compressed data
title_fullStr Efficient algorithms for robust recovery of images from compressed data
title_full_unstemmed Efficient algorithms for robust recovery of images from compressed data
title_short Efficient algorithms for robust recovery of images from compressed data
title_sort efficient algorithms for robust recovery of images from compressed data
topic compressed sensing
optimization
approximation algorithms
url http://hdl.handle.net/20.500.11937/17178