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...
| Main Authors: | , |
|---|---|
| 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 |