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Article: On ℓ1 data fitting and concave regularization for image recovery
Title | On ℓ1 data fitting and concave regularization for image recovery |
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Authors | |
Keywords | Regularization Continuation methods Image recovery Inverse problems MRI Multidimensional shrinkage Nonsmooth and nonconvex analysis Nonsmooth and nonconvex minimization Penalty methods Properties of minimizers Total variation Variable-splitting Variational methods ℓ data fitting 1 |
Issue Date | 2013 |
Citation | SIAM Journal on Scientific Computing, 2013, v. 35, n. 1, p. A397-A430 How to Cite? |
Abstract | We propose a new family of cost functions for signal and image recovery: they are composed of ℓ1 data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks. © 2013 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276948 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Nikolova, Mila | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Tam, Chi Pan | - |
dc.date.accessioned | 2019-09-18T08:35:08Z | - |
dc.date.available | 2019-09-18T08:35:08Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 2013, v. 35, n. 1, p. A397-A430 | - |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276948 | - |
dc.description.abstract | We propose a new family of cost functions for signal and image recovery: they are composed of ℓ1 data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks. © 2013 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | - |
dc.subject | Regularization | - |
dc.subject | Continuation methods | - |
dc.subject | Image recovery | - |
dc.subject | Inverse problems | - |
dc.subject | MRI | - |
dc.subject | Multidimensional shrinkage | - |
dc.subject | Nonsmooth and nonconvex analysis | - |
dc.subject | Nonsmooth and nonconvex minimization | - |
dc.subject | Penalty methods | - |
dc.subject | Properties of minimizers | - |
dc.subject | Total variation | - |
dc.subject | Variable-splitting | - |
dc.subject | Variational methods | - |
dc.subject | ℓ data fitting 1 | - |
dc.title | On ℓ1 data fitting and concave regularization for image recovery | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/10080172X | - |
dc.identifier.scopus | eid_2-s2.0-84876259435 | - |
dc.identifier.volume | 35 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | A397 | - |
dc.identifier.epage | A430 | - |
dc.identifier.eissn | 1095-7200 | - |
dc.identifier.isi | WOS:000315575000018 | - |