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Article: Efficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration

TitleEfficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration
Authors
Keywordsleast squares
least absolute deviation
interior point method
linear programming
quadratic programming
Issue Date2006
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SISC
Citation
SIAM Journal on Scientific Computing, 2006, v. 27 n. 6, p. 1881-1902 How to Cite?
AbstractImage restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the ℓ2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the ℓ1 norm. For the LMN solution, the regularization term is in the ℓ1 norm but the data-fitting term is in the ℓ2 norm. Since images often have nonnegative intensity values, the proposed algorithms provide the option of taking into account the nonnegativity constraint. The LMN and LAD solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images, using the minimization of mixed ℓ2-ℓ1 and ℓ1-ℓ1 norms, is better than that using only the ℓ2 norm.
Persistent Identifierhttp://hdl.handle.net/10722/44909
ISSN
2015 Impact Factor: 1.792
2015 SCImago Journal Rankings: 2.166
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorFu, HYen_HK
dc.contributor.authorNg, MKen_HK
dc.contributor.authorNikolova, Men_HK
dc.contributor.authorBarlow, JLen_HK
dc.date.accessioned2007-10-30T06:13:11Z-
dc.date.available2007-10-30T06:13:11Z-
dc.date.issued2006en_HK
dc.identifier.citationSIAM Journal on Scientific Computing, 2006, v. 27 n. 6, p. 1881-1902en_HK
dc.identifier.issn1064-8275en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44909-
dc.description.abstractImage restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the ℓ2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the ℓ1 norm. For the LMN solution, the regularization term is in the ℓ1 norm but the data-fitting term is in the ℓ2 norm. Since images often have nonnegative intensity values, the proposed algorithms provide the option of taking into account the nonnegativity constraint. The LMN and LAD solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images, using the minimization of mixed ℓ2-ℓ1 and ℓ1-ℓ1 norms, is better than that using only the ℓ2 norm.en_HK
dc.format.extent268876 bytes-
dc.format.extent1819 bytes-
dc.format.extent2254 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SISCen_HK
dc.relation.ispartofSIAM Journal on Scientific Computing-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectleast squaresen_HK
dc.subjectleast absolute deviationen_HK
dc.subjectinterior point methoden_HK
dc.subjectlinear programmingen_HK
dc.subjectquadratic programmingen_HK
dc.titleEfficient minimization methods of mixed l2-l1 and l1-l1 norms for image restorationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1064-8275&volume=27&issue=6&spage=1881&epage=1902&date=2006&atitle=Efficient+minimization+methods+of+mixed+l2-l1+and+l1-l1+norms+for+image+restorationen_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1137/040615079en_HK
dc.identifier.scopuseid_2-s2.0-33751208047-
dc.identifier.isiWOS:000236100100005-

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