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Article: Fast algorithms for l1 norm/mixed l1 and l2 norms for image restoration

TitleFast algorithms for l1 norm/mixed l1 and l2 norms for image restoration
Authors
KeywordsImage restoration
Interior point method
Least absolute deviation
Least mixed norm
Issue Date2005
PublisherSpringer Verlag. The Journal's web site is located at http://springerlink.com/content/105633/
Citation
Lecture Notes In Computer Science, 2005, v. 3483 IV, p. 843-851 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. The LAD and the LMN solutions are formulated as the solutions of a linear and a quadratic programming problems respectively, and 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 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 ℓ1 norm/mixed ℓ1 and ℓ2 norms is better than that using ℓ2 norm approach. © Springer-Verlag Berlin Heidelberg 2005.
Persistent Identifierhttp://hdl.handle.net/10722/123610
ISSN
2005 Impact Factor: 0.402
2015 SCImago Journal Rankings: 0.252
References

 

DC FieldValueLanguage
dc.contributor.authorFu, Hen_HK
dc.contributor.authorNg, MKen_HK
dc.contributor.authorNikolova, Men_HK
dc.contributor.authorBarlow, Jen_HK
dc.contributor.authorChing, WKen_HK
dc.date.accessioned2010-09-26T12:15:47Z-
dc.date.available2010-09-26T12:15:47Z-
dc.date.issued2005en_HK
dc.identifier.citationLecture Notes In Computer Science, 2005, v. 3483 IV, p. 843-851en_HK
dc.identifier.issn0302-9743en_HK
dc.identifier.urihttp://hdl.handle.net/10722/123610-
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. The LAD and the LMN solutions are formulated as the solutions of a linear and a quadratic programming problems respectively, and 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 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 ℓ1 norm/mixed ℓ1 and ℓ2 norms is better than that using ℓ2 norm approach. © Springer-Verlag Berlin Heidelberg 2005.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://springerlink.com/content/105633/en_HK
dc.relation.ispartofLecture Notes in Computer Scienceen_HK
dc.subjectImage restorationen_HK
dc.subjectInterior point methoden_HK
dc.subjectLeast absolute deviationen_HK
dc.subjectLeast mixed normen_HK
dc.titleFast algorithms for l1 norm/mixed l1 and l2 norms for image restorationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0302-9743&volume=3483&spage=843&epage=851&date=2005&atitle=Fast+Algorithms+for+l1+Norm/Mixed+l1+and+l2+Norms+for+Image+Restorationen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-24944486480en_HK
dc.identifier.hkuros98001en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-24944486480&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume3483en_HK
dc.identifier.issueIVen_HK
dc.identifier.spage843en_HK
dc.identifier.epage851en_HK
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridFu, H=9734298800en_HK
dc.identifier.scopusauthoridNg, MK=7202076432en_HK
dc.identifier.scopusauthoridNikolova, M=7102804796en_HK
dc.identifier.scopusauthoridBarlow, J=7402197869en_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK

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