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dc.contributor.authorMyllykoski, Mirko
dc.contributor.authorGlowinski, Roland
dc.contributor.authorKärkkäinen, Tommi
dc.contributor.authorRossi, Tuomo
dc.date.accessioned2015-01-29T09:59:30Z
dc.date.available2015-01-29T09:59:30Z
dc.date.issued2015
dc.identifier.citationMyllykoski, M., Glowinski, R., Kärkkäinen, T., & Rossi, T. (2015). A New Augmented Lagrangian Approach for L1-mean Curvature Image Denoising. <i>SIAM Journal on Imaging Sciences</i>, <i>8</i>(1), 95-125. <a href="https://doi.org/10.1137/140962164" target="_blank">https://doi.org/10.1137/140962164</a>
dc.identifier.otherCONVID_24491898
dc.identifier.otherTUTKAID_64896
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/45188
dc.description.abstractVariational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from existing augmented Lagrangian approaches for the solution of the same problem; indeed, the augmented Lagrangian functional we use here contains three Lagrange multipliers “only,” and the associated augmentation terms are all quadratic. In addition to the description of the solution algorithm, this paper contains the results of numerical experiments demonstrating the performance of the novel method discussed here.
dc.language.isoeng
dc.publisherSociety for Industrial and Applied Mathematics
dc.relation.ispartofseriesSIAM Journal on Imaging Sciences
dc.subject.otheralternating direction methods of multipliers
dc.subject.otheraugmented Lagrangian method
dc.subject.otherimage denoising
dc.subject.othermean curvature
dc.subject.othervariational model
dc.titleA New Augmented Lagrangian Approach for L1-mean Curvature Image Denoising
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201501261178
dc.contributor.laitosTietotekniikan laitosfi
dc.contributor.laitosDepartment of Mathematical Information Technologyen
dc.contributor.oppiaineTietotekniikkafi
dc.contributor.oppiaineMathematical Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2015-01-26T16:30:06Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange95-125
dc.relation.issn1936-4954
dc.relation.numberinseries1
dc.relation.volume8
dc.type.versionpublishedVersion
dc.rights.copyright© 2015 Society for Industrial and Applied Mathematics. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.subject.ysokuvankäsittely
jyx.subject.urihttp://www.yso.fi/onto/yso/p6449
dc.relation.doi10.1137/140962164


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