Show simple item record

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
*
hal.structure.identifier
dc.contributor.authorDeVore, Ron*
hal.structure.identifier
dc.contributor.authorLee, Nam-Yong*
hal.structure.identifier
dc.contributor.authorLucier, Bradley J.*
dc.date.accessioned2011-05-31T08:34:22Z
dc.date.available2011-05-31T08:34:22Z
dc.date.issued1998
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6370
dc.language.isoenen
dc.subjectvariational problemsen
dc.subjectwavelet-based image processing algorithmsen
dc.subject.ddc519en
dc.titleNonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkageen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem. Given an image F defined on a square I, minimize over all g in the Besov space B11(L1(I)) the functional |F-g|L2(I)2+λ|g|(B11(L1(I))). We use the theory of nonlinear wavelet image compression in L2(I) to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i.i.d., mean zero, Gaussian noise. A new signal-to-noise ratio (SNR), which we claim more accurately reflects the visual perception of noise in images, arises in this derivation. We present extensive computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F: the largest α for which F∈Bqα(Lq(I)),1/q=α/2+1/2, and the norm |F|Bqα(Lq(I)). Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Donoho and Johnstone's VisuShrink procedure; an example suggests, however, that Donoho and Johnstone's (1994, 1995, 1996) SureShrink method, which uses a different shrinkage parameter for each dyadic level, achieves a lower error than our procedure.en
dc.relation.isversionofjnlnameIEEE Transactions on Image Processing
dc.relation.isversionofjnlvol7en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate1998
dc.relation.isversionofjnlpages319-335en
dc.relation.isversionofdoihttp://dx.doi.org/10.1109/83.661182en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherIEEEen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record