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dc.contributor.authorFornasier, Massimo
dc.contributor.authorSchönlieb, Carola-Bibiane
dc.date.accessioned2016-02-28T06:10:01Z
dc.date.available2016-02-28T06:10:01Z
dc.date.issued2009-01
dc.identifier.citationFornasier M, Schönlieb C-B (2009) Subspace Correction Methods for Total Variation and $\ell_1$-Minimization. SIAM J Numer Anal 47: 3397–3428. Available: http://dx.doi.org/10.1137/070710779.
dc.identifier.issn0036-1429
dc.identifier.issn1095-7170
dc.identifier.doi10.1137/070710779
dc.identifier.urihttp://hdl.handle.net/10754/599796
dc.description.abstractThis paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces. On each subspace an iterative proximity-map algorithm is implemented via oblique thresholding, which is the main new tool introduced in this work. We provide convergence conditions for the algorithm in order to compute minimizers of the target energy. Analogous results are derived for a parallel variant of the algorithm. Applications are presented in domain decomposition methods for degenerate elliptic PDEs arising in total variation minimization and in accelerated sparse recovery algorithms based on 1-minimization. We include numerical examples which show e.cient solutions to classical problems in signal and image processing. © 2009 Society for Industrial and Applied Physics.
dc.description.sponsorshipThis work was based on work supported by Award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subject11-Minimization
dc.subjectConvex optimization
dc.subjectDegenerate elliptic PDEs
dc.subjectDiscontinuous solutions
dc.subjectDomain decomposition method
dc.subjectImage and signal processing
dc.subjectParallel computation
dc.subjectSubspace corrections
dc.subjectTotal variation minimization
dc.titleSubspace Correction Methods for Total Variation and $\ell_1$-Minimization
dc.typeArticle
dc.identifier.journalSIAM Journal on Numerical Analysis
dc.contributor.institutionJohann Radon Institute for Computational and Applied Mathematics, Linz, Austria
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
kaust.grant.numberKUK-I1-007-43


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