dc.contributor.author Fornasier, Massimo dc.contributor.author Schönlieb, Carola-Bibiane dc.date.accessioned 2016-02-28T06:10:01Z dc.date.available 2016-02-28T06:10:01Z dc.date.issued 2009-01 dc.identifier.citation Fornasier 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.issn 0036-1429 dc.identifier.issn 1095-7170 dc.identifier.doi 10.1137/070710779 dc.identifier.uri http://hdl.handle.net/10754/599796 dc.description.abstract This 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.sponsorship This work was based on work supported by Award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.subject 11-Minimization dc.subject Convex optimization dc.subject Degenerate elliptic PDEs dc.subject Discontinuous solutions dc.subject Domain decomposition method dc.subject Image and signal processing dc.subject Parallel computation dc.subject Subspace corrections dc.subject Total variation minimization dc.title Subspace Correction Methods for Total Variation and $\ell_1$-Minimization dc.type Article dc.identifier.journal SIAM Journal on Numerical Analysis dc.contributor.institution Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria dc.contributor.institution University of Cambridge, Cambridge, United Kingdom kaust.grant.number KUK-I1-007-43
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