Subspace Correction Methods for Total Variation and $\ell_1$-Minimization
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 |