Subspace Correction Methods for Total Variation and $\ell_1$-Minimization
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Publication:3056234
DOI10.1137/070710779zbMATH Open1203.65098arXiv0712.2258OpenAlexW2052972089MaRDI QIDQ3056234
Author name not available (Why is that?)
Publication date: 11 November 2010
Published in: (Search for Journal in Brave)
Abstract: This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm 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 emph{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 singular elliptic PDE's arising in total variation minimization and in accelerated sparse recovery algorithms based on -minimization. We include numerical examples which show efficient solutions to classical problems in signal and image processing.
Full work available at URL: https://arxiv.org/abs/0712.2258
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