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Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints Ehler, Martin Geisel, Simone Frames shrinkage variational problems sparse approximation Finding a sparse representation of a possibly noisy signal is a common problem in signal representation and processing. It can be modeled as a variational minimization with $ell_ au$-sparsity constraints for $ au<1$. Applications whose computation time is crucial require fast algorithms for this minimization. However, there are no fast methods for finding the exact minimizer, and to circumvent this limitation, we consider minimization up to a constant factor. We verify that arbitrary shrinkage rules provide closed formulas for such minimizers, and we introduce a new shrinkage strategy, which is adapted to $ au<1$. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Martin Ehler and Simone Geisel 2009 Is Part Of Dagstuhl Seminar Proceedings, Volume 8492, Structured Decompositions and Efficient Algorithms (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.08492.5 urn:nbn:de:0030-drops-18816 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08492.5 eng https://creativecommons.org/licenses/by/4.0/legalcode