DagSemProc.08492.5.pdf
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Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints
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Dagstuhl Seminar Proceedings, Volume 8492
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2009-02-24
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Martin Ehler and Simone Geisel. Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.08492.5
https://doi.org/10.4230/DagSemProc.08492.5
Abstract
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$.
Keywords
- Frames
- shrinkage
- variational problems
- sparse approximation
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