Entropic Regularization of the ℓ 0 Function

Jonathan M. Borwein () and D. Russell Luke
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Jonathan M. Borwein: University of Goettingen

Chapter Chapter 5 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 65-92 from Springer

Abstract: Abstract Many problems of interest where more than one solution is possible seek, among these, the one that is sparsest. The objective that most directly accounts for sparsity, the ℓ 0 metric, is usually avoided since this leads to a combinatorial optimization problem. The function $$\|{x\|}_{0}$$ is often viewed as the limit of the ℓ p metrics. Naturally, there have been some attempts to use this as an objective for p small, though this is a nonconvex function for p

Keywords: Convex optimization; Fenchel duality; Entropy; Regularization; Sparsity; Signal processing (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-9569-8_5

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