Regularization of Ill-Posed Problems with Non-negative Solutions

Christian Clason (), Barbara Kaltenbacher () and Elena Resmerita ()
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Christian Clason: University Duisburg-Essen, Faculty of Mathematics
Barbara Kaltenbacher: Alpen-Adria Universität Klagenfurt, Institute of Mathematics
Elena Resmerita: Alpen-Adria Universität Klagenfurt, Institute of Mathematics

Chapter Chapter 5 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 113-135 from Springer

Abstract: Abstract This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or constraints, and iterative methods involving projections or non-negativity-preserving multiplicative updates. We summarize known results and point out some open problems.

Keywords: Convex optimization; Fenchel duality; Entropy; Regularization; Sparsity; Signal processing; 49M20; 65K10; 90C30 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_5

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DOI: 10.1007/978-3-030-25939-6_5

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