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Tikhonov regularization with oversmoothing penalties

In the last decade l1-regularization became a powerful and popular tool for the regularization of Inverse Problems. While in the early years sparse solution were in the focus of research, recently also the case that the coefficients of the exact solution decay sufficiently fast was under consideration. In this paper we seek to show that l1-regularization is applicable and leads to optimal convergence rates even when the exact solution does not belong to l1 but only to l2. This is a particular example of over-smoothing regularization, i.e., the penalty implies smoothness properties the exact solution does not fulfill. We will make some statements on convergence also in this general context.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:20619
Date21 December 2016
CreatorsGerth, Daniel
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/submittedVersion, doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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