<?xml version="1.0" encoding="utf-8"?>
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  <doc>
    <id>160</id>
    <completedYear>2016</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>891</pageFirst>
    <pageLast>935</pageLast>
    <pageNumber>43</pageNumber>
    <edition/>
    <issue/>
    <volume>454</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-08-25</completedDate>
    <publishedDate>2017-08-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Analytical aspects of spatially adapted total variation regularisation</title>
    <abstract language="eng">In this paper we study the structure of solutions of the one dimensional weighted total&#13;
variation regularisation problem, motivated by its application in signal recovery tasks. We study&#13;
in depth the relationship between the weight function and the creation of new discontinuities in&#13;
the solution. A partial semigroup property relating the weight function and the solution is shown&#13;
and analytic solutions for simply data functions are computed. We prove that the weighted total&#13;
variation minimisation problem is well-posed even in the case of vanishing weight function, despite&#13;
the lack of coercivity. This is based on the fact that the total variation of the solution is bounded&#13;
by the total variation of the data, a result that it also shown here. Finally the relationship to the&#13;
corresponding weighted fidelity problem is explored, showing that the two problems can produce&#13;
completely different solutions even for very simple data functions.</abstract>
    <parentTitle language="eng">Journal of Mathematical Analysis and Applications</parentTitle>
    <enrichment key="review.accepted_by">2</enrichment>
    <author>Konstantinos Papafitsoros</author>
    <author>Michael Hintermüller</author>
    <author>Carlos Rautenberg</author>
    <collection role="institutes" number="">Humboldt-Universität zu Berlin</collection>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B02</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/160/[H_P_R]AnalyticalAspectsOfSpatiallyAdaptedTotalVariationRegularization.pdf</file>
  </doc>
</export-example>
