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  <doc>
    <id>3146</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>28</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>34</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient regularization with wavelet sparsity constraints in photoacoustic tomography</title>
    <abstract language="eng">In this paper, we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we derive a wavelet-vaguelette decomposition (WVD) for the PAT forward operator and a corresponding explicit reconstruction formula in the case of exact data. In the case of noisy data, we combine the WVD reconstruction formula with soft-thresholding, which yields a spatially adaptive estimation method. We demonstrate that our method is statistically optimal for white random noise if the unknown function is assumed to lie in any Besov-ball. We present generalizations of this approach and, in particular, we discuss the combination of PAT-vaguelette soft-thresholding with a total variation (TV) prior. We also provide an efficient implementation of the PAT-vaguelette transform that leads to fast image reconstruction algorithms supported by numerical results.</abstract>
    <parentTitle language="eng">Inverse Problems</parentTitle>
    <identifier type="doi">10.1088/1361-6420/aaa0ac</identifier>
    <note>Corresponding authors: Jürgen Frikel and Markus Haltmeier</note>
    <enrichment key="opus.import.date">2022-03-17T06:33:09+00:00</enrichment>
    <enrichment key="opus.source">sword</enrichment>
    <enrichment key="opus.import.user">importuser</enrichment>
    <enrichment key="BegutachtungStatus">peer-reviewed</enrichment>
    <author>Jürgen Frikel</author>
    <author>Markus Haltmeier</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Image reconstruction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>photoacoustic tomography</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sparsity constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>variational regularization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>wavelet-vaguelette decomposition</value>
    </subject>
    <collection role="institutes" number="FakIM">Fakultät Informatik und Mathematik</collection>
    <collection role="othforschungsschwerpunkt" number="16315">Information und Kommunikation</collection>
    <collection role="oaweg" number="">Hybrid Open Access - OA-Veröffentlichung in einer Subskriptionszeitschrift/-medium</collection>
    <collection role="oaweg" number="">Corresponding author der OTH Regensburg</collection>
  </doc>
</export-example>
