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  <doc>
    <id>6044</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A complementary ℓ1 -TV reconstruction algorithm for limited data CT</title>
    <abstract language="eng">In a variety of tomographic applications, data cannot be fully acquired, leading to severely underdetermined image reconstruction. Conventional methods result in reconstructions with significant artifacts. In order to remove these artifacts, regularization methods have to be applied that incorporate additional information. An important example is TV reconstruction which is well known to efficiently compensate for missing data and well reduces reconstruction artifacts. At the same time, however, tomographic data is also contaminated by noise, which poses an additional challenge. The use of a single regularizer within a variational regularization framework must therefore account for both the missing data and the noise. However, a single regularizer may not be ideal for both tasks. For example, the TV regularizer is a poor choice for noise reduction over different scales, in which case ℓ1 curvelet regularization methods work well. To address this issue, in this paper we introduce a novel variational regularization framework that combines the advantages of two different regularizers. The basic idea of our framework is to perform reconstruction in two stages, where the first stage mainly aims at accurate reconstruction in the presence of noise, and the second stage aims at artifact reduction. Both reconstruction stages are connected by a data proximity condition. The proposed method is implemented and tested for limited-view CT using a combined curvelet-TV approach. We define and implement a curvelet transform adapted to the limited view problem and demonstrate the advantages of our approach in a series of numerical experiments in this context.</abstract>
    <identifier type="arxiv">arXiv:2304.11599</identifier>
    <licence>Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG</licence>
    <author>Simon Göppel</author>
    <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>limited data</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>artifact reduction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sparse regularization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>complementary image reconstruction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>wedge-adapted curvelets</value>
    </subject>
    <collection role="institutes" number="FakIM">Fakultät Informatik und Mathematik</collection>
    <collection role="othforschungsschwerpunkt" number="16311">Digitalisierung</collection>
  </doc>
</export-example>
