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  <doc>
    <id>3592</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>8</issue>
    <volume>10</volume>
    <type>article</type>
    <publisherName>MDPI</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-04-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Feature Reconstruction from Incomplete Tomographic Data without Detour</title>
    <abstract language="eng">In this paper, we consider the problem of feature reconstruction from incomplete X-ray CT data. Such incomplete data problems occur when the number of measured X-rays is restricted either due to limit radiation exposure or due to practical constraints, making the detection of certain rays challenging. Since image reconstruction from incomplete data is a severely ill-posed (unstable) problem, the reconstructed images may suffer from characteristic artefacts or missing features, thus significantly complicating subsequent image processing tasks (e.g., edge detection or segmentation).&#13;
In this paper, we introduce a framework for the robust reconstruction of convolutional image features directly from CT data without the need of computing a reconstructed image first. Within our framework, we use non-linear variational regularization methods that can be adapted to a variety of feature reconstruction tasks and to several limited data situations. The proposed variational regularization method minimizes an energy functional being the sum of a feature dependent datafitting term and an additional penalty accounting for specific properties of the features. In our numerical experiments, we consider instances of edge reconstructions from angular under-sampled data and show that our approach is able to reliably reconstruct feature maps in this case.</abstract>
    <parentTitle language="eng">Mathematics</parentTitle>
    <identifier type="doi">10.3390/math10081318</identifier>
    <enrichment key="BegutachtungStatus">peer-reviewed</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Simon Göppel</author>
    <author>Jürgen Frikel</author>
    <author>Markus Haltmeier</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Computed tomography</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Radon transform</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reconstruction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>limited data</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sparse data</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>feature reconstruction,</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>edge detection</value>
    </subject>
    <collection role="ddc" number="5">Naturwissenschaften und Mathematik</collection>
    <collection role="institutes" number="FakIM">Fakultät Informatik und Mathematik</collection>
    <collection role="oaweg" number="">Gold Open Access- Erstveröffentlichung in einem/als Open-Access-Medium</collection>
    <collection role="othforschungsschwerpunkt" number="16315">Information und Kommunikation</collection>
  </doc>
</export-example>
