Document Zbl 1481.65092

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Imaging</a> <a href="/?q=in%3A474211" title="Articles in this Issue">15, No. 6, 1287-1306 (2021)</a>. </div> <div class="abstract">Summary: Limited-angle reconstruction is a very important but challenging problem in the field of computed tomography (CT) which has been extensively studied for many years. However, some difficulties still remain. Based on the theory of visible and invisible boundary developed by Quinto et al., we propose a reconstruction model for limited-angle CT, which encodes the visible edges as priors to recover the invisible ones. The new model utilizes generalized shrinkage operators as regularizers to perform edge-preserving smoothing such that the visible edges are employed as anchors to recover piecewise-constant or piecewise-smooth reconstructions, while noises and artifacts are suppressed or removed. This work extends our previous research on limited-angle reconstruction which employs gradient $\ell_0$ and $\ell_1$ norm regularizers. The effectiveness of the proposed model and its corresponding solving algorithm shall be verified by numerical experiments with simulated data as well as real data.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7454685">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65K10" title="MSC2020">65K10</a> </td> <td class="space"> Numerical optimization and variational techniques </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A52" title="MSC2020">47A52</a> </td> <td class="space"> Linear operators and ill-posed problems, regularization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A94A08" title="MSC2020">94A08</a> </td> <td class="space"> Image processing (compression, reconstruction, etc.) in information and communication theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alimited-angle">limited-angle</a>; <a href="/?q=ut%3ACT+reconstruction">CT reconstruction</a>; <a href="/?q=ut%3Avisible+boundary">visible boundary</a>; <a href="/?q=ut%3Ageneralized+shrinkage+operator">generalized shrinkage operator</a>; <a href="/?q=ut%3Aregularizer">regularizer</a>; <a href="/?q=ut%3Aalternating+minimization">alternating minimization</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1481.65092" data-ciurl="/ci/07454685" data-biburl="/bibtex/07454685.bib" data-amsurl="/amsrefs/07454685.bib" data-xmlurl="/xml/07454685.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07454685.pdf" title="Zbl 1481.65092 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.3934/ipi.2021019" aria-label="DOI for “Limited-angle CT reconstruction with generalized shrinkage operators as regularizers”" title="10.3934/ipi.2021019">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. 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