Document Zbl 1480.90259

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Math. Modelling</a> <a href="/?q=in%3A445719" title="Articles in this Issue">48, 410-422 (2017)</a>. </div> <div class="abstract">Summary: Low-rankness has been widely exploited for the tensor completion problem. Recent advances have suggested that the tensor nuclear norm often leads to a promising approximation for the tensor rank. It treats the singular values equally to pursue the convexity of the objective function, while the singular values for the practical images have clear physical meanings with different importance and should be treated differently. In this paper, we propose a non-convex logDet function as a smooth approximation for tensor rank instead of the convex tensor nuclear norm and introduce it into the low-rank tensor completion problem. An alternating direction method of multiplier (ADMM)-based method is developed to solve the problem. Experimental results have shown that the proposed method can significantly outperform existing state-of-the-art nuclear norm-based methods for tensor completion.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7163410">Cited in <strong>24</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C90" title="MSC2020">90C90</a> </td> <td class="space"> Applications of mathematical programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A69" title="MSC2020">15A69</a> </td> <td class="space"> Multilinear algebra, tensor calculus </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A86" title="MSC2020">15A86</a> </td> <td class="space"> Linear preserver problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C26" title="MSC2020">90C26</a> </td> <td class="space"> Nonconvex programming, global optimization </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atensor+completion">tensor completion</a>; <a href="/?q=ut%3Alow-rank+approximation">low-rank approximation</a>; <a href="/?q=ut%3Anon-convex+optimization">non-convex optimization</a>; <a href="/?q=ut%3Aalternating+direction+method+of+multipliers">alternating direction method of multipliers</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 1480.90259" data-ciurl="/ci/07163410" data-biburl="/bibtex/07163410.bib" data-amsurl="/amsrefs/07163410.bib" data-xmlurl="/xml/07163410.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07163410.pdf" title="Zbl 1480.90259 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/10.1016/j.apm.2017.04.002" aria-label="DOI for “A non-convex tensor rank approximation for tensor completion”" title="10.1016/j.apm.2017.04.002">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">Bertalmio, M.; Sapiro, G.; Caselles, V.; Ballester, C., Image inpainting, Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’00, 417-424 (2000), ACM Press/Addison-Wesley Publishing Co.: ACM Press/Addison-Wesley Publishing Co. 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