Document Zbl 08010676

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Imaging Sci.</a> <a href="/?q=in%3A523843" title="Articles in this Issue">18, No. 1, SC1-SC15 (2025)</a>. </div> <div class="abstract">Summary: The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play (<span class="zbmathjax-texttt">PnP</span>) and Regularization-by-Denoising (<span class="zbmathjax-texttt">RED</span>). We consider two specific algorithms, <span class="zbmathjax-texttt">PnP-FISTA</span> and <span class="zbmathjax-texttt">RED-APG</span>, where regularization is performed by replacing the proximal operator in the <span class="zbmathjax-texttt">FISTA</span> algorithm with a powerful denoiser. The iterate convergence of <span class="zbmathjax-texttt">FISTA</span> is known to be challenging with no universal guarantees. Yet, we show that for linear inverse problems and a class of linear denoisers, global linear convergence of the iterates of <span class="zbmathjax-texttt">PnP-FISTA</span> and <span class="zbmathjax-texttt">RED-APG</span> can be established through simple spectral analysis.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><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><tr> <td> <a class="mono" href="/classification/?q=cc%3A41A25" title="MSC2020">41A25</a> </td> <td class="space"> Rate of convergence, degree of approximation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F10" title="MSC2020">65F10</a> </td> <td class="space"> Iterative numerical methods for linear systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68U10" title="MSC2020">68U10</a> </td> <td class="space"> Computing methodologies for image processing </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C25" title="MSC2020">90C25</a> </td> <td class="space"> Convex programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aimage+regularization">image regularization</a>; <a href="/?q=ut%3Aplug-and-play">plug-and-play</a>; <a href="/?q=ut%3Aregularization-by-denoising">regularization-by-denoising</a>; <a href="/?q=ut%3AFISTA">FISTA</a>; <a href="/?q=ut%3Alinear+convergence">linear convergence</a></div> <div class="software"> <h3>Software:</h3><a href="/software/39678">DnCNN</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 08010676" data-ciurl="/ci/08010676" data-biburl="/bibtex/08010676.bib" data-amsurl="/amsrefs/08010676.bib" data-xmlurl="/xml/08010676.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/08010676.pdf" title="Zbl 08010676 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/10.1137/24M1656530" aria-label="DOI for “Short communication: FISTA iterates converge linearly for denoiser-driven regularization”" title="10.1137/24M1656530">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2411.10808"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Athalye, C. 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