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Imaging</a> <a href="/?q=in%3A495636" title="Articles in this Issue">17, No. 2, 362-380 (2023)</a>. </div> <div class="abstract">Summary: We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7675898">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%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%3A68T10" title="MSC2020">68T10</a> </td> <td class="space"> Pattern recognition, speech recognition </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C55" title="MSC2020">92C55</a> </td> <td class="space"> Biomedical imaging and signal processing </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A42A16" title="MSC2020">42A16</a> </td> <td class="space"> Fourier coefficients, Fourier series of functions with special properties, special Fourier series </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amulti-target+detection">multi-target detection</a>; <a href="/?q=ut%3Aautocorrelation+analysis">autocorrelation analysis</a>; <a href="/?q=ut%3Abispectrum">bispectrum</a>; <a href="/?q=ut%3Asingle-particle+reconstruction">single-particle reconstruction</a>; <a href="/?q=ut%3Acryo-EM">cryo-EM</a></div> <div class="software"> <h3>Software:</h3><a href="/software/39533">cryoSPARC</a>; <a href="/software/39537">crYOLO</a>; <a href="/software/9056">EMan</a>; <a href="/software/22792">RELION</a>; <a href="/software/19729">SIGNATURE</a>; <a href="/software/32498">cisTEM</a>; <a href="/software/14943">DeepPicker</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1511.94009" data-ciurl="/ci/07675898" data-biburl="/bibtex/07675898.bib" data-amsurl="/amsrefs/07675898.bib" data-xmlurl="/xml/07675898.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07675898.pdf" title="Zbl 1511.94009 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.2022046" aria-label="DOI for “Multi-target detection with rotations”" title="10.3934/ipi.2022046">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2101.07709"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">E. 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