Document Zbl 0874.93008

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When the system is time-invariant, this problem is often referred to as deconvolution. Three representative physiological problems, regarding hormone secretion, insulin dynamics, and hepatic glucose production, are used to illustrate the major challenges: ill-conditioning, confidence intervals assessment, infrequent and nonuniform sampling, nonnegativity constraints, and computational efficiency. The paper provides a critical overview of the existing techniques, focusing on regularization theory and Bayesian estimation. In order to overcome some inadequacies of the existing methods, some new results are derived. In particular, the connection between the maximum-likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied. Moreover, a fast SVD-based numerical algorithm is developed that includes the optimization of the regularization parameter, and the computation of confidence intervals. The proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1036530">Cited in <strong>21</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93A99" title="MSC2020">93A99</a> </td> <td class="space"> General systems theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C35" title="MSC2020">92C35</a> </td> <td class="space"> Physiological flow </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainverse+problems">inverse problems</a>; <a href="/?q=ut%3Asmoothing">smoothing</a>; <a href="/?q=ut%3Abiomedical+systems">biomedical systems</a>; <a href="/?q=ut%3Ainput+estimation">input estimation</a>; <a href="/?q=ut%3Aphysiological+systems">physiological systems</a>; <a href="/?q=ut%3Aill-conditioning">ill-conditioning</a>; <a href="/?q=ut%3Aconfidence+intervals+assessment">confidence intervals assessment</a>; <a href="/?q=ut%3Anonuniform+sampling">nonuniform sampling</a>; <a href="/?q=ut%3Amaximum-likelihood+estimate">maximum-likelihood estimate</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 0874.93008" data-ciurl="/ci/01036530" data-biburl="/bibtex/01036530.bib" data-amsurl="/amsrefs/01036530.bib" data-xmlurl="/xml/01036530.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01036530.pdf" title="Zbl 0874.93008 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/S0005-1098(96)00254-3" aria-label="DOI for “Nonparametric input estimation in physiological systems: Problems, methods, and case studies”" title="10.1016/S0005-1098(96)00254-3">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">Ahlen, A., Identifiability of the deconvolution problem, Automatica, 26, 177-181 (1990) · <a href="/0714.93054" class="nowrap">Zbl 0714.93054</a></td> </tr><tr> <td>[2]</td> <td class="space">Anderson, B. 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