Document Zbl 1375.47002

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Imaging</a> <a href="/?q=in%3A364753" title="Articles in this Issue">11, No. 2, 221-246 (2017)</a>. </div> <div class="abstract">Summary: We study Tikhonov regularization for solving ill-posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spline surfaces. Another contribution is that we highlight the analysis of regularization for functions with range in vector bundles over surfaces. We also present some practical applications, such as an inverse problem of gravimetry and an imaging problem for denoising vector fields on surfaces, and show the numerical verification.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6701100">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%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%3A65J20" title="MSC2020">65J20</a> </td> <td class="space"> Numerical solutions of ill-posed problems in abstract spaces; regularization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A53B20" title="MSC2020">53B20</a> </td> <td class="space"> Local Riemannian geometry </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46C99" title="MSC2020">46C99</a> </td> <td class="space"> Inner product spaces and their generalizations, Hilbert spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D07" title="MSC2020">65D07</a> </td> <td class="space"> Numerical computation using splines </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ATikhonov+regularization">Tikhonov regularization</a>; <a href="/?q=ut%3Aconvergence">convergence</a>; <a href="/?q=ut%3Avector+field">vector field</a>; <a href="/?q=ut%3Aambient+space">ambient space</a>; <a href="/?q=ut%3Asurface+approximation">surface approximation</a>; <a href="/?q=ut%3Amagnetization+computation">magnetization computation</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 1375.47002" data-ciurl="/ci/06701100" data-biburl="/bibtex/06701100.bib" data-amsurl="/amsrefs/06701100.bib" data-xmlurl="/xml/06701100.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06701100.pdf" title="Zbl 1375.47002 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.2017011" aria-label="DOI for “Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces”" title="10.3934/ipi.2017011">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1510.07028"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">J. 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