{"id":762,"date":"2024-12-23T07:02:45","date_gmt":"2024-12-23T07:02:45","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2024\/12\/23\/2412-16031\/"},"modified":"2024-12-23T07:02:45","modified_gmt":"2024-12-23T07:02:45","slug":"2412-16031","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2024\/12\/23\/2412-16031\/","title":{"rendered":"Learning sparsity-promoting regularizers for linear inverse problems"},"content":{"rendered":"<p>    Learning sparsity-promoting regularizers for linear inverse problems<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2412.16031v1 Announce Type: new<br \/>\nAbstract: This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes the inverse problem while promoting sparsity in the solution. The method leverages statistical properties of the underlying data and incorporates prior knowledge through the choice of $B$. We establish the well-posedness of the optimization problem, provide theoretical guarantees for the learning process, and present sample complexity bounds. The approach is demonstrated through examples, including compact perturbations of a known operator and the problem of learning the mother wavelet, showcasing its flexibility in incorporating prior knowledge into the regularization framework. This work extends previous efforts in Tikhonov regularization by addressing non-differentiable norms and proposing a data-driven approach for sparse regularization in infinite dimensions.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Giovanni S. Alberti, Ernesto De Vito, Tapio Helin, Matti Lassas, Luca Ratti, Matteo Santacesaria<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2412.16031\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Learning sparsity-promoting regularizers for linear inverse problems arXiv:2412.16031v1 Announce Type: new Abstract: This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes the inverse problem while promoting sparsity in the solution. The method [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,112,191],"tags":[199,873,872],"class_list":["post-762","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-learning","tag-promoting","tag-sparsity"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/762"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=762"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/762\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}