{"id":2642,"date":"2025-03-26T07:02:31","date_gmt":"2025-03-26T07:02:31","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/26\/2503-19190\/"},"modified":"2025-03-26T07:02:31","modified_gmt":"2025-03-26T07:02:31","slug":"2503-19190","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/26\/2503-19190\/","title":{"rendered":"Universal Architectures for the Learning of Polyhedral Norms and Convex Regularization Functionals"},"content":{"rendered":"

Universal Architectures for the Learning of Polyhedral Norms and Convex Regularization Functionals
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arXiv:2503.19190v1 Announce Type: new
\nAbstract: This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be expressed as a power of a seminorm. We then show that such functionals can be approximated to arbitrary precision with the help of polyhedral norms. In particular, we identify two dual parameterizations of such systems: (i) a synthesis form with an $ell_1$-penalty that involves some learnable dictionary; and (ii) an analysis form with an $ell_infty$-penalty that involves a trainable regularization operator. After having provided geometric insights and proved that the two forms are universal, we propose an implementation that relies on a specific architecture (tight frame with a weighted $ell_1$ penalty) that is easy to train. We illustrate its use for denoising and the reconstruction of biomedical images. We find that the proposed framework outperforms the sparsity-based methods of compressed sensing, while it offers essentially the same convergence and robustness guarantees.<\/div>\n

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\n Michael Unser, Stanislas Ducotterd
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Universal Architectures for the Learning of Polyhedral Norms and Convex Regularization Functionals arXiv:2503.19190v1 Announce Type: new Abstract: This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[2132,199,461],"class_list":["post-2642","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-functionals","tag-learning","tag-universal"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2642"}],"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=2642"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2642\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}