{"id":414,"date":"2021-12-07T08:48:15","date_gmt":"2021-12-07T07:48:15","guid":{"rendered":"https:\/\/yanntraonmilin.wordpress.com\/?p=414"},"modified":"2021-12-07T08:48:15","modified_gmt":"2021-12-07T07:48:15","slug":"new-preprint-4","status":"publish","type":"post","link":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/?p=414","title":{"rendered":"New preprint"},"content":{"rendered":"\n<p>We uploaded our new preprint:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><a href=\"https:\/\/hal.archives-ouvertes.fr\/hal-03467123v1\">\"A theory of optimal convex regularization for low-dimensional recovery\"<\/a>, Y. Traonmilin, R. Gribonval and S. Vaiter<\/pre>\n\n\n\n<p>Abstract  :  We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model, we ask ourselves what is the &#8220;best&#8221; convex regularizer to perform its recovery. To answer this question, we define an optimal regularizer as a function that maximizes a compliance measure with respect to the model. We introduce and study several notions of compliance. We give analytical expressions for compliance measures based on the best-known recovery guarantees with the restricted isometry property. These expressions permit to show the optimality of the \u2113 1-norm for sparse recovery and of the nuclear norm for low-rank matrix recovery for these compliance measures. We also investigate the construction of an optimal convex regularizer using the example of sparsity in levels.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We uploaded our new preprint: &#8220;A theory of optimal convex regularization for low-dimensional recovery&#8221;, Y. Traonmilin, R. Gribonval and S. Vaiter Abstract : We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-414","post","type-post","status-publish","format-standard","hentry","category-paper"],"_links":{"self":[{"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/414","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=414"}],"version-history":[{"count":0,"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/414\/revisions"}],"wp:attachment":[{"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yanntraonmilin.perso.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}