{"id":2835,"date":"2025-04-03T07:02:29","date_gmt":"2025-04-03T07:02:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/04\/03\/2504-01046\/"},"modified":"2025-04-03T07:02:29","modified_gmt":"2025-04-03T07:02:29","slug":"2504-01046","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/04\/03\/2504-01046\/","title":{"rendered":"Denoising guarantees for optimized sampling schemes in compressed sensing"},"content":{"rendered":"<p>    Denoising guarantees for optimized sampling schemes in compressed sensing<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2504.01046v1 Announce Type: new<br \/>\nAbstract: Compressed sensing with subsampled unitary matrices benefits from emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused by the measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming that the noise is Gaussian. We moreover provide similar guarantees for measurements sampled with-replacement with arbitrary probability weights. All our results hold on prior sets contained in a union of low-dimensional subspaces. Finally, we demonstrate that this denoising behavior appears in empirical experiments with a rate that closely matches our theoretical guarantees when the prior set is the range of a generative ReLU neural network and when it is the set of sparse vectors.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Yaniv Plan, Matthew S. Scott, Xia Sheng, Ozgur Yilmaz<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2504.01046\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Denoising guarantees for optimized sampling schemes in compressed sensing arXiv:2504.01046v1 Announce Type: new Abstract: Compressed sensing with subsampled unitary matrices benefits from emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,414,113,382,415,420,112],"tags":[2262,2263,125],"class_list":["post-2835","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-it","category-cs-lg","category-eess-sp","category-math-it","category-math-pr","category-stat-ml","tag-guarantees","tag-optimized","tag-sampling"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2835"}],"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=2835"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2835\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}