{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/from-denoising-to-compressed-sensing","title":"From Denoising to Compressed Sensing","arxiv_id":"1406.4175","date":"2014-06-16","proceeding":null,"authors":["Christopher A. Metzler","Arian Maleki","Richard G. Baraniuk"],"abstract":"A denoising algorithm seeks to remove noise, errors, or perturbations from a\nsignal. Extensive research has been devoted to this arena over the last several\ndecades, and as a result, today's denoisers can effectively remove large\namounts of additive white Gaussian noise. A compressed sensing (CS)\nreconstruction algorithm seeks to recover a structured signal acquired using a\nsmall number of randomized measurements. Typical CS reconstruction algorithms\ncan be cast as iteratively estimating a signal from a perturbed observation.\nThis paper answers a natural question: How can one effectively employ a generic\ndenoiser in a CS reconstruction algorithm? In response, we develop an extension\nof the approximate message passing (AMP) framework, called Denoising-based AMP\n(D-AMP), that can integrate a wide class of denoisers within its iterations. We\ndemonstrate that, when used with a high performance denoiser for natural\nimages, D-AMP offers state-of-the-art CS recovery performance while operating\ntens of times faster than competing methods. We explain the exceptional\nperformance of D-AMP by analyzing some of its theoretical features. A key\nelement in D-AMP is the use of an appropriate Onsager correction term in its\niterations, which coerces the signal perturbation at each iteration to be very\nclose to the white Gaussian noise that denoisers are typically designed to\nremove.","url_abs":"http://arxiv.org/abs/1406.4175v5","url_pdf":"http://arxiv.org/pdf/1406.4175v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"from-denoising-to-compressed-sensing","repo_url":"https://github.com/PSCLab-ASU/OpenICS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"from-denoising-to-compressed-sensing","repo_url":"https://github.com/ricedsp/D-AMP_Toolbox","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1406.4175","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}