{"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/fast-algorithm-for-constrained-linear-inverse","title":"Fast Algorithm for Constrained Linear Inverse Problems","arxiv_id":"2212.01068","date":"2022-12-02","proceeding":null,"authors":["Mohammed Rayyan Sheriff","Floor Fenne Redel","Peyman Mohajerin Esfahani"],"abstract":"We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable which makes them not amenable to the fast optimization methods existing in practice. We propose two equivalent reformulations of the constrained LIP with improved convex regularity: (i) a smooth convex minimization problem, and (ii) a strongly convex min-max problem. These problems could be solved by applying existing acceleration-based convex optimization methods which provide better $ O \\left( \\frac{1}{k^2} \\right) $ theoretical convergence guarantee, improving upon the current best rate of $ O \\left( \\frac{1}{k} \\right) $. We also provide a novel algorithm named the Fast Linear Inverse Problem Solver (FLIPS), which is tailored to maximally exploit the structure of the reformulations. We demonstrate the performance of FLIPS on the classical problems of Binary Selection, Compressed Sensing, and Image Denoising. We also provide open source \\texttt{MATLAB} package for these three examples, which can be easily adapted to other LIPs.","url_abs":"https://arxiv.org/abs/2212.01068v6","url_pdf":"https://arxiv.org/pdf/2212.01068v6.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":"fast-algorithm-for-constrained-linear-inverse","repo_url":"https://github.com/mrayyans/flips","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}