{"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/a-biconvex-analysis-for-lasso-l1-reweighting","title":"A biconvex analysis for Lasso l1 reweighting","arxiv_id":"1812.02990","date":"2018-12-07","proceeding":null,"authors":["Sophie M. Fosson"],"abstract":"l1 reweighting algorithms are very popular in sparse signal recovery and\ncompressed sensing, since in the practice they have been observed to outperform\nclassical l1 methods. Nevertheless, the theoretical analysis of their\nconvergence is a critical point, and generally is limited to the convergence of\nthe functional to a local minimum or to subsequence convergence. In this\nletter, we propose a new convergence analysis of a Lasso l1 reweighting method,\nbased on the observation that the algorithm is an alternated convex search for\na biconvex problem. Based on that, we are able to prove the numerical\nconvergence of the sequence of the iterates generated by the algorithm. This is\nnot yet the convergence of the sequence, but it is close enough for practical\nand numerical purposes. Furthermore, we propose an alternative iterative soft\nthresholding procedure, which is faster than the main algorithm.","url_abs":"http://arxiv.org/abs/1812.02990v1","url_pdf":"http://arxiv.org/pdf/1812.02990v1.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":"a-biconvex-analysis-for-lasso-l1-reweighting","repo_url":"https://github.com/sophie27/Lasso-l1-reweigthing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"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}