{"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/composite-optimization-for-robust-blind","title":"Composite optimization for robust blind deconvolution","arxiv_id":"1901.01624","date":"2019-01-06","proceeding":null,"authors":["Vasileios Charisopoulos","Damek Davis","Mateo Díaz","Dmitriy Drusvyatskiy"],"abstract":"The blind deconvolution problem seeks to recover a pair of vectors from a set\nof rank one bilinear measurements. We consider a natural nonsmooth formulation\nof the problem and show that under standard statistical assumptions, its moduli\nof weak convexity, sharpness, and Lipschitz continuity are all dimension\nindependent. This phenomenon persists even when up to half of the measurements\nare corrupted by noise. Consequently, standard algorithms, such as the\nsubgradient and prox-linear methods, converge at a rapid dimension-independent\nrate when initialized within constant relative error of the solution. We then\ncomplete the paper with a new initialization strategy, complementing the local\nsearch algorithms. The initialization procedure is both provably efficient and\nrobust to outlying measurements. Numerical experiments, on both simulated and\nreal data, illustrate the developed theory and methods.","url_abs":"http://arxiv.org/abs/1901.01624v2","url_pdf":"http://arxiv.org/pdf/1901.01624v2.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":"composite-optimization-for-robust-blind","repo_url":"https://github.com/COR-OPT/RobustBlindDeconv","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}