{"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/sparse-and-non-negative-bss-for-noisy-data","title":"Sparse and Non-Negative BSS for Noisy Data","arxiv_id":"1308.5546","date":"2013-08-26","proceeding":null,"authors":["Jérémy Rapin","Jérôme Bobin","Anthony Larue","Jean-Luc Starck"],"abstract":"Non-negative blind source separation (BSS) has raised interest in various\nfields of research, as testified by the wide literature on the topic of\nnon-negative matrix factorization (NMF). In this context, it is fundamental\nthat the sources to be estimated present some diversity in order to be\nefficiently retrieved. Sparsity is known to enhance such contrast between the\nsources while producing very robust approaches, especially to noise. In this\npaper we introduce a new algorithm in order to tackle the blind separation of\nnon-negative sparse sources from noisy measurements. We first show that\nsparsity and non-negativity constraints have to be carefully applied on the\nsought-after solution. In fact, improperly constrained solutions are unlikely\nto be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA\n(non-negative Generalized Morphological Component Analysis), makes use of\nproximal calculus techniques to provide properly constrained solutions. The\nperformance of nGMCA compared to other state-of-the-art algorithms is\ndemonstrated by numerical experiments encompassing a wide variety of settings,\nwith negligible parameter tuning. In particular, nGMCA is shown to provide\nrobustness to noise and performs well on synthetic mixtures of real NMR\nspectra.","url_abs":"http://arxiv.org/abs/1308.5546v1","url_pdf":"http://arxiv.org/pdf/1308.5546v1.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":"sparse-and-non-negative-bss-for-noisy-data","repo_url":"https://github.com/jbobin/pyGMCALab","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"blind-source-separation","task_name":"blind source separation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}