{"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/nmf-with-sparse-regularizations-in","title":"NMF with Sparse Regularizations in Transformed Domains","arxiv_id":"1407.7691","date":"2014-07-29","proceeding":null,"authors":["Jérémy Rapin","Jérôme Bobin","Anthony Larue","Jean-Luc Starck"],"abstract":"Non-negative blind source separation (non-negative BSS), which is also\nreferred to as non-negative matrix factorization (NMF), is a very active field\nin domains as different as astrophysics, audio processing or biomedical signal\nprocessing. In this context, the efficient retrieval of the sources requires\nthe use of signal priors such as sparsity. If NMF has now been well studied\nwith sparse constraints in the direct domain, only very few algorithms can\nencompass non-negativity together with sparsity in a transformed domain since\nsimultaneously dealing with two priors in two different domains is challenging.\nIn this article, we show how a sparse NMF algorithm coined non-negative\ngeneralized morphological component analysis (nGMCA) can be extended to impose\nnon-negativity in the direct domain along with sparsity in a transformed\ndomain, with both analysis and synthesis formulations. To our knowledge, this\nwork presents the first comparison of analysis and synthesis priors ---as well\nas their reweighted versions--- in the context of blind source separation.\nComparisons with state-of-the-art NMF algorithms on realistic data show the\nefficiency as well as the robustness of the proposed algorithms.","url_abs":"http://arxiv.org/abs/1407.7691v1","url_pdf":"http://arxiv.org/pdf/1407.7691v1.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":"nmf-with-sparse-regularizations-in","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":"retrieval","task_name":"Retrieval"},{"task_slug":"blind-source-separation","task_name":"blind source separation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}