{"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-unitary-transform-based-generalized","title":"A Unitary Transform Based Generalized Approximate Message Passing","arxiv_id":"2210.08861","date":"2022-10-17","proceeding":null,"authors":["Jiang Zhu","Xiangming Meng","Xupeng Lei","Qinghua Guo"],"abstract":"We consider the problem of recovering an unknown signal ${\\mathbf x}\\in {\\mathbb R}^n$ from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., ${\\mathbf y}= f\\left({\\mathbf A}{\\mathbf x}+{\\mathbf w}\\right)$, where $f(\\cdot)$ is a componentwise nonlinear function. Based on the unitary transform approximate message passing (UAMP) and expectation propagation, a unitary transform based generalized approximate message passing (GUAMP) algorithm is proposed for general measurement matrices $\\bf{A}$, in particular highly correlated matrices. Experimental results on quantized compressed sensing demonstrate that the proposed GUAMP significantly outperforms state-of-the-art GAMP and GVAMP under correlated matrices $\\bf{A}$.","url_abs":"https://arxiv.org/abs/2210.08861v1","url_pdf":"https://arxiv.org/pdf/2210.08861v1.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-unitary-transform-based-generalized","repo_url":"https://github.com/riverzhu/guamp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.08861","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}