{"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/bilinear-recovery-using-adaptive-vector-amp","title":"Bilinear Recovery using Adaptive Vector-AMP","arxiv_id":"1809.00024","date":"2018-08-31","proceeding":null,"authors":["Subrata Sarkar","Alyson K. Fletcher","Sundeep Rangan","Philip Schniter"],"abstract":"We consider the problem of jointly recovering the vector $\\boldsymbol{b}$ and the matrix $\\boldsymbol{C}$ from noisy measurements $\\boldsymbol{Y} = \\boldsymbol{A}(\\boldsymbol{b})\\boldsymbol{C} + \\boldsymbol{W}$, where $\\boldsymbol{A}(\\cdot)$ is a known affine linear function of $\\boldsymbol{b}$ (i.e., $\\boldsymbol{A}(\\boldsymbol{b})=\\boldsymbol{A}_0+\\sum_{i=1}^Q b_i \\boldsymbol{A}_i$ with known matrices $\\boldsymbol{A}_i$). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (BAd-VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear GAMP.","url_abs":"https://arxiv.org/abs/1809.00024v2","url_pdf":"https://arxiv.org/pdf/1809.00024v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"bilinear-recovery-using-adaptive-vector-amp","repo_url":"https://github.com/sbrsarkar/BAdVAMP","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}