{"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/unlabeled-compressed-sensing-from-multiple","title":"Unlabeled Compressed Sensing from Multiple Measurement Vectors","arxiv_id":"2406.08290","date":"2024-06-12","proceeding":null,"authors":["Mohamed Akrout","Amine Mezghani","Faouzi Bellili"],"abstract":"This paper introduces an algorithmic solution to a broader class of unlabeled sensing problems with multiple measurement vectors (MMV). The goal is to recover an unknown structured signal matrix, $\\mathbf{X}$, from its noisy linear observation matrix, $\\mathbf{Y}$, whose rows are further randomly shuffled by an unknown permutation matrix $\\mathbf{U}$. A new Bayes-optimal unlabeled compressed sensing (UCS) recovery algorithm is developed from the bilinear approximate message passing (Bi-VAMP) framework using non-separable and coupled priors on the rows and columns of the permutation matrix $\\mathbf{U}$. In particular, standard unlabeled sensing is a special case of the proposed framework, and UCS further generalizes it by neither assuming a partially shuffled signal matrix $\\mathbf{X}$ nor a small-sized permutation matrix $\\mathbf{U}$. For the sake of theoretical performance prediction, we also conduct a state evolution (SE) analysis of the proposed algorithm and show its consistency with the asymptotic empirical mean-squared error (MSE). Numerical results demonstrate the effectiveness of the proposed UCS algorithm and its advantage over state-of-the-art baseline approaches in various applications. We also numerically examine the phase transition diagrams of UCS, thereby characterizing the detectability region as a function of the signal-to-noise ratio (SNR).","url_abs":"https://arxiv.org/abs/2406.08290v1","url_pdf":"https://arxiv.org/pdf/2406.08290v1.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":"unlabeled-compressed-sensing-from-multiple","repo_url":"https://github.com/makrout/Unlabeled-Compressed-Sensing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}