{"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/compressed-sensing-with-prior-information","title":"Compressed Sensing with Prior Information: Optimal Strategies, Geometry, and Bounds","arxiv_id":"1408.5250","date":"2014-08-22","proceeding":null,"authors":["Joao F. C. Mota","Nikos Deligiannis","Miguel R. D. Rodrigues"],"abstract":"We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via L1-L1 and L1-L2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, L1-L1 minimization improves the performance of CS dramatically. In contrast, L1-L2 minimization has a performance very similar to classical CS and brings no significant benefits. All our findings are illustrated with experimental results.","url_abs":"http://arxiv.org/abs/1408.5250v1","url_pdf":"http://arxiv.org/pdf/1408.5250v1.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":"compressed-sensing-with-prior-information","repo_url":"https://github.com/joaofcmota/AdaptiveRateCompressiveForegroundExtraction","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"compressed-sensing-with-prior-information","repo_url":"https://github.com/joaofcmota/cs-with-prior-information","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}