{"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/multi-resolution-compressed-sensing-via","title":"Multi-Resolution Compressed Sensing via Approximate Message Passing","arxiv_id":"1508.02454","date":"2015-08-11","proceeding":null,"authors":["Xing Wang","Jie Liang"],"abstract":"In this paper, we consider the problem of multi-resolution compressed sensing (MR-CS) reconstruction, which has received little attention in the literature. Instead of always reconstructing the signal at the original high resolution (HR), we enable the reconstruction of a low-resolution (LR) signal when there are not enough CS samples to recover a HR signal. We propose an approximate message passing (AMP)-based framework dubbed MR-AMP, and derive its state evolution, phase transition, and noise sensitivity, which show that in addition to reduced complexity, our method can recover a LR signal with bounded noise sensitivity even when the noise sensitivity of the conventional HR reconstruction is unbounded. We then apply the MR-AMP to image reconstruction using either soft-thresholding or total variation denoiser, and develop three pairs of up-/down-sampling operators in transform or spatial domain. The performance of the proposed scheme is demonstrated by both 1D synthetic data and 2D images.","url_abs":"http://arxiv.org/abs/1508.02454v3","url_pdf":"http://arxiv.org/pdf/1508.02454v3.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":"multi-resolution-compressed-sensing-via","repo_url":"https://github.com/xingwangsfu/MR-AMP","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}