{"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/jump-sparse-and-sparse-recovery-using-potts","title":"Jump-sparse and sparse recovery using Potts functionals","arxiv_id":"1304.4373","date":"2013-04-16","proceeding":null,"authors":["Martin Storath","Andreas Weinmann","Laurent Demaret"],"abstract":"We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted $\\ell^1$ minimization (sparse signals).","url_abs":"https://arxiv.org/abs/1304.4373v2","url_pdf":"https://arxiv.org/pdf/1304.4373v2.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":"jump-sparse-and-sparse-recovery-using-potts","repo_url":"https://github.com/mstorath/Pottslab","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}