{"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/weighted-block-compressed-sensing-for","title":"Weighted block compressed sensing for parametrized function approximation","arxiv_id":"1811.04598","date":"2018-11-12","proceeding":null,"authors":["Jean-Luc Bouchot"],"abstract":"In this paper we extend results taken from compressed sensing to recover Hilbert-space valued vectors. This is an important problem in parametric function approximation in particular when the number of parameters is high. By expanding our target functions in a polynomial chaos and assuming some compressibility of such an expansion, we can exploit structured sparsity (typically a group sparsity structure) to recover the sequence of coefficients with high accuracy. While traditional compressed sensing would typically expect a number of snapshots scaling exponentially with the number of parameters, we can beat this dependence by adding weights. This anisotropic handling of the parameter space permits to compute approximations with a number of samples scaling only linearly (up to log-factors) with the intrinsic complexity of the polynomial expansion. Our results are applied to problems in high-dimensional parametric elliptic PDEs. We show that under some weighted uniform ellipticity assumptions of a parametric operator, we are capable of numerically approximating the full solution (in contrast to the usual quantity of interest) to within a specified accuracy.","url_abs":"https://arxiv.org/abs/1811.04598v3","url_pdf":"https://arxiv.org/pdf/1811.04598v3.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":"weighted-block-compressed-sensing-for","repo_url":"https://github.com/jlbouchot/CSPDEs","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}