{"paper":{"title":"Re-Weighted $\\ell_1$ Algorithms within the Lagrange Duality Framework: Bringing Interpretability to Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","eess.SP","math.NA"],"primary_cat":"math.OC","authors_text":"Marcelo Fiori, Mat\\'ias Vald\\'es","submitted_at":"2019-06-21T21:10:25Z","abstract_excerpt":"We consider an important problem in signal processing, which consists in finding the sparsest solution of a linear system $\\Phi x=b$. This problem has applications in several areas, but is NP-hard in general. Usually an alternative convex problem is considered, based on minimizing the (weighted) $\\ell_{1}$ norm. For this alternative to be useful, weights should be chosen as to obtain a solution of the original NP-hard problem. A well known algorithm for this is the Re-Weighted $\\ell_{1}$, proposed by Cand\\`es, Wakin and Boyd. In this article we introduce a new methodology for updating the weig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09329","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}