{"paper":{"title":"On the modified Basis Pursuit reconstruction for Compressed Sensing with partially known support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Stephane Chretien","submitted_at":"2009-06-02T20:20:09Z","abstract_excerpt":"The goal of this short note is to present a refined analysis of the modified Basis Pursuit ($\\ell_1$-minimization) approach to signal recovery in Compressed Sensing with partially known support, as introduced by Vaswani and Lu. The problem is to recover a signal $x \\in \\mathbb R^p$ using an observation vector $y=Ax$, where $A \\in \\mathbb R^{n\\times p}$ and in the highly underdetermined setting $n\\ll p$. Based on an initial and possibly erroneous guess $T$ of the signal's support ${\\rm supp}(x)$, the Modified Basis Pursuit method of Vaswani and Lu consists of minimizing the $\\ell_1$ norm of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0593","kind":"arxiv","version":3},"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"}