{"paper":{"title":"Coherence-Based Performance Guarantee of Regularized $\\ell_{1}$-Norm Minimization and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Feng Zhang, Jianjun Wang, Wendong Wang, Zhi Wang","submitted_at":"2018-12-10T11:22:48Z","abstract_excerpt":"In this paper, we consider recovering the signal $\\bm{x}\\in\\mathbb{R}^{n}$ from its few noisy measurements $\\bm{b}=A\\bm{x}+\\bm{z}$, where $A\\in\\mathbb{R}^{m\\times n}$ with $m\\ll n$ is the measurement matrix, and $\\bm{z}\\in\\mathbb{R}^{m}$ is the measurement noise/error. We first establish a coherence-based performance guarantee for a regularized $\\ell_{1}$-norm minimization model to recover such signals $\\bm{x}$ in the presence of the $\\ell_{2}$-norm bounded noise, i.e., $\\|\\bm{z}\\|_{2}\\leq\\epsilon$, and then extend these theoretical results to guarantee the robust recovery of the signals corru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03739","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"}