{"paper":{"title":"Efficient $\\ell_q$ Minimization Algorithms for Compressive Sensing Based on Proximity Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fei Wen, Peilin Liu, Rendong Ying, Yipeng Liu, Yuan Yang","submitted_at":"2015-06-17T15:58:29Z","abstract_excerpt":"This paper considers solving the unconstrained $\\ell_q$-norm ($0\\leq q<1$) regularized least squares ($\\ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via incorporating the proximity operator for nonconvex $\\ell_q$-norm functions into the fast iterative shrinkage/thresholding (FISTA) and the alternative direction method of multipliers (ADMM) frameworks, respectively. Furthermore, in solving the nonconvex $\\ell_q$-LS problem, a sequential minimization strategy is adopted in the new algorithms to gain better global "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05374","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"}