{"paper":{"title":"Does $\\ell_p$-minimization outperform $\\ell_1$-minimization?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Arian Maleki, Haolei Weng, Le Zheng, Teng Long, Xiaodong Wang","submitted_at":"2015-01-15T14:54:10Z","abstract_excerpt":"In many application areas we are faced with the following question: Can we recover a sparse vector $x_o \\in \\mathbb{R}^N$ from its undersampled set of noisy observations $y \\in \\mathbb{R}^n$, $y=A x_o+w$. The last decade has witnessed a surge of algorithms and theoretical results addressing this question. One of the most popular algorithms is the $\\ell_p$-regularized least squares (LPLS) given by the following formulation: \\[ \\hat{x}(\\gamma,p )\\in \\arg\\min_x \\frac{1}{2}\\|y - Ax\\|_2^2+\\gamma\\|x\\|_p^p, \\] where $p \\in [0,1]$. Despite the non-convexity of these problems for $p<1$, they are still "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03704","kind":"arxiv","version":2},"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"}