{"paper":{"title":"The Noise-Sensitivity Phase Transition in Compressed Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Arian Maleki, David L. Donoho","submitted_at":"2010-04-08T01:53:11Z","abstract_excerpt":"Consider the noisy underdetermined system of linear equations: y=Ax0 + z0, with n x N measurement matrix A, n < N, and Gaussian white noise z0 ~ N(0,\\sigma^2 I). Both y and A are known, both x0 and z0 are unknown, and we seek an approximation to x0. When x0 has few nonzeros, useful approximations are obtained by l1-penalized l2 minimization, in which the reconstruction \\hxl solves  min || y - Ax||^2/2 +  \\lambda ||x||_1.\n Evaluate performance by mean-squared error (MSE = E ||\\hxl - x0||_2^2/N). Consider matrices A with iid Gaussian entries and a large-system limit in which n,N\\to\\infty with n/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1218","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"}