{"paper":{"title":"Precise Error Analysis of the $\\ell_2$-LASSO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Ashkan Panahi, Babak Hassibi, Christos Thrampoulidis, Daniel Guo","submitted_at":"2015-02-17T17:49:46Z","abstract_excerpt":"A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, $k$-sparse signal $x_0\\in R^n$ from underdetermined, noisy, linear measurements $y=Ax_0+z\\in R^m$. One standard approach is to solve the following convex program $\\hat x=\\arg\\min_x \\|y-Ax\\|_2 + \\lambda \\|x\\|_1$, which is known as the $\\ell_2$-LASSO. We assume that the entries of the sensing matrix $A$ and of the noise vector $z$ are i.i.d Gaussian with variances $1/m$ and $\\sigma^2$. In the large system limit when the problem dimensions grow to infinity, but in constant rates, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04977","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"}