{"paper":{"title":"Simple Bounds for Noisy Linear Inverse Problems with Exact Side Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Babak Hassibi, Christos Thrampoulidis, Samet Oymak","submitted_at":"2013-12-02T22:07:05Z","abstract_excerpt":"This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\\cdot)$ that exploits the structure of the signal. For example, $\\ell_1$ norm can be used for sparse signals. To carry out the estimation, we consider two well-known convex programs: 1) Second order cone program (SOCP), and, 2) Lasso. Assuming Gaussian measurements, we show that, if precise information about the value $f(x)$ or the $\\ell_2$-norm of the noise is available, one can do a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0641","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"}