{"paper":{"title":"L2/L2-foreach sparse recovery with low risk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anna C. Gilbert, Atri Rudra, Ely Porat, Hung Q. Ngo, Martin J. Strauss","submitted_at":"2013-04-23T11:00:45Z","abstract_excerpt":"In this paper, we consider the \"foreach\" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \\times N$ matrices $\\Phi$ and a decoding algorithm $\\algo$ such that for every $\\vx\\in\\R^N$, we have the following error guarantee with probability at least $1-p$ \\[\\|\\vx-\\algo(\\Phi\\vx)\\|_2\\le C\\|\\vx-\\vx_k\\|_2,\\] where $C$ is a constant (ideally arbitrarily close to 1) and $\\vx_k$ is the best $k$-sparse approximation of $\\vx$.\n  Much of the sparse recovery or compressive sensing literature has focused on the case of either $p = 0$ or $p = \\Omega(1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6232","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"}