{"paper":{"title":"On the Theorem of Uniform Recovery of Random Sampling Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT"],"primary_cat":"cs.IT","authors_text":"Jan-Olov Str\\\"omberg, Joel Andersson","submitted_at":"2012-06-26T13:37:49Z","abstract_excerpt":"We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements (with high probability) is known to be $m\\gtrsim s(\\ln s)^3\\ln N$. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of $m\\times N$-matrices, by considering what we call \\emph{low entropy}. We also present an improved condition on the so-called restricted iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5986","kind":"arxiv","version":3},"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"}