{"paper":{"title":"Typical $l_1$-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.IT"],"primary_cat":"cs.IT","authors_text":"Mikko Vehkapera, Saikat Chatterjee, Yoshiyuki Kabashima","submitted_at":"2012-08-23T09:09:54Z","abstract_excerpt":"We consider the problem of recovering an $N$-dimensional sparse vector $\\vm{x}$ from its linear transformation $\\vm{y}=\\vm{D} \\vm{x}$ of $M(< N)$ dimension. Minimizing the $l_{1}$-norm of $\\vm{x}$ under the constraint $\\vm{y} = \\vm{D} \\vm{x}$ is a standard approach for the recovery problem, and earlier studies report that the critical condition for typically successful $l_1$-recovery is universal over a variety of randomly constructed matrices $\\vm{D}$. For examining the extent of the universality, we focus on the case in which $\\vm{D}$ is provided by concatenating $\\nb=N/M$ matrices $\\vm{O}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4696","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"}