{"paper":{"title":"Sparse approximation based on a random overcomplete basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"Masato Okada, Tomoyuki Obuchi, Yoshinori Nakanishi-Ohno, Yoshiyuki Kabashima","submitted_at":"2015-10-08T03:09:13Z","abstract_excerpt":"We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given overcomplete basis, according to a given compression rate, such that they compactly represent the target data with as small a distortion as possible. As a selection method, we study the $\\ell_0$- and $\\ell_1$-based methods, which employ the exhaustive search and $\\ell_1$-norm regularization techniques, respectively. The performance is assessed in terms of the trade-of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02189","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"}