{"paper":{"title":"A typical reconstruction limit of compressed sensing based on Lp-norm minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"T. Tanaka, T. Wadayama, Y. Kabashima","submitted_at":"2009-07-06T05:38:16Z","abstract_excerpt":"We consider the problem of reconstructing an $N$-dimensional continuous vector $\\bx$ from $P$ constraints which are generated by its linear transformation under the assumption that the number of non-zero elements of $\\bx$ is typically limited to $\\rho N$ ($0\\le \\rho \\le 1$). Problems of this type can be solved by minimizing a cost function with respect to the $L_p$-norm $||\\bx||_p=\\lim_{\\epsilon \\to +0}\\sum_{i=1}^N |x_i|^{p+\\epsilon}$, subject to the constraints under an appropriate condition. For several $p$, we assess a typical case limit $\\alpha_c(\\rho)$, which represents a critical relatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0914","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"}