{"paper":{"title":"Leveraging Diversity and Sparsity in Blind Deconvolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Ahmed, Laurent Demanet","submitted_at":"2016-10-19T16:35:07Z","abstract_excerpt":"This paper considers recovering $L$-dimensional vectors $\\boldsymbol{w}$, and $\\boldsymbol{x}_1,\\boldsymbol{x}_2, \\ldots, \\boldsymbol{x}_N$ from their circular convolutions $\\boldsymbol{y}_n = \\boldsymbol{w}*\\boldsymbol{x}_n, \\ n = 1,2,3, \\ldots, N$. The vector $\\boldsymbol{w}$ is assumed to be $S$-sparse in a known basis that is spread out in the Fourier domain, and each input $\\boldsymbol{x}_n$ is a member of a known $K$-dimensional random subspace.\n  We prove that whenever $K + S\\log^2S \\lesssim L /\\log^4(LN)$, the problem can be solved effectively by using only the nuclear-norm minimizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06098","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"}