{"paper":{"title":"A robust parallel algorithm for combinatorial compressed sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.NA","authors_text":"Florian Wechsung, Jared Tanner, Rodrigo Mendoza-Smith","submitted_at":"2017-04-28T17:17:07Z","abstract_excerpt":"In previous work two of the authors have shown that a vector $x \\in \\mathbb{R}^n$ with at most $k < n$ nonzeros can be recovered from an expander sketch $Ax$ in $\\mathcal{O}(\\mathrm{nnz}(A)\\log k)$ operations via the Parallel-$\\ell_0$ decoding algorithm, where $\\mathrm{nnz}(A)$ denotes the number of nonzero entries in $A \\in \\mathbb{R}^{m \\times n}$. In this paper we present the Robust-$\\ell_0$ decoding algorithm, which robustifies Parallel-$\\ell_0$ when the sketch $Ax$ is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.09012","kind":"arxiv","version":1},"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"}