{"paper":{"title":"One-bit compressive sensing with norm estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.OC","math.PR"],"primary_cat":"stat.ML","authors_text":"Karin Knudson, Rachel Ward, Rayan Saab","submitted_at":"2014-04-28T02:01:33Z","abstract_excerpt":"Consider the recovery of an unknown signal ${x}$ from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that ${x}$ is sparse, and that the measurements are of the form $\\operatorname{sign}(\\langle {a}_i, {x} \\rangle) \\in \\{\\pm1\\}$. Since such measurements give no information on the norm of ${x}$, recovery methods from such measurements typically assume that $\\| {x} \\|_2=1$. We show that if one allows more generally for quantized affine measurements of the form $\\operatorname{sign}(\\langle {a}_i, {x} \\rangle + b_i)$, and if the vectors ${a}_i$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6853","kind":"arxiv","version":3},"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"}