{"paper":{"title":"Comment on \"Asymptotic Achievability of the Cram\\'{e}r-Rao Bound for Noisy Compressive Sampling\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behtash Babadi, Nicholas Kalouptsidis, Vahid Tarokh","submitted_at":"2015-09-15T02:18:04Z","abstract_excerpt":"In [1], we proved the asymptotic achievability of the Cram\\'{e}r-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of $\\alpha \\sigma^2$ for the genie-aided Cram\\'{e}r-Rao bound $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ from Lemma 3.5, which appears in Eqs. (20) and (29). The proof, however, holds if one avoids replacing $\\sigma^2 \\textrm{Tr} (\\mathbf{A}^*_\\mathcal{I} \\mathbf{A}_\\mathcal{I})^{-1}$ by the expression of Lemma 3.5, and hence the claim of the Main Theorem stands t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04375","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"}