{"paper":{"title":"Wiener Filters in Gaussian Mixture Signal Estimation with Infinity-Norm Error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dror Baron, Jin Tan, Liyi Dai","submitted_at":"2014-05-17T02:56:46Z","abstract_excerpt":"Consider the estimation of a signal ${\\bf x}\\in\\mathbb{R}^N$ from noisy observations ${\\bf r=x+z}$, where the input~${\\bf x}$ is generated by an independent and identically distributed (i.i.d.) Gaussian mixture source, and ${\\bf z}$ is additive white Gaussian noise (AWGN) in parallel Gaussian channels. Typically, the $\\ell_2$-norm error (squared error) is used to quantify the performance of the estimation process. In contrast, we consider the $\\ell_\\infty$-norm error (worst case error). For this error metric, we prove that, in an asymptotic setting where the signal dimension $N\\to\\infty$, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4345","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"}