{"paper":{"title":"Linear signal recovery from $b$-bit-quantized linear measurements: precise analysis of the trade-off between bit depth and number of measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.ME"],"primary_cat":"cs.IT","authors_text":"Martin Slawski, Ping Li","submitted_at":"2016-07-09T19:49:14Z","abstract_excerpt":"We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. Our interest is in linear approaches to signal recovery, where \"linear\" means that non-linearity resulting from quantization is ignored and the observations are treated as if they arose from a linear measurement model. Specifically, the focus is on a generalization of a method for one-bit observations due to Plan and Vershynin [\\emph{IEEE~Trans. Inform. Theory, \\textbf{59} (2013), 482--494}]. At the heart of the present paper is a prec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02649","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"}