{"paper":{"title":"Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"A. Powell, \\\"O. Y{\\i}lmaz, R. Saab, S. G\\\"unt\\\"urk","submitted_at":"2010-02-01T08:12:24Z","abstract_excerpt":"Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\\delta$ is used to quantize $m$ measurements $y = \\Phi x$ of a $k$-sparse signal $x \\in \\R^N$, where $\\Phi$ satisfies the restricted isometry property, then the approximate recovery $x^#$ via $\\ell_1$-minimization is within $O(\\delta)$ of $x$. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an $r$th order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0182","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"}