{"paper":{"title":"Super-Resolution from Noisy Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Carlos Fernandez-Granda, Emmanuel Candes","submitted_at":"2012-11-01T20:04:31Z","abstract_excerpt":"This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off frequency and seek to obtain a higher resolution estimate by extrapolating the spectrum up to a higher frequency. We show that as long as the sources are separated by twice the inverse of the cut-off frequency, solving a simple convex program produces a stable estimate in the sense that the approximation error between the higher-resolution reconstruction and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0290","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"}