{"paper":{"title":"A Sublinear Algorithm of Sparse Fourier Transform for Nonequispaced Data","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Computational Mathematics, Jing Zou (1) ((1) Program in Applied, Princeton University.)","submitted_at":"2005-02-16T17:25:20Z","abstract_excerpt":"We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L<N are available. If the ratio p=L/N is not close to 1, the available data are typically non-equispaced samples. Then our algorithm reconstructs a near-optimal B-term representation R with high probability 1-delta, in time and space poly(B,log(L),log p, log(1/delta), epsilon^{-1}, such that ||S-R||^2 < (1+epsilon) ||S-R_{opt}^B||^2, where R_{opt}^B is the optimal B-term Fourier representation of signal S. The su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0502357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}