{"paper":{"title":"Accuracy of spike-train Fourier reconstruction for colliding nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrey Akinshin, Dmitry Batenkov, Yosef Yomdin","submitted_at":"2015-02-24T20:11:49Z","abstract_excerpt":"We consider Fourier reconstruction problem for signals F, which are linear combinations of shifted delta-functions. We assume the Fourier transform of F to be known on the frequency interval [-N,N], with an absolute error not exceeding e > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the \"worst case\" reconstruction error of F in situations where the nodes (i.e. the positions of the shifted delta-functions in F) are known to form an l elements cluster of a size h << 1. Using \"decimation\" reconstruction algorithm we provide an upper bound for the reconst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06932","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"}