{"paper":{"title":"Sparse Fast DCT for Vectors with One-block Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Gerlind Plonka, Sina Bittens","submitted_at":"2018-03-14T11:23:23Z","abstract_excerpt":"In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II that reconstructs the input vector $\\mathbf{x}\\in\\mathbb{R}^{N}$, $N=2^{J-1}$, with short support of length $m$ from its discrete cosine transform $\\mathbf{x}^{\\widehat{\\mathrm{II}}}=\\mathbf{C}_N^{\\mathrm{II}}\\mathbf{x}$.\n  The resulting algorithm has a runtime of $\\mathcal{O}\\left(m\\log m\\log \\frac{2N}{m}\\right)$ and requires $\\mathcal{O}\\left(m\\log \\frac{2N}{m}\\right)$ samples of $\\mathbf{x}^{\\widehat{\\mathrm{II}}}$.\n  In order to derive this algorithm we also develop a new fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05207","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/1803.05207/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"}