{"paper":{"title":"Real Sparse Fast DCT for Vectors with Short Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gerlind Plonka, Sina Bittens","submitted_at":"2018-07-19T13:27:35Z","abstract_excerpt":"In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector $\\mathbf x\\in\\mathbb R^N$, $N=2^J$, with short support of length $m$ from its discrete cosine transform $\\mathbf x^{\\widehat{\\mathrm{II}}}=C^{\\mathrm{II}}_N\\mathbf x$ if an upper bound $M\\geq m$ is known. The resulting algorithm only uses real arithmetic, has a runtime of $\\mathcal{O}\\left(M\\log M+m\\log_2\\frac{N}{M}\\right)$ and requires $\\mathcal{O}\\left(M+m\\log_2\\frac{N}{M}\\right)$ samples of $\\mathbf x^{\\widehat{\\mathrm{II}}}$. For $m,M\\righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07397","kind":"arxiv","version":2},"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"}