{"paper":{"title":"Sparse Recovery for Orthogonal Polynomial Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Albert Gu, Anna Gilbert, Atri Rudra, Christopher Re, Mary Wootters","submitted_at":"2019-07-19T03:44:05Z","abstract_excerpt":"In this paper we consider the following sparse recovery problem. We have query access to a vector $\\vx \\in \\R^N$ such that $\\vhx = \\vF \\vx$ is $k$-sparse (or nearly $k$-sparse) for some orthogonal transform $\\vF$. The goal is to output an approximation (in an $\\ell_2$ sense) to $\\vhx$ in sublinear time. This problem has been well-studied in the special case that $\\vF$ is the Discrete Fourier Transform (DFT), and a long line of work has resulted in sparse Fast Fourier Transforms that run in time $O(k \\cdot \\mathrm{polylog} N)$. However, for transforms $\\vF$ other than the DFT (or closely relate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08362","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"}