{"paper":{"title":"De-noising by thresholding operator adapted wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Gene Ryan Yoo, Houman Owhadi","submitted_at":"2018-05-28T02:23:57Z","abstract_excerpt":"Donoho and Johnstone proposed a method from reconstructing an unknown smooth function $u$ from noisy data $u+\\zeta$ by translating the empirical wavelet coefficients of $u+\\zeta$ towards zero. We consider the situation where the prior information on the unknown function $u$ may not be the regularity of $u$ but that of $ \\L u$ where $\\L$ is a linear operator (such as a PDE or a graph Laplacian). We show that the approximation of $u$ obtained by thresholding the gamblet (operator adapted wavelet) coefficients of $u+\\zeta$ is near minimax optimal (up to a multiplicative constant), and with high p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10736","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"}