@article{912c8820568d42a289c66f4dbfed97b9,
title = "Universal Frame Thresholding",
abstract = "We provide the first frame agnostic thresholding scheme based on risk minimization, which can be applied to arbitrary frames and provide its theoretical guarantees. We investigate the proposed scheme, study its empirical risk, and demonstrates how it falls back to the standard Donoho thresholding scheme for orthogonal basis. We then validate our technique and apply it to the overcomplete wavelet transforms of the Deep Scattering Network. We are thus obtaining an invariant and thresholded representation of the signals providing significant performance gains compared to the non-thresholded version.",
keywords = "Bird song, classification, frame, overcomplete, scattering network, sparsity, thresholding, wavelet",
author = "Romain Cosentino and Randall Balestriero and Baraniuk, {Richard G.} and Behnaam Aazhang",
note = "Funding Information: Manuscript received February 21, 2020; revised May 1, 2020; accepted May 24, 2020. Date of publication June 10, 2020; date of current version July 14, 2020. The work of Romain Cosentino and Behnaam Aazhang was supported in part by the NSF under Grant SCH-1838873 and in part by the NIH under Grant R01HL144683-CFDA. The work of Randall Balestriero and Richard G. Baraniuk was supported in part by the NSF under Grant CCF-1911094, Grant IIS-1838177, and Grant IIS-1730574, in part by the ONR under Grant N00014-18-12571 and Grant N00014-17-1-2551, in part by the AFOSR under Grant FA9550-18-1-0478, in part by the DARPA under Grant G001534-7500, in part by the Vannevar Bush Faculty Fellowship, ONR under Grant N00014-18-1-2047, and in part by the Ken Kennedy Institute 2019/20 BP Graduate Fellowship. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Qing Ling. (Corresponding author: Romain Cosentino.) The authors are with the E.C.E. Department, Rice University, Houston, TX 77005 USA (e-mail: rc57@rice.edu; rb42@rice.edu; richb@rice.edu; aaz@rice.edu). Digital Object Identifier 10.1109/LSP.2020.3001457 Publisher Copyright: {\textcopyright} 1994-2012 IEEE. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
doi = "10.1109/LSP.2020.3001457",
language = "English (US)",
volume = "27",
pages = "1115--1119",
journal = "IEEE Signal Processing Letters",
issn = "1070-9908",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
}