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On Robustness of l(1)-Regularization Methods for Spectral Estimation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-5158-9255
Harvard Univ, Brigham & Womens Hosp, Sch Med, Boston, MA 02115 USA..
2014 (English)In: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2014, p. 1767-1773Conference paper, Published paper (Refereed)
Abstract [en]

The use of l(1)-regularization in sparse estimation methods has received huge attention during the last decade, and applications in virtually all fields of applied mathematics have benefited greatly. This interest was sparked by the recovery results of Cands, Donoho, Tao, Tropp, et al. and has resulted in a framework for solving a set of combinatorial problems in polynomial time by using convex relaxation techniques. In this work we study the use of l(1)-regularization methods for high-resolution spectral estimation. In this problem, the dictionary is typically coherent and existing theory for robust/exact recovery does not apply. In fact, the robustness cannot be guaranteed in the usual strong sense. Instead, we consider metrics inspired by the Monge-Kantorovich transportation problem and show that the magnitude can be robustly recovered if the original signal is sufficiently sparse and separated. We derive both worst case error bounds as well as error bounds based on assumptions on the noise distribution.

Place, publisher, year, edition, pages
IEEE , 2014. p. 1767-1773
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
Keywords [en]
Spectral estimation, sparse recovery, robustness, error bounds, coherent dictionaries
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-243778ISI: 000370073801147ISBN: 978-1-4673-6090-6 (print)OAI: oai:DiVA.org:kth-243778DiVA, id: diva2:1287677
Conference
53rd IEEE Annual Conference on Decision and Control (CDC), DEC 15-17, 2014, Los Angeles, CA
Note

QC 20190211

Available from: 2019-02-11 Created: 2019-02-11 Last updated: 2019-02-11Bibliographically approved

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Karlsson, Johan

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CiteExportLink to record
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