On robustness of ℓ1-regularization methods for spectral estimation
2014 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, 1767-1773 p.Conference paper (Refereed)
The use of ℓ<inf>1</inf>-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 Candès, 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<inf>1</inf>-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 conference proceedings, 2014. no February, 1767-1773 p.
coherent dictionaries, error bounds, robustness, sparse recovery, Spectral estimation
IdentifiersURN: urn:nbn:se:kth:diva-176148DOI: 10.1109/CDC.2014.7039654ScopusID: 2-s2.0-84931864201OAI: oai:DiVA.org:kth-176148DiVA: diva2:875048
2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, 15 December 2014 through 17 December 2014
QC 201511302015-11-302015-11-022015-11-30Bibliographically approved