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On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

Liu, Chunguang and Shi, Zuoqiang and Hou, Thomas Y. (2015) On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. Multiscale Modeling and Simulation, 13 (3). pp. 790-811. ISSN 1540-3459. http://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257

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Abstract

In this paper, we analyze the uniqueness of the sparse time-frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time-frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time-frequency decomposition using nonlinear matching pursuit.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/141002098DOIArticle
http://epubs.siam.org/doi/10.1137/141002098PublisherArticle
http://arxiv.org/abs/1501.04707arXivDiscussion Paper
Additional Information:© 2015 SIAM. Received by the editors December 30, 2014; accepted for publication (in revised form) May 6, 2015; published electronically July 8, 2015. This work was supported by NSF FRG grants DMS-1159138 and DMS-1318377, AFOSR MURI grant FA9550-09-1-0613, and DOE grant DE-FG02-06ER25727.
Funders:
Funding AgencyGrant Number
NSFDMS-1159138
NSFDMS-1318377
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0613
Department of Energy (DOE)DE-FG02-06ER25727
Subject Keywords:sparse time-frequency decomposition, scale separation, nonlinear matching pursuit
Classification Code:AMS subject classifications. 94A12, 42A20
Record Number:CaltechAUTHORS:20151023-103928257
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61483
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Oct 2015 20:06
Last Modified:26 Oct 2015 20:06

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