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Sparse time-frequency decomposition based on dictionary adaptation

Hou, Thomas Y. and Shi, Zuoqiang (2016) Sparse time-frequency decomposition based on dictionary adaptation. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 374 (2065). Art. No. 20150192. ISSN 1364-503X . PMCID PMC4792402. https://resolver.caltech.edu/CaltechAUTHORS:20160315-095503958

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Abstract

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1098/rsta.2015.0192DOIArticle
http://rsta.royalsocietypublishing.org/content/374/2065/20150192PublisherArticle
http://arxiv.org/abs/1311.1163arXivDiscussion Paper
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4792402/PubMed CentralArticle
Alternate Title:Sparse Time-Frequency decomposition by dictionary learning, Sparse Time-Frequency decomposition by adaptive basis pursuit
Additional Information:© 2016 The Author(s). Published by the Royal Society. Accepted: 29 September 2015; Published 7 March 2016. Data accessibility. Data in examples 6.1, 6.2 and 6.4 are synthetic data. They can be reproduced following the descriptions in the paper. Data used in example 6.3 can be downloaded at http://www.ece.rice.edu/dsp/software/bat.shtml. Authors’ contributions. Both authors, T.Y.H. and Z.S., worked together to propose the proper formulation for this problem. Z.S. carried out most of the work in the design and the implementation of the numerical algorithms. He also drafted the manuscript. T.Y.H. revised the manuscript and made sure that we have done a thorough study to demonstrate the accuracy and robustness of the proposed method. Both authors gave final approval for publication. We declare we have no competing interests. This research was supported in part by NSF grants nos. DMS-318377 and DMS-1159138, DOE grant no. DE-FG02-06ER25727, and AFOSR MURI grant no. FA9550-09-1-0613. The research of Z.S. was supported by a NSFC grant no. 11201257.
Funders:
Funding AgencyGrant Number
NSFDMS-318377
NSFDMS-1159138
Department of Energy (DOE)DE-FG02-06ER25727
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0613
National Natural Science Foundation of China11201257
Subject Keywords:Sparse time-frequency decomposition, instantaneous frequency, dictionary adaptation
Issue or Number:2065
PubMed Central ID:PMC4792402
Record Number:CaltechAUTHORS:20160315-095503958
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160315-095503958
Official Citation:Hou TY, Shi Z. 2016 Sparse time-frequency decomposition based on dictionary adaptation. Phil. Trans. R. Soc. A 374: 20150192. http://dx.doi.org/10.1098/rsta.2015.0192
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65354
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Mar 2016 19:18
Last Modified:03 Oct 2019 09:46

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