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Adaptive data analysis via sparse time-frequency representation

Hou, Thomas Y. and Shi, Zuoqiang (2011) Adaptive data analysis via sparse time-frequency representation. Advances in Adaptive Data Analysis, 3 (1-2). pp. 1-28. ISSN 1793-5369.

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We introduce a new adaptive method for analyzing nonlinear and nonstationary data. This method is inspired by the empirical mode decomposition (EMD) method and the recently developed compressed sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {α(t) cos(θ(t))}, where α ≥ 0 is assumed to be smoother than cos(θ(t)) and θ is a piecewise smooth increasing function. We formulate this problem as a nonlinear L^1 optimization problem. Further, we propose an iterative algorithm to solve this nonlinear optimization problem recursively. We also introduce an adaptive filter method to decompose data with noise. Numerical examples are given to demonstrate the robustness of our method and comparison is made with the EMD method. One advantage of performing such a decomposition is to preserve some intrinsic physical property of the signal, such as trend and instantaneous frequency. Our method shares many important properties of the original EMD method. Because our method is based on a solid mathematical formulation, its performance does not depend on numerical parameters such as the number of shifting or stop criterion, which seem to have a major effect on the original EMD method. Our method is also less sensitive to noise perturbation and the end effect compared with the original EMD method.

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Additional Information:© 2011 World Scientific Publishing Co. This work was in part supported by the NSF grant DMS-0908546. We would like to thank Professors Norden E. Huang and Zhaohua Wu for many stimulating discussions on EMD/EEMD and topics related to the research presented here. Professor Hou would like to express his gratitude to the National Central University (NCU) for their support and hospitality during his visits to NCU in the past two years.
Funding AgencyGrant Number
National Central University (Taiwan)UNSPECIFIED
Subject Keywords:Time-frequency analysis; instantaneous frequency; empirical mode decomposition; sparse representation of signal; L1 minimization
Issue or Number:1-2
Record Number:CaltechAUTHORS:20120314-131024684
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29719
Deposited By: Ruth Sustaita
Deposited On:14 Mar 2012 20:42
Last Modified:03 Oct 2019 03:43

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