[975] - An optimization based empirical mode decomposition scheme

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Citation
Huang, B., Kunoth, A., 2013. An optimization based empirical mode decomposition scheme. Journal of Computational and Applied Mathematics, 240, 174 - 183. DOI: 10.1016/j.cam.2012.07.012.
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Identification
Title(s):Main Title: An optimization based empirical mode decomposition scheme
Description(s):Abstract: The empirical mode decomposition (EMD) has been developed by N.E. Huang et al. in 1998 as an iterative method to decompose a nonlinear and nonstationary univariate function additively into multiscale components. These components, called intrinsic mode functions (IMFs), are constructed such that they are approximately orthogonal to each other with respect to the L2L2 inner product. Moreover, the components allow for a definition of instantaneous frequencies through complexifying each component by means of the application of the Hilbert transform. This approach via analytic signals, however, does not guarantee that the resulting frequencies of the components are always non-negative and, thus, ‘physically meaningful’, and that the amplitudes can be interpreted as envelopes. In this paper, we formulate an optimization problem which takes into account important features desired of the resulting EMD. Specifically, we propose a data-adapted iterative method which minimizes in each iteration step a smoothness functional subject to inequality constraints involving the extrema. In this way, our method constructs a sparse data-adapted basis for the input function as well as a mathematically stringent envelope for the function. Moreover, we present an optimization based normalization to extract instantaneous frequencies from the analytic function approach. We present corresponding algorithms together with several examples.
Identifier(s):DOI: 10.1016/j.cam.2012.07.012
Responsible Party
Creator(s):Author: Boqiang Huang
Author: Angela Kunoth
Publisher:Elsevier
Topic
TR32 Topic:Other
Related Sub-project(s):C7
Subject(s):CRC/TR32 Keywords: Empirical Mode Decomposition (EMD), Convex Optimization
GEMET: mathematical analysis
File Details
File Name:Huang_2013_JCAM.pdf
Data Type:Text
File Size:1573 kB (1.536 MB)
Date(s):Date Submitted: 2012-02-01
Available: 2012-07-24
Mime Type:application/pdf
Data Format:PDF
Language:English
Status:Completed
Constraints
Download Permission:OnlyTR32
Download Information:Copyright © 2012 Elsevier B.V. All rights reserved.
General Access and Use Conditions:For internal use in TR32 only.
Access Limitations:For internal use in TR32 only.
Licence:TR32DB Data policy agreement
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Measurement Region:Other
Measurement Location:--Other--
Specific Informations - Publication
Status:PeerReviewed
Review:PeerReview
Year:2013
Type:Article
Article Type:Journal
Source:Journal of Computational and Applied Mathematics
Volume:240
Page Range:174 - 183
Metadata Details
Metadata Creator:Angela Kunoth
Metadata Created:2014-07-16
Metadata Last Updated:2014-07-16
Subproject:C1
Funding Phase:2
Metadata Language:English
Metadata Version:V40
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Metadata Downloads:0
Dataset Downloads:1
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