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EMD Empirical Mode Decomposition for Nonlinear and Non-stationary Time Series AnalysisPatrycia Klavdianos & Abdoulaye Diakit

Content

Motivation EMD: Empirical Mode Decomposition BEMD: Bidimensional EMD Drawbacks Applications Conclusion

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MotivationData Analysis of real-world systems

MotivationReal-world Systems

NonStationary

NonLinear

Data Analysi s

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Motivationbut, what we have is simplified models

Fourier Analysis

Wavelet Analysis

and what we want is a real model

Non-Linear

NonStationary

Real Model

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EMDEmpirical Mode Decomposition

EMDNorden E. Huang et al. proposed a new data analysis method (1998).

HHT

Non-Linear

NonStationary

HSA

EMD

Real Model

HHT: Hilbert-Huang Transform EMD: Signal decomposition HSA: Hilbert Signal analysis

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EMD ProcessSifting Process Local Extremas IdentificationInput Data

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Upper and Lower envelops Mean envelops

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IMFs derivation (intrinsic mode functions)The IMFs has physical meaning!

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EMD Process1)Identification of local extremas (local

maxima and local minima);

Input Data

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EMD ProcessII) Compute the upper and lower envelope (cubic spline fitting); III) Compute the mean envelope;

(local maxima / local minima)

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EMD ProcessIV) Compute the IMF component (hi)

IMF is given by: mean envelop original signal

h1 is an IMF?

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EMD Process this h1 component is not an IMF. Then, we need to iterate.

Residue= original data h1

until to find C1 (IMF)

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EMD Process but until now we have found only the first IMF (C1)

Residue(i)= residue(i-1) Ci Iterate until finding Ci (IMF)

Iterate until finding all Ci (IMFs)13

EMD Process (review)

Ci (IMFs) 14

BEMDBidimensional EMD

BEMD: Bidimensional EMDInput Data

2D - Sifting Process Local Extremas Identification

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2

Upper and Lower envelops Mean envelops

BIMFs derivation 3The BIMFs has physical meaning!

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DrawbacksNothing is perfect!

Drawbacks Issues

in the following aspects:

(a) lack of mathematical formalism; (b) local extremas computation in BEMD; (c) interpolation of envelopes; (d) definition of the stoppage rules; (e) processing time.

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ApplicationsIs this really useful?

Applications

Engineering (mechanical, electrical, etc) Medical and Biomedical Finance Computer Vision . many others

Feature and texture extraction, filtering and denoising images.

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Applications

for signal analysis, EMD proved to be useful as a time series analysis tool. N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.Huang,Example: tide and tsunami dataC. Yen, C. C. Tung, and H. H. Liu, 1998: The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis. Proc. R. Soc. London, Ser. A, 454, 903995.

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Applications

for image processing, BEMD has being employed for feature and texture extraction and for image filtering and denoising. extraction Example: Iris feature

Iris Feature Extraction and Recognition Based on Empirical Mode Decomposition - Zhang Shunli, Han Min, Sun Weifeng, Yang Mingqiang, School of Information Science and Engineering, Shandong University, Jinan 250100, China

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ApplicationsImage Analysis Examples Texture Analysis

MRI Analysis

Nunes, J.C., Bouaoune, Y., Delechelle, E., Niang, O., Bunel, P., 2003. Image analysis by bidimensional empirical mode decomposition. Image and Vision Computing 21 (12), 1019 1026. 23

ApplicationsImage Analysis Examples Extraction of inhomogeneous illumination

Nunes, J.C., Bouaoune, Y., Delechelle, E., Niang, O., Bunel, P., 2003. Image analysis by bidimensional empirical mode decomposition. Image and Vision Computing 21 (12), 1019 1026. 24

Conclusion

Comparison table: Fourier, Wavelet and Hilbert

EMD is part of Hilbert Analysis

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Conclusion

EMD was developed for non-linear and nonstationary data which implies in data-dependence and an adaptive approach. Introduces the idea of physical significance related to the instantaneous frequency for each mode of a complicated data set. Introduction of the IMFs and BIMFs which are a new way of seeing the data set.But, needs more investigation!

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