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EMD – Empirical Mode Decomposition for Non-linear and Non-stationary Time Series

Analysis

Patrycia Klavdianos & Abdoulaye Diakité

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

Motivation

Data Analysis of real-world systems

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Motivation

Real-world Systems

Data Analys

is

Non-Linear

Non-

Stationar

y

5

Motivation…but, what we have is simplified models

Fourier Analysis Wavelet Analysis

…and what we want is a real model

Non-Linear Non-Stationary

Real Model

EMD

Empirical Mode Decomposition

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EMD

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

HHT

EMDHSA

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

Non-Linear

Non-Stationar

y

Real Model

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EMD Process

1•Local

Extremas Identification

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•Upper and Lower envelops

•Mean envelops

3

•IMF’s derivation (intrinsic mode functions)

Sifting Process Input Data

The IMF’s has physical meaning!

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EMD Process

Input Data

1)Identification of local extremas (local maxima and local minima);

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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.

…until to find C1 (IMF)

Residue= original data – h1

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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 all Ci (IMF’s)

Iterate until finding Ci (IMF)

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EMD Process (review)

Ci (IMF’s)

BEMD

Bidimensional EMD

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BEMD: Bidimensional EMD

1•Local

Extremas Identification

2

•Upper and Lower envelops

•Mean envelops

3 •BIMF’s derivation

2D - Sifting Process

The BIMF’s has physical meaning!

Input Data

Drawbacks

Nothing is perfect!

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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.

Applications

Is this really useful?

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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.

Example: tide and tsunami data

Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, 1998: The

Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis. Proc. R.

Soc. London, Ser. A, 454, 903–995.

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Applications for image processing, BEMD has being employed for feature

and texture extraction and for image filtering and denoising.

Example: Iris feature extraction

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.

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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.

Conclusion

What about now?

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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 non-

stationary 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 IMF’s and BIMF’s which are a new way of seeing the data set.

But, needs more investigation!

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About our work

I. IntroductionII. Data Analysis

OverviewIII. Empirical Mode

DecompositionIV. Bidimensional

Empirical Mode Decomposition

V. DrawbacksVI. ApplicationsVII. Conclusion

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