presentation emd
TRANSCRIPT
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
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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
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•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
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•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