Ensemble Empirical Mode Decomposition: Image Data Analysis with White-noise Reflection

M Kopecký

doi:10.14311/1291

Abstract

During the last decade, Zhaohua Wu and Norden E. Huang announced a new improvement of the original Empirical Mode Decomposition method (EMD). Ensemble Empirical Mode Decomposition and its abbreviation EEMD represents a major improvement with great versatility and robustness in noisy data filtering. EEMD consists of sifting and making an ensemble of a white noise-added signal, and treats the mean value as the final true result. This is due to the use of a finite, not infinitesimal, amplitude of white noise which forces the ensemble to exhaust all possible solutions in the sifting process. These steps collate signals of different scale in a proper intrinsic mode function (IMF) dictated by the dyadic filter bank. As EEMD is a time–space analysis method, the added white noise is averaged out with a sufficient number of trials. Here, the only persistent part that survives the averaging process is the signal component (original data), which is then treated as the true and more physically meaningful answer. The main purpose of adding white noise was to provide a uniform reference frame in the time–frequency space. The added noise collates the portion of the signal of comparable scale in a single IMF. Image data taken as time series is a non-stationary and nonlinear process to which the new proposed EEMD method can be fitted out. This paper reviews the new approach of using EEMD and demonstrates its use on the example of image data analysis, making use of some advantages of the statistical characteristics of white noise. This approach helps to deal with omnipresent noise.

Highlights

Empirical Mode Decomposition (EMD) has been proposed as an adaptive time-frequency data analysis method
The first major weakness of the original EMD is the frequent occurrence of mode mixing, which is defined as a single Intrinsic Mode Function (IMF)
In the EMD approach, the data, time series x(t), is decomposed in terms of IMFs, as has been described in [4] by Huang, n x(t) = cn + rn j=1 where rn is the residue of the original data x(t) and n is the number of steps for extracting IMFs

Summary

Introduction

Empirical Mode Decomposition (EMD) has been proposed as an adaptive time-frequency data analysis method. An intermittent signal cannot only cause serious aliasing in the time–frequency distribution, but can make the physical meaning of individual IMFs seriously unclear To alleviate this drawback, Huang proposed the intermittence test [3, 2, 4]. To overcome the scale separation issue without introducing a subjective intermittence test, Huang and Wu proposed a new Noise-Assigned Data Analysis (NADA) method, known as Ensemble EMD (EEMD), which defines the true IMF components as the mean value of an ensemble of trials [2]. Finite magnitude noise makes the different scale signals reside in the corresponding IMF, dictated by the dyadic filter banks, and renders the resulting ensemble mean more meaningful.

Introduction to Ensemble Empirical Mode Decomposition over EMD

A definition of mode mixing based on EMD

Ensemble empirical mode decomposition

EMD is a dyadic filter bank for any Gaussian white noise-only series

EEMD method implemented in image data analysis

Conclusion