Ensemble Empirical Mode Decomposition

Zhaohua Wu
Florida State University

In this talk, I will introduce the Ensemble Empirical Mode Decomposition (EEMD), a new variation of the Empirical Mode Decomposition (EMD). EMD is a one-dimensional analysis method that is based on the principles of temporal-spatial locality and adaptiveness. It has many striking mathematical properties that other methods do not own. However, EMD lacks the ‘physical uniqueness’ when it is applied to real world data due to the scale mixing in the decomposition. The EEMD is developed in light of many mathematical properties of EMD. EEMD consists of an ensemble of decompositions of data with added finite amplitude white noise, and then treats the resultant means of the corresponding components from different decompositions as the final result. This new method uses white noise to provide a dyadic filter bank for the decomposition of data, and then cancels the added white noise out via ensemble averaging; therefore, it is truly a noise-assisted data analysis (NADA) method. After the concepts and details of EEMD algorithm are explained, I will then introduce the new development of the multi-dimensional EEMD for the decomposition and analysis of multi-dimensional spatial-temporal or multi-dimensional spatial data (including images). This new development deviates philosophically from the simple extensions of one-dimensional data decomposition to two-dimensional image decomposition using membrane fitting instead of curve fitting in the one-dimensional EMD, which naturally inherit the scale mixing problem of its one-dimensional version. In this new development of the multi-dimensional EEMD, we invented the “minimum scale strategy” to combine the components obtained from applying EEMD consecutively in all spatial-temporal directions. Some properties of EEMD and its multi-dimensional version will be demonstrated using both the decompositions of real world data and images.

Presentation (PDF File)

Back to Adaptive Data Analysis and Sparsity