Partial Differential Equation-Based Approach for Empirical Mode Decomposition: Application on Image Analysis
Résumé
The major problem with Empirical Mode Decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose in the two dimensional case, the use of an alternative implementation to the algorithmic definition of the so-called sifting process used in the original Huangs Empirical Mode Decomposition method. This approach, especially based on Partial Differential Equations (PDE) was presented by O. Niang and al. in previous works, in 2005 and 2007 and lays on a nonlinear diffusion-based filtering process to solve the meanenvelope estimation problem. In 1D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, is also illustrated in recent paper [1]. Recently, several bidimensional extensions for EMD method were proposed. Despite some efforts, 2D versions for EMD appear poorly performing and are very time consuming. So in this work, an extension to 2D space of the PDE-based approach is extensively described. This approach has been applied in case of both signal and image decomposition. Obtained results confirm the usefulness of the new PDE-based sifting process for decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its usage in a number of signal and image applications such as denoising, detrending, or texture analysis.
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