A Diffusion-Based Two-Dimensional Empirical Mode Decomposition (EMD) Algorithm for Image Analysis

We propose a novel diffusion-based, empirical mode decomposition (EMD) algorithm for image analysis. Although EMD has been a powerful tool in signal processing, its algorithmic nature has made it difficult to analyze theoretically. For example, many EMD procedures rely on the location of local maxima and minima of a signal followed by interpolation to find upper and lower envelope curves which are then used to extract a "mean curve" of a signal. These operations are not only sensitive to noise and error but they also present difficulties for a mathematical analysis of EMD. Two-dimensional extensions of the EMD algorithm also suffer from these difficulties. Our PDEs-based approach replaces the above procedures by simply using the diffusion equation to construct the mean curve (surface) of a signal (image). This procedure also simplifies the mathematical analysis. Numerical experiments for synthetic and real images are presented. Simulation results demonstrate that our algorithm can outperform the standard two-dimensional EMD algorithms as well as requiring much less computation time.