Optimal and Bidirectional optimal Empirical Mode Decomposition

The empirical mode decomposition (EMD) was recently proposed as a new time-frequency analysis tool for nonstationary and nonlinear signals. Although the EMD is able to find the intrinsic modes of the signal and is completely self-adaptive, it does not have any implication on optimality. In some situation, when certain optimality is considered, we need a more flexible signal decomposition and reconstruction scheme. We propose a modified version of the EMD, which enhances the capability of the EMD. The proposed modified EMD algorithm gives the best estimate to a given signal in the minimum mean square error sense. Two different formulations are proposed. The first one utilizes a linear weighting for the intrinsic mode functions (IMF). The second algorithm adopts a bidirectional weighting, namely, it not only uses weighting for IMF modes, but also exploits the correlations between samples in a specific window and carries out filtering in the window. These two new EMD methods extend the capability of the traditional EMD and is well suited for optimal signal recovery. Simulation studies are performed to show the application of the proposed optimal EMD algorithms to denoising problem.