Least-squares error based optimal signal reconstruction using time-varying weighted empirical mode decomposition

Abstract

The empirical mode decomposition (EMD) is a popular tool that is valid for nonlinear and nonstationary signal analysis. Applying this tool to any given signal reveals a finite set of oscillatory modes termed intrinsic mode functions (IMFs) and a residual. The sum of all extracted IMFs and the residual reconstructs the original signal without any information loss. Although the EMD satisfies the perfect reconstruction property, it is not based on any optimality criterion. This is an important issue especially in using the EMD for reconstructing the original signal from its noisy versions. At this point, a more flexible form of the EMD is required. Related to this issue, recently, only a few formulations are developed. In addition to these ones, in this paper, a new signal reconstruction algorithm termed time-varying weighted EMD is proposed. This algorithm is optimal in the least-squares error sense and tries to reconstruct the original signal by the sum of time-varying weighted IMFs and residual signal. It is demonstrated by simulations that the proposed algorithm introduces superior performance than that of the existing ones in reconstructing the desired signal after denoising.