Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Abstract

This study proposes an integer quadratic programming method for grouping and selecting the singular spectral analysis components based on the empirical mode decomposition for performing the denoising. Here, the total number of the grouped singular spectral analysis components is equal to the total number of the intrinsic mode functions. The singular spectral analysis components are assigned to the group indexed by the corresponding intrinsic mode function where the two norm error between the corresponding intrinsic mode function and the sum of the grouped singular spectral analysis components is minimum. Actually, this assignment of the singular spectral analysis components to a particular group is an integer quadratic programming problem. However, the required computational power for finding the solution of the integer quadratic programming problem is high. On the other hand, by representing the integer quadratic programming problem as an integer linear programming problem and employing an existing numerical optimisation computer aided design tool for finding the solution of the integer linear programming problem, the solution can be found efficiently. Computer numerical simulation results are presented.