Adaptive Gaussian Filter Based on ICEEMDAN Applying in Non-Gaussian Non-stationary Noise

Gaussian filter (GF) is a commonly used linear filter in signal and image noise reduction. However, its limitation is that it cannot adapt parameters to deal with non-stationary noise that varies over time. To address this problem and improve the filtering effectiveness of GF in the face of non-stationary non-Gaussian (NSNG) noise, this paper proposes a new approach called adaptive Gaussian filter based on improved complete ensemble empirical mode decomposition (ICEEMDAN-AGF). The ICEEMDAN-AGF firstly uses the fusion information of the dispersion entropy (DE) and the power spectral entropy (PSE) to divide the intrinsic mode functions (IMFs) into two groups. One group is called guiding IMFs, which contains the high-frequency components of the NSNG noise, and the other group is called hybrid IMFs, which contains the low-frequency components of the NSNG noise and all the noise-free signals. Next, a method called multi-resolution local similarity (MRLS) is proposed to identify the mixed modes presented in the guiding IMFs. Then, the variance of the guiding IMFs is used to adjust the window width w and kernel parameter sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} of GF. Finally, the adaptive Gaussian filter (AGF) obtained above is used to filter the hybrid IMFs. The experiments shows that ICEEMDAN-AGF performs better than other conventional algorithms on known signals.