Adaptive diffusion using Hesse matrix for detecting nonstationary signals

Abstract

Adaptive diffusion, using a gradient‐square tensor, was proposed to improve the readability of time frequency representations (TFRs) of the Cohen class and the affine class in 2005. It works with a signal‐dependent kernel and can adapt to a wide range of nonstationary signals. Here we substitute the Hesse matrix for the gradient‐square tensor after making an analysis of local diffusion behavior in an adaptive diffusion process, in close conjunction with the local signature of the auto terms and the interference terms. The eigenvectors of the Hesse matrix not only can give the local average gradient direction and thus the local diffusion direction, but also can provide an explicit mathematical explanation for local diffusion behavior. The Hesse method is capable of providing TFRs of better readability than the gradient square tensor. The validity of the new method is verified by computational simulations.