Wavelet/frame shrinkage and nonlinear diffusion filtering are two popular methods for signal and image denoising. The relationship between these two methods has been studied recently. This relationship leads to new types of diffusion equations and helps to design the wavelet/frame-inspired diffusivity functions, and on the other hand it helps to design the diffusion-inspired shrinkage functions with a better performance in signal and image denoising.

Multiwavelets have important properties such as orthogonality, short support, and symmetry, etc. that scalar orthogonal wavelets cannot possess simultaneously. There is rich literature on the theoretical study, construction and applications of multiwavelets. In particular, it has been shown that multiwavelets perform better than the scalar wavelets in signal and image denoising. Recently multiwavelet denoising has been applied in different applications including rolling bearing fault detection and study of load spectrum of computer numerical control lathe. Therefore it is worth to further study multiwavelet denoising.

In this paper we investigate the correspondence between multiwavelet denoising and nonlinear diffusion.

We show that the multiwavelet shrinkages of the commonly used CL(2) and DGHM multiwavelets are associated with a second-order nonlinear diffusion equation. We also derive high-order nonlinear diffusion equations associated with general multiwavelet shrinkages. The experimental results carried out in this paper show that the diffusion-inspired multiwavelet shrinkage performs better than the traditional multiwavelet hard- and soft-thresholding shrinkages.