The second-order partial differential equations have good performances on noise smoothing and edge preservation. However, for low signal-to-noise ratio (SNR) images, the discrimination between edges and noise is a challenging problem. In this paper, the authors propose a kernel based telegraph-diffusion equation (KTDE) for noise removal. In this method, a kernelized gradient operator is introduced in the second-order telegraph-diffusion equation (TDE), which leads to more effective noise removal capability. Experiment results show that this method outperforms several anisotropic diffusion methods and the TDE method for noise removal and edge preservation
