A non-divergence diffusion equation for removing impulse noise and mixed Gaussian impulse noise

Abstract

In this paper, a non-divergence diffusion equation consisting of an impulse noise indicator λ and a regularized Perona–Malik (RPM) diffusion operator is proposed for the removal of impulse noise. The impulse noise indicator λ is designed to keep values of noise-free pixels unaltered while the Gaussian kernel in the RPM operator makes the proposed equation insensitive to impulse noise. As a result, the proposed equation succeeds in noise suppression as well as edge preserving and shows better performance than state-of-the-art PDE-based methods and variational regularization methods. In addition, the numerical solution of the proposed equation has a certain asymptotic behavior: it converges to the solution we are interested in automatically. This property avoids the problem of choosing a stopping time in numerical experiments and allows us to continue removing impulse noise and mixed Gaussian impulse noise by using the proposed equation.