A nonlinear second-order partial differential equation-based algorithm for additive noise reduction

Abstract

An effective nonlinear anisotropic diffusion-based algorithm for image restoration is proposed in this work. The technique considered here employs a novel second-order partial di_erential equation (PDE) model, composed of a hyperbolic equation and several boundary conditions. Our method provides satisfactory feature-preserving filtering results and overcomes successfully the blurring and staircase effects. It also produces sharper edges because of its hyperbolic equation that is based on a second-time derivative. The proposed PDE model is well-posed, admitting a unique and weak solution under certain assumptions, which is computed by using an iterative finite difference-based explicit numerical approximation scheme. Some successful restoration experiments and method comparisons are also described in this paper.