A New Gradient Fidelity Term for Avoiding Staircasing Effect

Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PDEs to solve the problem. At first, we smooth the normal vector fields (i.e., the gradient fields) of the noisy image by total variation (TV) minimization and make the gradient of desirable image close to the smoothed normals, which is the idea of our gradient fidelity term. Then, we introduce the Euler-Lagrange equation of the gradient fidelity term into nonlinear diffusion PDEs for noise and staircasing removal. To speed up the computation of the vectorial TV minimization, the dual approach proposed by Bresson and Chan is employed. Some numerical experiments demonstrate that our gradient fidelity term can help to avoid the staircasing effect effectively, while preserving sharp discontinuities in images.