Staircase effect alleviation by coupling gradient fidelity term

Image denoising with second order nonlinear PDEs often leads to an undesirable staircase effect, namely, the transformation of smooth regions into piecewise constant ones. In this paper, the similarity in gradient between the noisy images and the restored ones is described and preserved by the gradient fidelity term during the noise removal. The introduction of the Euler equation derived from the gradient fidelity term into nonlinear diffusion PDEs helps to alleviate staircase effect efficiently, while preserving sharp discontinuities in images. The gradient fidelity term is integrable in bounded variation function space, which makes our models outperform fourth order nonlinear PDE-based denoising methods in the preservation of edges and textures. In addition, the necessity of introducing spatial regularization into gradient estimation is theoretically analyzed and experimentally emphasized.