The well-known methods based on gradient dependent regularizers such as total variation (TV) model often suffer the staircase effect and the loss of edge details. In order to overcome such drawbacks, an adaptive variational approach is proposed. First, we introduced a Gaussian smoothed image as the variable of the Lp norm, and then we employed the difference curvature instead of gradient as new edge indicator, which can effectively distinguish between ramps and edges. In the proposed model, the regularization term and fidelity term are both adaptive. At object edges, the regularization term is approximate to the TV norm in order to preserving the edges; in flat and ramp regions, the regularization term is approximate to the L2 norm in order to avoid the staircase effect. Meanwhile, we added a spatially varying fidelity term that locally controls the extent of denoising over image regions according to their content. Local variance measures of the oscillatory part of the signal are to compute the adaptive fidelity term. Comparative results on both natural and medical images demonstrate that the new method can avoid the staircase effect and better preserve fine details than the other variational models.
