A variational model of image restoration based on first and second order derivatives and its Split Bregman algorithm

The variational models of diffusion using first order derivatives can efficiently remove the noises of images with edge preserving property, but they usually lead to staircase effects. This problem can be overcome via mixed regularizers using first order and second order derivatives, but it is complex to implement and the computation efficiency is low. In this paper, a variational model via convex combination of regularizers based on first and second derivatives to realize image denoising with edge and smoothness preserving is proposed along with its fast Split Bregman algorithm. They are then extended to the problems of color image denoising. Finally, the denoising quality of the proposed model and the models using first order derivative is compared and the efficiency between the Split Bregman algorithm and the method based on gradient descent equations is compared also.