New model based on first and second order derivatives and its application to variational image denoising

In order to overcome the staircase effects in first order model, a new combinational model based on first order derivative and second order derivative is proposed in this paper. The fidelity term (data term) is the same as the classic TV-L1 model, which denotes the fidelity between the original image and the clear image. The regularized terms with penalty parameters to control the smoothness include two parts, one is based on gradient, the other is based on Laplace operator. To speed up the computation, the Split Bregman algorithm is designed for the proposed model. Finally, the denoising quality between the proposed models and the classical ones such as the median filter, PM model, TV-L1 model is compared. The experiments shows that the proposed models can remove both gauss noise and salt-pepper noise with high computational efficiency.