Image deblurring and denoising by an improved variational model

Total variation method has been widely used in image processing. However, it produces undesirable staircase effect. To alleviate the staircase effect, some fourth order variational models were studied, which lead to the restored images smoothing and some details lost. In this paper, a low-order variational model for image deblurring and denoising is proposed, which is based on the splitting technique for the regularizer. Different from the general split technique, the improved variational model adopts the L1 norm. To compute the new model effectively, we employ an alternating iterative method for recovering images from the blurry and noisy observations. The iterative algorithm is based on decoupling of deblurring and denoising steps in the restoration process. In the deblurring step, an efficient fast transforms can be employed. In the denoising step, the primal-dual method can be adopted. The numerical experiments show that the new model can obtain better results than those by some recent methods.