An efficient nonconvex regularization for wavelet frame and total variation based image restoration

In order to improve the quality of the image, many works impose explicit priors on the solution to regularize the ill-posed inverse problem. In this paper, we propose a hybrid variational model which takes advantages of the wavelet tight frame model and the total variation model for image restoration. The core of the method is a new, nonconvex penalty function that is designed for efficient minimization by means of the firm thresholding and soft shrinkage operations. We address the proposed optimization problem by converting it to a constrained problem with variable splitting and using the alternating direction method of multipliers. Numerical examples for image restoration are given to show that the proposed method outperforms some existing methods in terms of the peak signal-to-noise ratio and structural similarity index.