Multiplicative noise removal via using nonconvex regularizers based on total variation and wavelet frame

Abstract

Total variation based regularization and wavelet frame based regularization are two different methods for image restoration. Moreover, nonconvex regularization has advantages over convex regularization for preserving edges in images. In this paper, a variational model consisting of two nonconvex regularizers based respectively on total variation and wavelet frame is proposed for multiplicative noise removal. The proposed model combines the advantages of the nonconvex regularization and the hybrid regularization. So it can more effectively preserve edges and details in images than any single regularization can. The alternating minimization method is proposed to solve the novel model. Although the corresponding minimization problem is nonconvex, the convexity of all subproblems is guaranteed under some mild conditions. Therefore, we study the convergence property of the algorithm. Numerical experiments have proved that the proposed model with the corresponding algorithm outperforms some state-of-the-art models in terms of the peak signal-to-noise ratio and the relative error of the restored images.