A nonconvex hybrid regularization model for restoring blurred images with mixed noises

Abstract

Nonconvex regularization has advantages over convex regularization for preserving the edges of images, and hybrid regularization method based on total variation and wavelet frames is also highly effective for improving the quality of restoring images. Therefore, this paper proposes a nonconvex hybrid regularization model for restoring blurred images with additive noises and multiplicative noises, which is a quite challenging problem compared with the problem of restoring blurred images with a single type of noise. Although the proposed model is jointly nonconvex, every subproblem is convex under some mild conditions when the alternating minimization method is used to solve the proposed model. At the same time, the convergence property of the corresponding algorithm is discussed. Numerical experiments show that the proposed model is effective in edge-preserving, staircase-reduction and detail-reserving in image restoration and it outperforms the state-of-the-art model in terms of the PSNR, ReErr and MSSIM values.