Constrained Minimization Problem for Image Restoration Based on Non-Convex Hybrid Regularization

It is widely known that the classic total variation(TV) model has been proven to be very effective in preserving sharp edges. However, the TV model suffers from the staircase effects which produce blocking artifacts in the restored images. In this paper, we propose a new hybrid regularization model by combining non-convex second order total variation with wavelet transform to restrain staircase effects and protect some details of the images. To compute the new model effectively, we propose an alternating minimization method for recovering images from the blurry and noisy observations. The new model is first transformed into several sub-problems, and the generalized iterated shrinkage algorithm, the Fourier transform method and projection method are used to solve these sub-problems, respectively. Numerical experiments show that the proposed model can restrain blocking artifacts while projecting sharp edges, and the restoration quality outperforms several state-of-the-art methods.