Mixed higher order variational model for image recovery (Q1719403)

Summary: A novel mixed higher order regularizer involving the first and second degree image derivatives is proposed in this paper. Using spectral decomposition, we reformulate the new regularizer as a weighted \(L_{1}\)-\(L_{2}\) mixed norm of image derivatives. Due to the equivalent formulation of the proposed regularizer, an efficient fast projected gradient algorithm combined with monotone fast iterative shrinkage thresholding, called, FPG-MFISTA, is designed to solve the resulting variational image recovery problems under majorization-minimization framework. Finally, we demonstrate the effectiveness of the proposed regularization scheme by the experimental comparisons with total variation (TV) scheme, nonlocal TV scheme, and current second degree methods. Specifically, the proposed approach achieves better results than related state-of-the-art methods in terms of peak signal to ratio (PSNR) and restoration quality.