TV+TV 2 Regularization with Nonconvex Sparseness-Inducing Penalty for Image Restoration

In order to restore the high quality image, we propose a compound regularization method which combines a new higher-order extension of total variation (TV+TV 2 ) and a nonconvex sparseness-inducing penalty. Considering the presence of varying directional features in images, we employ the shearlet transform to preserve the abundant geometrical information of the image. The nonconvex sparseness-inducing penalty approach increases robustness to noise and image nonsparsity. In what follows, we present the numerical solution of the proposed model by employing the split Bregman iteration and a novel p -shrinkage operator. And finally, we perform numerical experiments for image denoising, image deblurring, and image reconstructing from incomplete spectral samples. The experimental results demonstrate the efficiency of the proposed restoration method for preserving the structure details and the sharp edges of image.