Multiple Degree Total Variation (MDTV) Regularization for Image Restoration.

We introduce a novel image regularization termed as multiple degree total variation (MDTV). This type of regularization combines the first and second degree directional derivatives, thus providing a good balance between preservation of edges and region smoothness. In order to solve the resulting optimization problem, we proposed a fast majorize minimize algorithm. We demonstrate the utility of the MDTV regularization in the context of image denoising and compressed sensing. We compare the proposed method with standard TV, and the state of the art higher degree methods, including higher degree total variation (HDTV) and total generalized variation (TGV) based schemes. Numerical results indicate that MDTV penalty provides improved image recovery performance.