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 propose an iteratively reweighted majorize minimize algorithm. We demonstrate the utility of the MDTV regularization in the context of image denoising and compressed sensing image reconstruction. We compare the proposed method with the 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 the MDTV penalty provides improved image recovery performance.