Before revision: Image restoration problems were traditionally formulated as the minimization of variational models, including data-fidelity and regularization terms, performed by optimization methods with well-established convergence properties. Recently, Plug-and-Play (PnP) methods for image restoration have obtained very good results and popularity by introducing, in iterative proximal algorithms, any off-the-shelf denoiser as priors. Deep Convolutional Neural Network (CNN) denoisers specify external priors (related to an outer training set) which well reflect image statistics; however they fail when dealing with unseen noise variance and image patterns in the given image. Conversely, the so-called internal denoisers induce internal priorsta ilored on the observed data, by forcing specific features on the desired image. We propose a new PnP scheme, based on the Half-Quadratic Splitting proximal algorithm, combining external and internal priors.
After revision: Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the diagnosis. In this paper, we present a novel gradient-based Plug-and-Play algorithm, constructed on the Half-Quadratic Splitting proximal algorithm, combining external and internal priors.