  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 scheme, and we apply it to restore CT images. In
particular, we consider different schemes encompassing external and internal
denoisers as priors, defined on the image gradient domain. The internal prior
is based on the Total Variation functional. The external denoiser is
implemented by a deep Convolutional Neural Network (CNN) trained on the
gradient domain (and not on the image one, as in state-of-the-art works). We
also prove a general fixed-point convergence theorem under weak assumptions on
both internal and external denoisers. The experiments confirm the effectiveness
of the proposed framework in restoring blurred noisy CT images, both in
simulated and real medical settings. The achieved enhancements in the restored
images are really remarkable, if compared to the results of many
state-of-the-art methods.
