• The paper proposes three algorithms for deblurring and denoising of Computed Tomography (CT) images, which are usually characterized by a sparse gradient domain. • The proposed methods include gradient-based regularization inducing sparsity in the gradient image domain. • The proposed methods exploit in the Plug-and-Play (PnP) framework, where one or more denoisers are plugged in as priors. • In our methods we propose as denoisers in the PnP framework: 1. A Convolutional Neural Network (CNN) trained on the image gradients (GCNN algorithm) 2. A combination of a CNN trained on the image gradients and a Total Variation (TV) gradient-based (GCNN-TV algorithm) 3. A combination of a CNN trained on the images and a Total Variation (TV) gradientbased (ICNN-TV algorithm). • The proposed GCNN, GCNN-TV and ICNN-TV methods are tested on synthetic and real CT images and compared with state-of-art algorithms. The results obtained show that the proposed GCNN gradient-based outperforms all the other denoisers in recovering edges of low-contrasted objects, whereas the combination of a Neural Network and of Total Variation in the ICNN-TV and GCNN-TV methods suppresses the residual noise, while preserving the details and contours. Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the consequent diagnosis. In this paper, we present a novel gradient-based Plug-and-Play (PnP) algorithm and we apply it to restore CT images. The plugged denoiser is implemented as a deep Convolutional Neural Network (CNN) trained on the gradient domain (and not on the image one, as in state-of-the-art works) and it induces an external prior onto the restoration model. We further consider a hybrid scheme which combines the gradient-based external denoiser with an internal one, obtained from the Total Variation functional. The proposed frameworks rely on the Half-Quadratic Splitting scheme and we prove a general fixed-point convergence theorem, under weak assumptions on both the denoisers. The experiments confirm the effectiveness of the proposed gradient-based approach in restoring blurred noisy CT images, both in simulated and real medical settings. The obtained performances outperform the achievements of many state-of-the-art methods. [ABSTRACT FROM AUTHOR]