In X-ray tomography, reconstructing an image from projection data amounts to solving an integral equation of the Radon transform, a classical inverse problem that is ill-posed and highly sensitive to noise and incomplete data. Deep learning has recently shown great promise in addressing such imaging challenges; however, in medical contexts, its direct application is often limited by the lack of ground truth data and concerns over interpretability. In this talk, I will present a hybrid reconstruction approach that integrates a neural network within an iterative model-based solver. Notably, the network can be trained without requiring ground truth images, making the method practical for real-world clinical scenarios. Furthermore, it can be incorporated into advanced hybrid frameworks to accelerate convergence and enhance stability, while preserving the mathematical structure of the reconstruction process. I will demonstrate the application of this scheme to clinical Digital Breast Tomosynthesis, showing how it reduces artifacts and improves image quality in sparse-view and limited-angle settings.