We propose IntraTomo, a powerful framework that com- bines the benefits of learning-based and model-based ap- proaches for solving highly ill-posed inverse problems in the Computed Tomography (CT) context. IntraTomo is composed of two core modules: a novel sinogram prediction module, and a geometry refinement module, which are applied it- eratively. In the first module, the unknown density field is represented as a continuous and differentiable function, parameterized by a deep neural network. This network is learned, in a self-supervised fashion, from the incomplete or/and degraded input sinogram. After getting estimated through the sinogram prediction module, the density field is consistently refined in the second module using local and non-local geometrical priors. With these two core modules, we show that IntraTomo significantly outperforms existing approaches on several ill-posed inverse problems, such as limited angle tomography with a range of 45 degrees, sparse view tomographic reconstruction with as few as eight views, or super-resolution tomography with eight times increased resolution. The experiments on simulated and real data show that our approach can achieve results of unprecedented quality.