Tomographic imaging via penetrating waves generates cross-sectional views of the internal anatomy of a living subject. For artefact-free volumetric imaging, projection views from a large number of angular positions are required. Here, we show that a deep-learning model trained to map projection radiographs of a patient to the corresponding 3D anatomy can subsequently generate volumetric tomographic X-ray images of the patient from a single projection view. We demonstrate the feasibility of the approach with upper-abdomen, lung, and head-and-neck computed tomography scans from three patients. Volumetric reconstruction via deep learning could be useful in image-guided interventional procedures such as radiation therapy and needle biopsy, and might help simplify the hardware of tomographic imaging systems. The ability of computed tomography (CT) to take a deep and quantitative look of a patient or an object with high spatial resolution holds significant value in scientific explorations and in medical practice. Traditionally, a tomographic image is obtained via the mathematical inversion of the encoding function of the imaging wave for a given set of measured data from different angular positions (Figs. 1a,b). A prerequisite for artefact-free inversion is the satisfaction of the classical Shannon-Nyquist theorem in angular-data sampling, which Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use: