In computed tomography we mimic the brain’s ability to synthesize an object’s 3D structure from many projections by solving thousands of equations. Many efficient methods have been developed to do that, and the results can be impressive when the object is illuminated from many angles and the noise is negligible. However, one decisive factor behind the human brain's unrivalled success with 3D reconstruction remains to be incorporated into computed tomography: The ability to use prior information – an organized accumulation of experience with other objects in the world. The goal of the project is to accomplish this.The time is ripe to use the power of state-of-the-art mathematics and scientific computing to develop the enabling mathematical technology for next-generation tomographic reconstruction algorithms that are flexible enough to incorporate a variety of available prior information, and thus achieve major improvements in the details and reliability of high-definition reconstructions – sharper images with reliable details. In contrast to existing approaches our goal is to make it possible to incorporate all available prior information in various forms, by replacing ad-hoc assumptions in the current tomography algorithms with prior-driven data representation models and reconstruction methods.We will look outside the world of classical tomography and incorporate elements and techniques from related areas, tuned to the particular problems that arise in tomography. While research in tomography is often performed either in the application areas or in specialized mathematical communities, we will create a unique research environment with tight collaborations between all the necessary activities as well as scientific and industrial users of tomography. For the first time we will be able to compute reliable high-definition 3D / 4D reconstructions based on the total amount of prior information, without the reconstructions being deteriorated by algorithmic limitations.