A 3D image of a region of an object is computed from truncated cone beam projection data acquired with an x-ray device and a prior CT image representing a larger region of the object. The truncated projection data are extrapolated to derive pseudoprojection data associated with projection directions outside the detector, and an intermediate CT image is reconstructed based on the truncated projection data completed with the pseudoprojection data. The prior CT image is then registered with the intermediate CT image. Forward projection data associated with projection directions outside the detector are computed from the truncated projection data and the registered prior CT image. The 3D image is finally reconstructed based on the truncated projection data completed with the forward projection data.