A multiple-source CT system has an annular vacuum chamber surrounding a passage wherein lies an object. A target is in the chamber, the passage passing through an opening of the target. Multiple electron beam emitters are on an emitter gantry within the chamber, each emitting an electron beam towards the target to cause x-rays. An x-ray detector array is mounted on a detector gantry and feeds an image processing system configured to generate tomographic images of the object from detector data. In embodiments, multiple electron beam emitters energize simultaneously. In embodiments, target and emitter gantry counter-rotate. The method includes rotating electron-beam emitters with respect to the target to generate x-rays from the target while rotating a detector about a passage and acquiring data from the detector while multiple detector elements receive x-rays stimulated by multiple emitters, forming a sinogram, and processing the sinogram into a tomographic image of the object.