It is a tomography or x-ray fluoroscopy - ct - with a reduced radiation exposure in an x-ray - ct - device (100) or an x-ray ct fluoroscopy apparatus - - described. A channel directional - x-ray collimator (31) or an x-ray beam shaping filter (32) is position-controlled in the channel direction, in order to carry out a rötgendatenakquisition, while the irradiated with x-rays limited to only the region of interest is. It is either the profile of the entire object is obtained or the profile of the entire object is made of views or survey images of the irradiation of the entire object outside of the x-ray projection data is calculated in advance. An image reconstruction of views, in which it is not the entire object is irradiated, outside of the collected x-ray projection data is carried out by missing parts of the profile of the entire object to be predicted and corrections are performed. In this way, it is possible only the region of interest to be irradiated with x-rays, in order to the x-ray beam dose for the object in the case of the tomography by means of the x-ray - ct - device (100) or the exposure of the object with x-rays and the radiation exposure of the hands of an operator at the time of a by means of x-ray - ct - fluoroscopy supported to reduce the puncture.
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