It is proposed to estimate the scattered radiation on the basis of a sinogram, which is measured in any case. In at least one embodiment, a method includes determining the potential scattering site for each measuring beam from the object tangents in the sinogram and calculating the scattered intensity from the primary radiation striking the scattering site and the angle ratios of scattering beam, object tangent and measuring beam. Also proposed, in at least one embodiment, is an X-ray CT having at least bifocal detector systems and a control and computer unit for producing tomographic pictures, the control and arithmetic unit of which contains a program code that, upon being executed, carries out the method.