1. A method for determining attenuation coefficients for an object using a movable x-ray source and a detector for recording projections, the method comprising: defining a trajectory for the movable x-ray source; defining filtering lines for the filtering of projection data; defining positions on the filtering lines, at which a projection derivative is to be formed using a mathematical algorithm for a back-projection; defining sampling positions on the trajectory; traversing along the trajectory with the x-ray source and recording a projection for each of the sampling positions, wherein the projection comprises radiation intensity values recorded by detector elements; directly calculating, using the recorded radiation intensity values, the projection derivatives with respect to the trajectory path for each of the positions on the filtering lines; and determining, from the calculated projection derivatives, attenuation coefficients for the object for the reconstruction, using a mathematical algorithm.