A method and a system are disclosed for obtaining image data from inside an examination object from images of a computed tomograph. In an embodiment, the method includes accepting first measurement data of the examination object, acquired based on x-ray radiation of a first energy, and second measurement data of the examination object, acquired based on x-ray radiation of a second energy differing from the first energy; setting an optimized output of target image points on the basis of the first and second measurement data at the respective target image points, each as a function of local optimization parameter values of the target image points determined locally from the first and second measurement data in the area of the target image points, while deriving image point reproduction parameter values representing the optimized output; and determining the output data based on optimized output of the target image points.