A method and a computed tomography system are disclosed for generating tomographic image datasets of a measurement object with multiple simultaneously operable sets of detector elements. In at least one embodiment, at least one first set measures incident radiation over the entire energy spectrum of the incident radiation in an integrating manner and at least one second set measures incident radiation in at least two energy ranges in a resolving manner, wherein furthermore by way of the integrating measurements, the energy-resolving measurements relating in each case to rays traversing a measurement object in a spatially identical manner are corrected and a tomographic image dataset of the measurement object is reconstructed at least from the corrected energy-resolving measurements.