1. A method for generating at least one X-ray image of a patient with incorporated contrast medium, the at least one X-ray image being generated using an X-ray detector and X-ray radiation generated at an anode, the X-ray radiation including an energy spectrum of braking rays and characteristic radiation, the method comprising: modifying the energy spectrum by using at least one first filter arranged in a beam path in front of the patient, the at least one first filter being a beam hardening filter; generating detector data for the X-ray image upon the patient absorbing a dose of X-ray radiation, the X-ray image including a contrast-to-noise ratio (CNR) value representing a ratio of a maximum contrast in the X-ray image to noise; selecting an additional filter, from among a plurality of additional filters, to be inserted into the beam path in front of the patient to further adjust the energy spectrum, the additional filter being selected based on an examination protocol of the patient, the incorporated contrast medium, a tube voltage, and patient data, and the additional filter being selected according to a product of (i) a ratio (CNR 2 /D γ ) of the square of the contrast-to-noise ratio (CNR 2 ) of the X-ray image of the patient to the radiation dose (D γ ) received by the patient for the X-ray image and (ii) a ratio (CNR/D K ) of the contrast-to-noise ratio (CNR) of the X-ray image of the patient to the contrast medium dose (D K ) incorporated into the patient; moving the selected additional filter into the beam path in front of the patient to further adjust the energy spectrum, the energy spectrum being further adjusted taking into account a thickness of the patient; and generating the X-ray image of the patient with the incorporated contrast medium using the X-ray detector and X-ray radiation generated at the anode, the X-ray radiation including the energy spectrum of braking rays and characteristic radiation; wherein the additional filter is composed of a filter material including at least one of iridium (atomic number Z=77), platinum (Z=78), gold (Z=79), mercury (Z=80), lead (Z=82), and bismuth (Z=83); and wherein a contrast-creating material in the contrast medium includes different materials or material combinations including at least one of rhenium (atomic number Z=75), hafnium (Z=72), tantalum (Z=73), tungsten (Z=74), and elements from the group of lanthanides (atomic number Z=58 to 71).