1. An apparatus for computed tomography image processing, comprising: an X-ray detector that detects an X-ray beam having passed through a subject and outputs an energy value thereof; a processor that calculates line integral values of attenuation coefficients representing attenuation of the energy value of the X-ray beam having passed through the subject and been detected, based on the energy value, and reconstructs a tomogram based on the line integral values; and a display that displays the tomogram; wherein the processor calculates, based on simultaneous equations obtained from a projection function of two different energy spectra and the energy value of the detected X-ray beam, line integral values of attenuation coefficients included in the projection function of the two different energy spectra and energy values satisfying the simultaneous equations; wherein the processor calculates approximate values of the energy values satisfying the simultaneous equations based on first approximate values of the line integral values of the attenuation coefficients, and calculates second approximate values of the line integral values of the attenuation coefficients based on the approximate values of the energy values satisfying the simultaneous equations; wherein the processor selects at least one of the lowest energy values and the highest energy values as the approximate values of the energy values satisfying the simultaneous equations, among energy values satisfying an equation in which the line integral values of the attenuation values in the simultaneous equations are replaced by the first approximate values of the line integral values of the attenuation values.