Spectral CT algorithms generally target two different tasks: On one hand, it is of interest to distinguish between two materials that yield the same range of CT numbers in a standard CT image. Two or more spectral CT measurement channels with distinct spectral weightings often yield an improved segmentation between the two materials, both in a visual assessment and in a computational segmentation algorithm. The separation of bone and blood mixed with iodine contrast media is a prominent clinical example.

On the other hand, spectral CT data follow well-known physical attenuation rules. In many cases, the measurement process description can be inverted to yield quantitative material information, e.g., concentrations or atomic number information of the material constituents. In this chapter, we summarize the main algorithms dedicated to this target of spectral CT imaging.