Spectral information from photon statistics in x-ray radiography and computed tomography

Measuring spectral information requires distinguishing photons of different energies, typically achieved using filters or advanced detectors sensitive to individual photons. We prove that when the arrival of photons follows a Poisson distribution (i.e., is shot-noise dominated), the variance and mean of the total photon energy collected over a fixed interval provide independent information about the photon energy spectrum. This immediately leads to several striking corollaries. First, the variance data can be used in the same way as the mean data in both x-ray radiography and tomography. Second, the ratio of the variance data and mean data provides an indication of the average energy of the photon spectrum. Third, the variance data, when compared to the mean data, reveal information analogous to using a higher-energy spectrum. These corollaries show that spectral information can be recovered even from common x-ray detectors which only measure aggregate photon energy. As a demonstration, we performed beam-hardening correction in computed tomography using variance data for both simulations and experiments. We also achieved quantitative tomographic reconstruction in simulation and recover accurate attenuation coefficient values in addition to material density and atomic number.