A polychromatic adaption of the Beer-Lambert model for spectral decomposition

We present a semi-empirical forward-model for spectral photon-counting CT which is fully compatible with state-of-the-art maximum-likelihood estimators (MLE) for basis material line integrals. The model relies on a minimum calibration effort to make the method applicable in routine clinical set-ups with the need for periodic re-calibration. In this work we present an experimental verifcation of our proposed method. The proposed method uses an adapted Beer-Lambert model, describing the energy dependent attenuation of a polychromatic x-ray spectrum using additional exponential terms. In an experimental dual-energy photon-counting CT setup based on a CdTe detector, the model demonstrates an accurate prediction of the registered counts for an attenuated polychromatic spectrum. Thereby deviations between model and measurement data lie within the Poisson statistical limit of the performed acquisitions, providing an effectively unbiased forward-model. The experimental data also shows that the model is capable of handling possible spectral distortions introduced by the photon-counting detector and CdTe sensor. The simplicity and high accuracy of the proposed model provides a viable forward-model for MLE-based spectral decomposition methods without the need of costly and time-consuming characterization of the system response.