Optimal energy threshold arrangement in photon-counting spectral x-ray imaging

We study the influence of the locations of energy thresholds on the basis image noise in spectral X-ray imaging using photon counting devices. Our simulations assume photon counting detectors equipped with up to four discriminator units allowing the binning of photons into up to four distinct energy windows. We use the binned counting data in order to compute the Cramer-Rao lower bound (CRB) for the basis image noise in a photo-effect -Compton-effect decomposition of the attenuation. By studying the variations of the CRB with respect to the threshold energies, we obtain optimized arrangements for each number of energy thresholds and for different values of external copper filtration. We compare the basis image noise for the optimal arrangement with the noise corresponding to an equidistant threshold arrangement and with the results of a tube dual-energy acquisition. Our simulations were performed on two different X-ray paths corresponding to two perpendicular directions through the human thorax. Our results show that in many cases the basis image noise can be strongly reduced by optimizing the locations of the threshold energies.