An indirect transmission measurement-based spectrum estimation method for computed tomography

The characteristics of an x-ray spectrum can greatly influence imaging and related tasks. In practice, due to the pile-up effect of the detector, it's difficult to directly measure the spectrum of a CT scanner using an energy resolved detector. An alternative solution is to estimate the spectrum using transmission measurements with a step phantom or another CT phantom. In this work, we present a new spectrum estimation method based on indirect transmission measurement and a model spectra mixture approach. The estimated x-ray spectrum was expressed as a weighted summation of a set of model spectra, which can significantly reduce the degrees of freedom of the spectrum estimation problem. Next, an estimated projection was calculated with the assumed spectrum. By iteratively updating the unknown weights, we minimized the difference between the estimated projection data and the raw projection data. The final spectrum was calculated with these calibrated weights and the model spectra. Both simulation and experimental data were used to evaluate the proposed method. In the simulation study, the estimated spectra were compared to the raw spectra which were used to generate the raw projection data. For the experimental study, the ground truth measurement of the raw x-ray spectrum was not available. Therefore, the estimated spectrum was compared against the spectra generated using the SpekCalc software with tube configurations provided by the scanner manufacturer. The results show the proposed method has the potential to accurately estimate x-ray spectra using the raw projection data. The difference between the mean energy of the raw spectra and the mean energy of the estimated spectra was less than 0.5 keV for both the simulation and experimental data. Further tests show the method was robust with respect to the model spectra generator.