  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 other CT phantom. In this
work, we present a new spectrum estimation method based on indirect
transmission measurement and model spectra mixture approach. The estimated
x-ray spectrum was expressed as weighted summation of a set of model spectra,
which can significantly reduce the degrees of freedom (DOF) of the spectrum
estimation problem. Next, an estimated projection can be 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 spectra
generated using the SpekCalc software with tube configurations provided by the
scanner manufacturer. The results show the proposed method has 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 were smaller than 0.5 keV for both simulation and experimental data.
Further tests show the method was robust with respect to the model spectra
generator.
