Background: The energy spectrum is the property of the X-ray tube that describes the energy fluence per unit interval of photon energy. The existing indirect methods for estimating the spectrum ignore the influence caused by the voltage fluctuation of the X-ray tube.
Methods: In this work, we propose a method for estimating the X-ray energy spectrum more accurately by including the voltage fluctuation of the X-ray tube. It expresses the spectrum as the weighted summation of a set of model spectra within a certain voltage fluctuation range. The difference between the raw projection and the estimated projection is considered as the objective function for obtaining the corresponding weight of each model spectrum. The equilibrium optimizer (EO) algorithm is used to find the weight combination that minimizes the objective function. Finally, the estimated spectrum is obtained. We refer to the proposed method as the poly-voltage method. The method is mainly aimed at the cone-beam computed tomography (CBCT) system.
Results: The model spectra mixture evaluation and projection evaluation showed that the reference spectrum can be combined by multiple model spectra. They also showed that it is appropriate to choose about 10% of the preset voltage as the voltage range of the model spectra, which can match the reference spectrum and projection quite well. The phantom evaluation showed that the beam-hardening artifact can be corrected using the estimated spectrum via the poly-voltage method, and the poly-voltage method provides not only the accurate reprojection but also an accurate spectrum. The normalized root mean square error (NRMSE) index between the spectrum generated via the poly-voltage method and the reference spectrum could be kept within 3% according to above evaluations. There existed a 1.77% percentage error between the estimated scatter of polymethyl methacrylate (PMMA) phantom using the two spectra generated via the poly-voltage method and the single-voltage method, and it could be considered for scatter simulation.
Conclusions: Our proposed poly-voltage method could estimate the spectrum more accurately for both ideal and more realistic voltage spectra, and it is robust to the different modes of voltage pulse.
Keywords: Spectrum estimation; cone-beam computed tomography (CBCT); ray-tracing algorithm; transmission measurement; voltage fluctuation.
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