Penumbra-Effect Induced Spectral Mixing in X-ray Computed Tomography: A Multi-Ray Spectrum Estimation Model and Subsampled Weighting Algorithm

Purpose: With the development of spectral CT, several novel spectral filters have been introduced to modulate the spectra, such as split filters and spectral modulators. However, due to the finite size of the focal spot of X-ray source, these filters cause spectral mixing in the penumbra region. Traditional spectrum estimation methods fail to account for it, resulting in reduced spectral accuracy. Methods: To address this challenge, we develop a multi-ray spectrum estimation model and propose an Adaptive Subsampled WeIghting of Filter Thickness (A-SWIFT) method. First, we estimate the unfiltered spectrum using traditional methods. Next, we model the final spectra as a weighted summation of spectra attenuated by multiple filters. The weights and equivalent lengths are obtained by X-ray transmission measurements taken with altered spectra using different kVp or flat filters. Finally, the spectra are approximated by using the multi-ray model. To mimic the penumbra effect, we used a spectral modulator (0.2 mm Mo, 0.6 mm Mo) and a split filter (0.07 mm Au, 0.7 mm Sn) in simulations, and used a copper modulator and a molybdenum modulator (0.2 mm, 0.6 mm) in experiments. Results: Simulation results show that the mean energy bias in the penumbra region decreased from 7.43 keV using the previous SCFM method (Spectral Compensation for Modulator) to 0.72 keV using the A-SWIFT method for the split filter, and from 1.98 keV to 0.61 keV for the spectral modulator. In experiments, the root mean square error of the selected ROIs was decreased from 77 to 7 Hounsfield units (HU) for the pure water phantom with a molybdenum modulator, and from 85 to 21 HU with a copper modulator. Conclusion: Based on a multi-ray spectrum estimation model, the A-SWIFT method provides an accurate and robust approach for spectrum estimation in penumbra region of CT systems utilizing spectral filters.