Spectrum reconstruction method based on the detector response model calibrated by x-ray fluorescence.

Accurate estimation of distortion-free spectra is important but difficult in various applications, especially for spectral computed tomography. Two key problems must be solved to reconstruct the incident spectrum. One is the acquisition of the detector energy response. It can be calculated by Monte Carlo simulation, which requires detailed modeling of the detector system and a high computational power. It can also be acquired by establishing a parametric response model and be calibrated using monochromatic x-ray sources, such as synchrotron sources or radioactive isotopes. However, these monochromatic sources are difficult to obtain. Inspired by x-ray fluorescence (XRF) spectrum modeling, we propose a feasible method to obtain the detector energy response based on an optimized parametric model for CdZnTe or CdTe detectors. The other key problem is the reconstruction of the incident spectrum with the detector response. Directly obtaining an accurate solution from noisy data is difficult because the reconstruction problem is severely ill-posed. Different from the existing spectrum stripping method, a maximum likelihood-expectation maximization iterative algorithm is developed based on the Poisson noise model of the system. Simulation and experiment results show that our method is effective for spectrum reconstruction and markedly increases the accuracy of XRF spectra compared with the spectrum stripping method. The applicability of the proposed method is discussed, and promising results are presented.