A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data

Knowledge of the x-ray spectrum in diagnostic imaging is important for dose calculations, correction for beam-hardening artifacts, and dual-energy computed tomography. One way to determine the x-ray source spectrum is to estimate it from transmission data of a known phantom. Although such an approach is experimentally simple, spectrum estimation from transmission data is known to be an ill-conditioned problem. The contribution of this work is twofold. First, we present a systematic method of designing the transmission measurements to reduce the mathematical instability of spectrum estimation. Second, we apply the expectation-maximization (EM) method, which is known to yield robust solutions to positive, linear integral equations such as the one that describes spectrum estimation from transmission data. The proposed EM method is compared to other algorithms in the literature on simulated data from x-ray spectra typical to mammography and computed tomography. The EM method appears to outperform existing algorithms for spectrum estimation.