Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization (Wooseok Ha) Photon-counting detectors acquire spectral information for the scanned object by separating incoming photons into pre-defined energy windows based on their energies. Using this energy information in computed tomography (CT) imaging, also called spectral CT, can mitigate beam-hardening artifacts and allows to estimate two or more basis material maps from the measured counts data. An important step for realizing spectral CT with photon-counting detectors is calibrating the spectral response of the imaging system. In this work, we propose a new method for estimating x-ray spectrum in computed tomography by formulating spectrum estimation as an optimization problem. The novelty of this work is that we place a Kullback-Leibler (KL) divergence constraint on the x-ray spectrum to effectively control the deviation from prior information. The KL-divergence constraint appears to capture important features of x-ray spectrum, therefore allowing accurate and robust estimation of x-ray spectrum in CT imaging. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. Our work provides a mathematically flexible and interpretable framework of estimating x-ray spectrum from transmission measurements.
Selected as one of the featured articles in this month’s issue of Medical Physics.