Estimating the spectrum in computed tomography via Kullback–Leibler divergence constrained optimization

Wooseok Ha, Emil Y. Sidky, Rina Foygel Barber, Taly Gilat Schmidt, Xiaochuan Pan

Medical Physics
October 28, 2018

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.



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Wooseok Ha

Statistics, FODA Institute