AUTHOR=Li Mengzhou , Fan Feng-Lei , Cong Wenxiang , Wang Ge 

TITLE=EM Estimation of the X-Ray Spectrum With a Genetically Optimized Step-Wedge Phantom

JOURNAL=Frontiers in Physics

VOLUME=9

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.678171

DOI=10.3389/fphy.2021.678171

ISSN=2296-424X

ABSTRACT=<p>The energy spectrum of an X-ray tube plays an important role in computed tomography (CT), and is often estimated from physical measurement of dedicated phantoms. Usually, this estimation problem is reduced to solving a system of linear equations, which is generally ill-conditioned. In this paper, we optimize a phantom design to find the most effective combinations of thicknesses for different materials. First, we analyze the ill-posedness of the energy spectrum inversion when the number of unknown variables (<italic>N</italic>) and measurements (<italic>M</italic>) are equal, and show the condition number of the system matrix increases exponentially with <italic>N</italic> if the transmission thicknesses are linearly changed. Then, we present a genetic optimization algorithm to minimize the condition number of the system matrix in a general case (<italic>M</italic> &lt; <italic>N</italic>) with respect to the selection of thicknesses and types of phantom materials. Finally, in the simulation with Poisson noise we study the accuracy of the spectrum estimation using the expectation-maximum algorithm. Our results indicate that the proposed method allows high-quality spectrum estimation, and the number of measurements is reduced over two thirds of that required by the widely-used method using a phantom with linearly-changed thicknesses.</p>