Frontiers in Physics | |
EM Estimation of the X-Ray Spectrum With a Genetically Optimized Step-Wedge Phantom | |
Mengzhou Li1  Wenxiang Cong1  Feng-Lei Fan1  Ge Wang2  | |
[1] Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, United States;null; | |
关键词: spectrum estimation; genetic algorithm; X-ray spectrum; transmission measurement; polychromatic reprojection; | |
DOI : 10.3389/fphy.2021.678171 | |
来源: Frontiers | |
【 摘 要 】
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 (N) and measurements (M) are equal, and show the condition number of the system matrix increases exponentially with N 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 (M < N) 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.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202107125522511ZK.pdf | 3444KB | download |