Herman G T
Phys Med Biol. 1979 Jan;24(1):81-106. doi: 10.1088/0031-9155/24/1/008.
We investigate how one can estimate from the total attenuation, p, of a polyenergetic X-ray beam what the total attenuation, m, of a monoenergetic beam would have been along the same ray. We find that for beams with typical diagnostic X-ray spectra passing through the human body one can find a simple function f such that f(p) is a sufficiently close estimate of m to allow good reconstructions. We also find that m cannot be accurately estimated from p based on the assumption that the human body consists of water alone. Our results are demonstrated by reconstructions of a mathematical model of a cross-section of the human thorax. This article is self-contained and includes in its Appendices a detailed discussion of the mathematical nature of the problem of bean hardening in computed tomography.
我们研究了如何根据多能X射线束的总衰减p来估计单能束沿同一路径的总衰减m。我们发现，对于具有典型诊断X射线光谱且穿过人体的光束，可以找到一个简单函数f，使得f(p)是对m的足够接近的估计，从而实现良好的重建。我们还发现，基于人体仅由水组成的假设，无法从p准确估计m。我们通过对人体胸部横截面数学模型的重建来证明我们的结果。本文内容完整，附录中详细讨论了计算机断层扫描中束硬化问题的数学性质。
