Correction for beam hardening in computed tomography.

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.