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Computerized X-ray tomography is a completely new way of using X-rays for medical diagnosis. It gives physicians a more accurate way of seeing inside the human body and permits safe, convenient, and quantitative location of tumors, blood clots and other conditions which would be painful, dangerous, or even impossible to locate by other methods. Although each tomography machine costs hundreds of thousands of dollars, hundreds of tomography machines are already in use.A mathematical algorithm to convert X-ray attenuation measurements into a cross-sectional image plays a central role in tomography. Sophisticated mathematical analysis using Fourier transforms has led to algorithms which are much more accurate and efficient than the algorithm used in the first commercial tomography machines. We show how some of the algorithms in actual use have been developed. We also discuss some related mathematical theorems and open questions.
Shepp et al. (Thu,) studied this question.