Mathematical problems of computerized tomography

The data measured in computerized tomography; e.g., the X-ray attenuation in X-ray tomography or the resonance phenomena in nuclear magnetic resonance tomography, have to be processed to produce the pictures on which the diagnostic evaluation of the physician is based. This process consists of the solution of the following mathematical problem. The data depend on the searched-for distribution and this dependence can be described as an integral transform. To produce the final picture amounts to the inversion of the integral transform. This paper is concerned with the description of the integral transforms modeling the different techniques in computerized tomography. Among other things, the following questions are treated. Which numerical problems do we have to encounter in inverting the transforms; e.g., what accuracy in the reconstruction can we expect in dependence on the accuracy of the data. To what extent is a distribution determined by a finite number of measurements. Is it possible to recover the distribution reliably if the data are incomplete.