Reconstruction algorithms for nonstandard CT scanner designs

Data collected by a CT scanner provide estimates of line integrals of the X-ray attenuation distribution in a cross section of the human body. The lines along which integrals are collected are determined by the positions of the source-detector pairs during the data collection. Since only the lines are important (and not the positions of the source and the detector on the line), essentially the same data may be collected by scanners of very different design. In this article we illustrate that in certain situations the problem of reconstruction from data collected by a CT scanner of a new (and nonstandard) design can be "reduced" to the problem of reconstruction from data collected by a CT scanner for which the problem has already been solved. The "reduction" involves identifying values of free parameters in the old design (such as the radius of the circle in which the source rotates), which would make the geometry of data collection essentially identical to that of the proposed new design. Since reconstruction algorithms for the old design already exist, they can be applied without any change to the data collected by the new scanner. In other words, the problem of finding a reconstruction algorithm for a nonstandard mode of data collection can sometimes be solved by describing a (virtual) machine of standard design whose reconstruction algorithms are immediately applicable to the data collected by the nonstandard machine. The method is demonstrated on a recently proposed concept for transforming a radiotherapy simulator into a CT scanner.