Two Big Theorems

Abstract

The ideas discussed in this chapter involve interactions between three transforms—the Radon transform, the Fourier transform, and the back-projection transform. Each of these transforms is defined in terms of improper integrals on infinite intervals. This raises the somewhat technical matter of determining which functions may appropriately be considered, an issue that is addressed in Appendix A. For the time being, we assume that any function being considered here meets the requirements. For those functions that arise in the practical world of medical imaging this is certainly the case.