On the exponential radon transform

This is an introduction to an interesting application of Fourier analysis in tomography and image processing. The Radon transform and the exponential Radon transform are reviewed. Two medical imaging modalities are presented, the Computed Tomography (CT) and the Single Photon Emission Computed Tomography (SPECT). Differences between SPECT and CT are discussed. In CT, the source of radiation is outside the patient, while SPECT deals with self-radiating bodies. CT is concern with imaging structure since attenuation of x-rays is related to the density of the tissue and not to metabolic function. Furthermore, the mathematics of SPECT involves more challenges due to the presence of an exponential factor. The mathematical models of these technologies are presented with a synthetic example.