Emission tomography: a concise theoretical overview

A concise theoretical overview of emission tomography is presented aiming at physical interpretation of the equations so that fundamental concepts, similarities and differences between SPECT and PET, become transparent. The framework is that of an indirect sensing problem and image reconstruction from projections. The projections are expressed in terms of: the activity distribution, the attenuation distribution, the interactions of the radiation with matter, and the measurement geometry. In discussing the attenuation problem, recourse is made to the projections obtained by a gamma-ray (or a hypothetical monoenergetic X-ray) transmission CT scanner. This expression would be the one to which the corresponding expressions for SPECT and PET would reduce to if the attenuation distributions were known. Although the attenuation problem is less severe in PET, its extent is demonstrated with results from computer simulations. Finally, under conditions of 'adequate sampling', equations are given relating administered activity to spatial resolution, time for data collection, noise/signal ratio and system sensitivity.