We describe the continuous and discrete mathematical models for Emission Computed Tomography (ECT) and the need for attenuation correction. Then we analyse the problem of retrieving the attenuation directly from the emission data, nonuniqueness and its consequences. We present the existing and new approaches for solving the problem. Methods are compared and illustrated by numerical simulations. The presentation focuses on Positron Emission Tomography, but we also discuss the extensions to Single Photon Emission Computed Tomography.
Attenuated Radon Transform; maximum likelihood; emission tomography
