The inverse problem of emission tomography

The image reconstruction process in emission computed tomography (ECT) is an inverse problem for the photon transport equation. For monochromatic emission sources it is closely related to the inversion of the attenuated Radon transform, a nonlinear ill posed inverse problem. Due to its practical importance for medical diagnostics, this problem has been addressed various times. Here we present the theoretical setting of ECT and discuss some new numerical strategies based on regularization techniques. We include experiments to compare some of the numerical approaches.