Reconstruction Methods for Positron Emission Tomography with Short Scan Time

Positron Emission Tomography is an important functional imaging technique in nuclear medicine, where the measured data are corrupted by Poisson noise. Hence, this thesis begins with an overview on PET and the introduction of a mathematical and statistically motivated model in order to deal with the emerging inverse problem. At this point numerical methods like regularization are required for image reconstruction so we introduce iterative reconstruction algorithms. These methods are presented, discussed and also combined to yield more accurate results. On the basis of two data sets, which are taken from a computationally generated software phantom and a hardware phantom resembling the human thorax, we present explicit error estimates and reconstructed images as well as explain the effects that are theoretically expected and evaluate the results critically.