Reconstruction of PET images including data of the anatomy

PET images suffer from both low resolution and high statistical noise. Using statistical methods the reconstruction of PET images can be improved by involving high resolution anatomical information obtained from MR images. In this work two methods were developed that utilized MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the Expectation Maximization type algorithm with a maximum a posteriori estimator can be derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighbouring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. The algorithms were tested with simulated and phantom data and the results were compared to the conventional reconstruction algorithms, namely the filtered backprojection and the maximum likelihood reconstruction. Further, the algorithms were investigated under the following aspects: Count density, object size, missing anatomical information and misregistration of the anatomical information. Compared with the filtered backprojection and the maximum likelihood algorithm the results of both algorithms show a large reduction in noise and a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction but suffers on sensitivity to small errors in the a priori information. Regarding missing a priori information or mismatch of the a priori information the Markov-GEM showed greater stability with only small changes in the recovery coefficients. (orig./VHE)