Chapter 24 - MR-Guided PET Reconstruction and Problems with Anatomical Misinformation

Abstract

This chapter describes two algorithms for positron emission tomography (PET) reconstruction that incorporate anatomical information into the reconstruction process. Both algorithms are based on the maximum likelihood-expectation maximization (ML–EM) algorithm, into which anatomical information can be included easily by taking into account the anatomical knowledge as a so-called a priori distribution. The difference between the two algorithms is the way in which they model this distribution. The Markov–GEM (Gauss–EM) algorithm uses a Gibbs distribution, whereas the Gauss–EM uses a Gaussian distribution. Both algorithms are based on the assumption that the radioactivity is distributed homogeneously within anatomical regions that are separable by segmentation of the magnetic resonance (MR) data. The resulting images show a considerable noise reduction and an improved delineation of borders. Furthermore, the algorithm is tested for effects of erroneous anatomical information by means of simulated and physical phantoms. Even though the Gauss–EM algorithm is superior in its use of accurate anatomical information, it is not stable in the case of a defective a priori distribution, with changes in the reconstructed activity of up to 50%. The Markov–GEM yielded only small errors in the case of anatomical misinformation.