Magnetic resonance imaging based correction and reconstruction of positron emission tomography images (in English)

Abstract

Reconstruction of positron emission tomography (PET) images with good quantitative and qualitative resolution is a difficult problem. Mathematically the problem is ill-posed, and a regularization of the reconstruction solution is necessary. Such constraints range from simply smoothing the data to the use of elaborate models employed within a Bayesian framework. The goal of optimum resolution, however, is typically not compatible with any of these schemes. This thesis presents new methods for dealing with the projection data on an anisotropic basis. This is done in order to compromise the need for regularization and the drive toward better resolutions. An appropriate resolution is chosen in accordance to either the quality of the projection data (based on local estimates of noise), or known regions of interest (taken, for example, from associated anatomical images). As such it addresses the issues of noise artifact whilst avoiding any unnecessary loss in resolution. A second key element is the development of a Bayesian algorithm to improve resolution in order to address the so-called partial volume effect. Magnetic resonance imaging (MRI) data provides significant information about the expected distribution of radioactivity in the brain. Using this explicit information, corrections to the PET image can be made in a quantitative manner, but one must be cautious in its application. The thesis describes how to incorporate MRI data into the reconstruction process of the PET image in an adaptive manner. The adaptational nature of the process is driven solely by good heuristics designed to avoid both an overbiased usage of the a priori information and any assumptions made on the [supposed] homogeneous characteristic of the activity distribution. © 2000, American Association of Physicists in Medicine. All rights reserved.