Efficient projection-space resolution modelling for image reconstruction in Positron Emission Tomography

Positron Emission Tomography (PET) is a functional imaging technique used for the measurement of the spatial distribution of a radiotracer in a living subject. PET images are typically obtained using iterative reconstruction algorithms, instead of analytical methods, as they provide superior image quality thanks to better modelling of the statistical properties of the data and to an accurate description of the acquisition process. The acquisition process, in terms of the relation between the object space and the measurement (or projection) space, is defined into the so-called system model, and the modelling of the phenomena that occur during the process is referred to as resolution modelling. The accuracy with which the system model is defined plays a critical role in the quality of the reconstructed images, as the model can incorporate various resolution degrading factors. However, its efficient application to the reconstruction process remains a challenging aspect. In fact, accurate models require high computational resources when computed on-the-fly during the reconstruction process or high memory resources when pre-computed stored models are used. The main purposes of this thesis are the development of an efficient method to perform the resolution modelling for pixellated non-TOF PET scanners and its implementation in a generic reconstruction software to provide fast and accurate image reconstruction for user-defined scanner geometries. This thesis targets pre- clinical and application dedicated scanners (like brain tomographs), in which the reconstructed field of view extends to a large portion of the scanner bore and the detector response is the main degrading factor of the image quality. The approach used in this work is the factorization of the system model into several components, with particular regard to the e#cient computation and application of the geometric (G) component and projection-space (D) component.