The work presented here is devoted to the proposal and investigation of 3D image reconstruction algorithms suitable for high resolution positron emission tomography (PET). In particular, we have studied imaging techniques applicable to the high resolution research tomograph (HRRT): a 3Donly state-of-the-art dedicated brain tomograph. The HRRT poses a number of unique challenges, most significant of which include presence of gaps in-between the detector heads, as well as the very large number of

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... lines-ofresponse (LORs) which it is able to measure (~4.5x10⁹), exceeding most modern PET scanners by 2-3 orders of magnitude. To address the existing issues, we have developed and implemented statistical list-mode image reconstruction as a powerful technique applicable to the high resolution data obtained by the HRRT. We have furthermore verified applicability of this technique to dynamic (4D) PET imaging, thus qualifying the technique as viable and accurate for the research intended to be performed on the scanner. We have paid particular attention to the study of convergent algorithms; i.e. iterative algorithms which (with further iterations) consistently improve such figures of merit as resolution and contrast, relevant to research and clinical tasks. With the spatial resolution in modern high resolution tomographs (including the HRRT) reaching the 2-3mm FWHM range, small patient movements during PET imaging can become a significant source of resolution degradation. We have thus devoted a portion of this dissertation to the proposal of new, accurate and practical motion-compensation techniques, and studied them on the HRRT. We have theoretically proposed and experimentally validated the benefits of modeling the motion into the reconstruction task, thus signaling the way beyond the existing purely event-driven motioncompensation techniques.