With continuing improvements in spatial resolution of positron emission tomography (PET) scanners, small patient movements during PET imaging become a significant source of resolution degradation. This work develops and investigates a comprehensive formalism for accurate motion-compensated reconstruction which at the same time is very feasible in the context of high-resolution PET. In particular, this paper proposes an effective method to incorporate presence of scattered and random coincidences in the context of motion (which is similarly applicable to various other motion correction schemes). The overall reconstruction framework takes into consideration missing projection data which are not detected due to motion, and additionally, incorporates information from all detected events, including those which fall outside the field-of-view following motion correction. The proposed approach has been extensively validated using phantom experiments as well as realistic simulations of a new mathematical brain phantom developed in this work, and the results for a dynamic patient study are also presented.

Modern high-resolution PET is now more than ever in need of scrutiny into the nature and limitations of the imaging modality itself as well as image reconstruction techniques. In this work, we have reviewed, analysed and addressed the following three considerations within the particular context of state-of-the-art dynamic PET imaging: (i) the typical average numbers of events per line-of-response (LOR) are now (much) less than unity, (ii) due to the physical and biological decay of the activity distribution, one requires robust and efficient reconstruction algorithms applicable to a wide range of statistics and (iii) the computational considerations in dynamic imaging are much enhanced (i.e., more frames to be stored and reconstructed). Within the framework of statistical image reconstruction, we have argued theoretically and shown experimentally that the sinogram non-negativity constraint (when using the delayed-coincidence and/or scatter-subtraction techniques) is especially expected to result in an overestimation bias. Subsequently, two schemes are considered: (a) subtraction techniques in which an image non-negativity constraint has been imposed and (b) implementation of random and scatter estimates inside the reconstruction algorithms, thus enabling direct processing of Poisson-distributed prompts. Both techniques are able to remove the aforementioned bias, while the latter, being better conditioned theoretically, is able to exhibit superior noise characteristics. We have also elaborated upon and verified the applicability of the accelerated list-mode image reconstruction method as a powerful solution for accurate, robust and efficient dynamic reconstructions of high-resolution data (as well as a number of additional benefits in the context of state-of-the-art PET).

The authors observed that 3D-MAP produces more accurate activity concentration estimates than 2D-FBP or 2D-OSEM at all practical levels of statistics and contrasts due to improved spatial resolution leading to lesser partial volume effect.

HighlY constrained back-PRojection (HYPR) is a post-processing de-noising technique originally developed for time-resolved magnetic resonance imaging. It has been recently applied to dynamic imaging for positron emission tomography and shown promising results. In this work, we have developed an iterative reconstruction algorithm (HYPR-OSEM) which improves the signal-to-noise ratio (SNR) in static imaging (i.e. single frame reconstruction) by incorporating HYPR de-noising directly within the ordered subsets expectation maximization (OSEM) algorithm. The proposed HYPR operator in this work operates on the target image(s) from each subset of OSEM and uses the sum of the preceding subset images as the composite which is updated every iteration. Three strategies were used to apply the HYPR operator in OSEM: (i) within the image space modeling component of the system matrix in forward-projection only, (ii) within the image space modeling component in both forward-projection and back-projection, and (iii) on the image estimate after the OSEM update for each subset thus generating three forms: (i) HYPR-F-OSEM, (ii) HYPR-FB-OSEM, and (iii) HYPR-AU-OSEM. Resolution and contrast phantom simulations with various sizes of hot and cold regions as well as experimental phantom and patient data were used to evaluate the performance of the three forms of HYPR-OSEM, and the results were compared to OSEM with and without a post reconstruction filter. It was observed that the convergence in contrast recovery coefficients (CRC) obtained from all forms of HYPR-OSEM was slower than that obtained from OSEM. Nevertheless, HYPR-OSEM improved SNR without degrading accuracy in terms of resolution and contrast. It achieved better accuracy in CRC at equivalent noise level and better precision than OSEM and better accuracy than filtered OSEM in general. In addition, HYPR-AU-OSEM has been determined to be the more effective form of HYPR-OSEM in terms of accuracy and precision based on the studies conducted in this work.

Positron emission tomography (PET), like other imaging modalities, has resolution limitations. Two general/common approaches to improve reconstructed image resolution include: (i) the de-convolution scheme, and (ii) system matrix modeling (in statistical image reconstruction methods). An interesting observation about (ii) is that it is able to improve both resolution and noise characteristics of the reconstructed images (unlike (i) which offers a trade-off). In this work, we have used the unified noise model developed by Qi [5] to perform image covariance calculations without and with the inclusion of resolution modeling in the system matrix of the EM algorithm.We have in particular shown that, while system matrix modeling of finite resolution effects improves the image resolution by direct contribution to the reconstruction task, it is at the same time able to lower the reconstructed image noise due to a compression/widening effect in inter-voxel correlations. We have also experimentally verified this effect.