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“Statistical Image Reconstruction and Performance Analysis for Dynamic Positron Emission Tomography”
by Evren Asma
August 2004
We developed dynamic PET image reconstruction algorithms for the penalized likelihood estimation of voxelwise time activity curves directly from list-mode data. We used an efficient format for the spatiotemporal data in which we augmented the sinogram with an associated list of event arrival times indexed by the sinogram entries. We combined our accurate system model developed for static PET with an accurate statistical model that models the emission from each voxel as an inhomogeneous Poisson process to reconstruct dynamic images with high spatial and temporal resolution.
We derived computationally efficient methods for the estimation of the mean and variance properties of penalized likelihood dynamic PET images. This allowed us to predict the accuracy of reconstructed activity estimates and to compare reconstruction algorithms theoretically. We combined a bin-mode approach in which data is modeled as a collection of independent Poisson random variables at each spatiotemporal bin with the space-time separabilities in the imaging equation and penalties to derive rapidly computable analytic mean and variance approximations. We used these approximations to show that our dynamic PET image reconstruction algorithm has superior bias/variance properties over multiframe static PET reconstructions.
We also studied the spatial and temporal resolution properties of penalized likelihood dynamic PET images and showed that approximately uniform spatial resolution over time could be achieved by applying spatiotemporally varying smoothing. The degree of smoothing at each voxel is determined by the corresponding diagonal entry of the dynamic Fisher Information Matrix. We also showed that by performing the reconstruction in a transformed time domain, we could also make the spatial resolution not only uniform in space but also approximately constant over time.
In order to take advantage of the full spatiotemporal content of list-mode data, we proved the convergence of a globally convergent, fully four-dimensional, incremental gradient dynamic PET image reconstruction algorithm and demonstrated its feasibility by reconstructing simulated four-dimensional PET data from a small-animal scanner.
We also developed an efficient algorithm to compress large dynamic PET datasets that provided an additional 35-40% compression over standard compression software for datasets with more than 60 frames.
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