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“Bayesian Image Estimation for Fully Three-D Positron emission Tomography ”
by Jinyi Qi
December 1998
3D data acquisition in Positron Emission Tomography (PET) increases the sensitivity of the scanner by a factor of four to seven compared to the conventional 2D acquisition mode. This increase in sensitivity can be used to obtain higher resolution images, or to reduce the injection dose and scan durations. Most 3D PET data sets are reconstructed using analytical methods where resolution is limited by the line integral assumption. Bayesian methods can reconstruct high quality PET images through accurately modeling both the mapping between the source distribution and the measured data, and the statistical distribution of the noise. However, the huge data size in 3D PET systems presents a daunting challenge in both computation and storage requirements. We develop a maximum {em a posteriori} (MAP) Bayesian estimation algorithm for fully 3D PET image reconstruction. A factored detection probability matrix is used, which not only accurately models the photon detection process in PET systems, but saves reconstruction time and storage size as well. The log posterior density function is maximized using a preconditioned conjugate gradient algorithm. It is further accelerated using multi-threaded programming techniques. An ordered subset EM (OSEM) method is also derived using the same detection model. Both the MAP and the OSEM algorithms have been implemented for the microPET animal PET scanner and the Siemens/CTI ECAT HR+ whole-body PET scanner. The algorithms were evaluated using various data sets with comparison to the widely used 3D re-projection (3DRP) method. Experimental results show that the proposed MAP method can achieve higher resolution and contrast recovery than the OSEM and the 3DRP methods at all matched noise levels. The resolution and noise properties of MAP reconstructions have also been theoretically studied. Simplified expressions for the local impulse response and the covariance of the noise are derived, which allow fast evaluation of the bias and reliability of the reconstructed images. Based on this analysis we also develop a method for reconstructing uniform resolution images and a hyperparameter selection scheme for optimal lesion detection.