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Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

K. Gong, J. Zhou, M. Tohme, M. Judenhofer, Y. Yang, J. Qi
IEEE Trans Med Imaging

Positron emission tomography (PET) is a medical imaging technique widely used in cancer detection and staging. An accurate system matrix is essential for reconstructing high-quality PET images. One critical component in the system matrix is the sinogram blurring matrix, which models various resolution degradation effects in the photon detection process. One way to obtain an accurate sinogram blurring matrix in a real PET scanner is to estimate it from point source measurements. However, the estimation can be noisy due to the large number of unknowns in the sinogram blurring matrix. As a result, it often requires a large number of point source scans. Scanning a large number of point sources can be difficult in terms of experimental set up and long scan time. Here we propose a rank-one decomposition, which is referred to as "p-q" kernel, to reduce the number of unknown parameters in the sinogram blurring matrix and hence reduce the noise amplification in the estimation process. Using both computer simulations and real data from a preclinical microPET scanner, we have demonstrated the proposed rank-one approximation can substantially improve the robustness of the sinogram blurring matrix estimation with much less modeling error than either a 3D sinogram blurring matrix or an unconstrained 4D sinogram blurring matrix and produce images with better spatial resolution.