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Globally convergent 3D dynamic PET reconstruction with patch-based non-convex low rank regularization

Dynamic positron emission tomography (PET) is widely used to measure variations of radiopharmaceuticals within the organs over time. However, conventional reconstruction algorithm can produce a noisy reconstruction if there are not sufficient photon counts. Hence, the main goal of this paper is to develop a novel spatio-temporal regularization approach that exploits inherent similarities within intra- and inter-frames to overcome the limitation. One of the main contributions of this paper is to demonstrate that such correlations can be exploited using a low rank constraint of overlapping similarity blocks. The resulting optimization framework is, however, non-smooth and non Lipschitz due to the low-rank penalty terms and Poisson log-likelihood. Therefore, we propose a novel globally convergent optimization method using the concave-convex procedure (CCCP) by exploiting Legendre-Fenchel transform, which overcomes the memory and computational limitations. We confirm that the proposed algorithm can provide significantly improved image quality and extract accurate kinetic parameters.