Dynamic 3D PET reconstruction for kinetic analysis using patch-based low-rank penalty

Dynamic positron emission tomography (PET) is widely used to identify metabolism over time. However, conventional reconstruction algorithm provides a noisy reconstruction due to the lack of photon counts in each frame. Therefore, the main goal of this paper is to develop a novel spatio-temporal regularization approach that exploits inherent similarities within intra- and inter- frames. 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.We confirm that the proposed algorithm can provide significantly improved image quality.