Simultaneous Reconstruction and Segmentation of Dynamic PET via Low-Rank and Sparse Matrix Decomposition

Although of great clinical value, accurate and robust reconstruction and segmentation of dynamic positron emission tomography (PET) images are great challenges due to low spatial resolution and high noise. In this paper, we propose a unified framework that exploits temporal correlations and variations within image sequences based on low-rank and sparse matrix decomposition. Thus, the two separate inverse problems, PET image reconstruction and segmentation, are accomplished in a simultaneous fashion. Considering low signal to noise ratio and piece-wise constant assumption of PET images, we also propose to regularize low-rank and sparse matrices with vectorial total variation norm. The resulting optimization problem is solved by augmented Lagrangian multiplier method with variable splitting. The effectiveness of proposed approach is validated on realistic Monte Carlo simulation datasets and the real patient data.