Nonlocal Low-Rank and Total Variation Constrained PET Image Reconstruction

Many efforts have been made for decades in order to improve the accuracy of radioactivity map in positron emission tomography (PET) images, which has important clinical implications for better diagnosis and understanding of diseases. However, there is still a challenging problem for reconstructing high resolution image with the limited acquired photon counts. In this paper, we present a nonlocal self-similar constraint for the purpose of exploiting structured sparsity within the PET reconstructed images. It is based on image patches and approached by low-rank approximation. Moreover, we adopt total variation regulation into our method to further denoise and compensate the demerits inherited in patch-based methods. These two regulation terms are firstly employed in the Poisson model, and are jointly solved in a distributed optimization framework. Experiments have presented that our proposed PNLTV method substantially outperforms existing state-of-the-art methods in PET reconstruction.