A Weighted Least Squares Reconstruction Method for PET Data Using Nonlinear Anisotropic Diffusion Regularization

Due to the inherent ill-posedness of PET image reconstruction, the reconstructed images will have noise and edge artifacts. A roughness penalty is often imposed on the solution to control noise. In this paper, we propose a new weighted least squares (WLS) image reconstruction method for PET based on nonlinear anisotropic diffusion (AD) regularization. The use of AD is because it is extremely effective for reducing noise in 2D images while preserving edges. The weighted factor is used to balance data consistency and regularization terms. The application of the proposed approach to simulated and real PET emission data show that it more effective than the common WLS algorithm, especially for noisy projection data.