Low-Count PET Image Reconstruction with Generalized Sparsity Priors via Unrolled Deep Networks

Deep learning has demonstrated remarkable efficacy in reconstructing low-count PET (Positron Emission Tomography) images, attracting considerable attention in the medical imaging community. However, most existing deep learning approaches have not fully exploited the unique physical characteristics of PET imaging in the design of fidelity and prior regularization terms, resulting in constrained model performance and interpretability. In light of these considerations, we introduce an unrolled deep network based on maximum likelihood estimation for the Poisson distribution and a Generalized domain transformation for Sparsity learning, dubbed GS-Net. To address this complex optimization challenge, we employ the Alternating Direction Method of Multipliers (ADMM) framework, integrating a modified Expectation Maximization (EM) approach to address the primary objective and utilize the shrinkage thresholding approach to optimize the L1 norm term. Additionally, within this unrolled deep network, all hyperparameters are adaptively adjusted through end-to-end learning to eliminate the need for manual parameter tuning. Through extensive experiments on simulated patient brain datasets and real patient whole-body clinical datasets with multiple count levels, our method has demonstrated advanced performance compared to traditional non-iterative and iterative reconstruction, deep learning-based direct reconstruction, and hybrid unrolled methods, as demonstrated by qualitative and quantitative evaluations.