DeepSPIM: Deep Semi-Proximal Iterative Method for Sparse-View CT Reconstruction with Convergence Guarantee (CSIAM Transactions on Applied Mathematics, 2024)
Computed tomography (CT) reconstruction with sparse-view projections isa challenging problem in medical imaging. The learning-based methods lack generalization ability and mathematical interpretability. Since the model-based iterative reconstruction (IR) methods need inner gradient-based iterations to deal with the CTsystem matrix, the algorithms may not be efficient enough, and IR methods with deepnetworks have no convergence guarantees. In this paper, we propose an efficient deepsemi-proximal iterative method (DeepSPIM) to reconstruct CT images from sparse-view projections. Unlike the existing IR methods, a carefully designed semi-proximalterm is introduced to make the system matrix-related subproblem solvable. Theoretically, we give some useful mathematical analysis, including the existence of thesolutions to the reconstruction model with an implicit image prior, the global convergence of the proposed method under gradient step denoiser assumption. Experimentalresults show that DeepSPIM is efficient and outperforms the closely related state-of-the-art methods regarding quantitative image quality values, details preservation, andstructure recovery.
Keywords: Computed tomography; sparse-view reconstruction; iterative method; semi-proximal term; global convergence.