TY - JOUR T1 - DeepSPIM: Deep Semi-Proximal Iterative Method for Sparse-View CT Reconstruction with Convergence Guarantee AU - Wei , Deliang AU - Li , Fang AU - Shen , Xiao AU - Zeng , Tieyong JO - CSIAM Transactions on Applied Mathematics VL - 3 SP - 421 EP - 447 PY - 2024 DA - 2024/08 SN - 5 DO - http://doi.org/10.4208/csiam-am.SO-2023-0037 UR - https://global-sci.org/intro/article_detail/csiam-am/23305.html KW - Computed tomography, sparse-view reconstruction, iterative method, semi-proximal term, global convergence. AB -

Computed tomography (CT) reconstruction with sparse-view projections is a 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 CT system matrix, the algorithms may not be efficient enough, and IR methods with deep networks have no convergence guarantees. In this paper, we propose an efficient deep semi-proximal iterative method (DeepSPIM) to reconstruct CT images from sparse-view projections. Unlike the existing IR methods, a carefully designed semi-proximal term is introduced to make the system matrix-related subproblem solvable. Theoretically, we give some useful mathematical analysis, including the existence of the solutions to the reconstruction model with an implicit image prior, the global convergence of the proposed method under gradient step denoiser assumption. Experimental results show that DeepSPIM is efficient and outperforms the closely related state-of-the-art methods regarding quantitative image quality values, details preservation, and structure recovery.