Learned proximal gradient flow matching for limited-angle CT reconstruction

The primary objective of this research is to address the challenges of limited-angle computed tomography (CT) reconstruction that arises when projection data are acquired over an angular range smaller than that required for theoretically exact reconstruction. This ill-posed problem leads to severe artifacts compromising diagnostic quality. The study aims to develop a robust and efficient framework to achieve high-fidelity image reconstruction. Approach: The proposed method, termed Learned Proximal Gradient Flow Matching (LPGFM), introduces a novel framework that synergistically combines explicit optimization principles with deep generative models. First, a pre-trained flow matching network is applied to transform the initialized solution along a learned gradient field, effectively removing artifacts while preserving anatomical details. Secondly, a proximal correction step enforces strict data consistency, enhancing robustness against deviations. This approach decouples data fidelity from prior application, preventing error propagation and ensuring stability, particularly under out-of-distribution conditions. Main Results: The proposed LPGFM method demonstrates significant advantages in limited-angle CT reconstruction. Experiments on the medical and head datasets show that LPGFM outperforms comparative methods. Quantitative evaluations reveal that LPGFM achieves the highest PSNR and SSIM scores with the lowest RMSE. For instance, in the 150° medical data, LPGFM attains a PSNR of 30.14 dB, indicating superior artifact suppression and detail preservation. Under the more challenging 120° condition, LPGFM maintains robustness with minimal quality degradation, highlighting its generalization capability. Significance: This work introduces a framework that combines model-based optimization with data-driven generative priors in limited-angle CT reconstruction by bridging the gap between model-based optimization and data-driven generative models. The LPGFM framework offers theoretical advantages, such as interpretability and robustness, while practical benefits include reduced reliance on large training datasets and adaptability to diverse scanning geometries. Its ability to deliver high-quality reconstructions under extreme limited-angle conditions has implications for clinical applications.