Image reconstruction from incomplete data via approximated pseudo-inverse and dual-domain coupled diffusion posterior sampling.

Background: Sparse-view (SV) and limited-angle (LA) computed tomography (CT) represent typical incomplete-data reconstruction scenarios, which are essential for reducing patient radiation exposure while expanding clinical applications. However, data incompleteness frequently induces severe streaking artifacts, compromising diagnostic reliability and hindering clinical translation. This study examined an optimized dual-domain coupled diffusion posterior sampling (DPS) framework integrated with an approximated pseudo-inverse method. By synergistically combining artifact suppression with anatomical detail preservation, the proposed approach aims to enhance CT image quality under incomplete-data conditions. Methods: This study developed an approximated pseudo-inverse-guided dual-domain stochastic diffusion model (API-DDM), which provides improved posterior diffusion generative framework. Specifically, in the reverse diffusion stage, API-DDM constructs a stochastic process that couples the sinogram domain and the image domain. By leveraging the approximated pseudo-inverse of the measurement matrix using the filtered back-projection operator, the model integrates the diffusion generative prior to guiding the reverse diffusion process, thereby enhancing the consistency between the reconstructed image and the measured data. This strategy substantially improves the stability of the inverse problem solution and achieves superior reconstruction quality and generalizability in CT imaging. Results: Extensive experiments were conducted with diffusion models pretrained on publicly available CT datasets under two sampling conditions: sparse view (≤50 views) and limited angle (≤120°). For SV CT with 50 views, the proposed method achieved a peak signal-to-noise ratio (PSNR) of 41.21 dB and a structural similarity index measure (SSIM) of 0.9527. For LA CT in the 1°-120° range, the method yielded a PSNR of 39.78 dB and an SSIM of 0.9550. Notably, even under extreme undersampling (9 views or 60° angular range), the algorithm maintained robust performance (PSNR: 36.53 dB/34.49 dB; SSIM: 0.9276/0.9069). These results verified the effectiveness of the proposed method for incomplete CT image reconstruction. Conclusions: The proposed API-DDM algorithm effectively addresses the challenge of incomplete CT data reconstruction by establishing a stable bridge between physical measurement consistency and deep generative priors. The demonstrated robustness under SV and LA conditions suggests potential clinical utility in low-dose screening protocols and intraoperative imaging scenarios for which radiation reduction is critical.