ODE-Driven Deterministic Diffusion Posterior Sampling for Sparse-View CT Image Reconstruction

Sparse-view sampling for computed tomography (CT) reduces radiation exposure in medical imaging but suffers from severe artifacts due to ill-posed nature of under-sampled reconstruction. While diffusion posterior sampling (DPS) leverages data-driven priors for improved results, its stochastic nature impedes clinical reproducibility, and inefficient noise-perturbed likelihood estimation limits practicality. This work proposes the probabilistic ordinary differential equation (ODE)-driven deterministic diffusion posterior sampling (ODDPS) framework to enable stable, high-quality sparse-view CT reconstruction by combining physical constraints with deterministic generative sampling. ODDPS reformulates stochastic diffusion into a probability flow ODE, ensuring deterministic sampling from noise to image. In this work, a dual-domain solver is proposed, which integrates diffusion processes in the image domain and sinogram domain, and decouples the problem into a physics-based likelihood term and a diffusion-based prior term under the Bayesian framework. Specifically, the prior term is solved using the recently proposed first-order solver of diffusion probabilistic model, while the likelihood term adopts an efficient physics-based likelihood gradient to avoid neural backpropagation in each iteration. This design bridges tomographic physics and the learned diffusion prior within a unified framework, ensuring the consistency between the reconstruction results and the physical constraints of CT imaging. Evaluated on public LIDC dataset, ODDPS achieved average improvements of 1.2 dB and 5.82% in peak signal-to-noise ratio and structural similarity index measured under the 30 views, and is 48.6% faster reconstruction than DPS. Ablation studies confirmed near-zero variance in outputs and significant artifact suppression. By unifying ODE-driven deterministic sampling with dual-domain diffusion, ODDPS delivers reproducible, high-fidelity sparse-view CT reconstructions. Its efficiency and repeatability advance the clinical translation of diffusion models for inverse problems.