NERD: Network-Regularized Diffusion Sampling For 3D Computed Tomography

Abstract: Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces measurement consistency, forward diffusion consistency, and both step-wise and backward diffusion consistency. However, these methods have only considered 2D reconstruction tasks and do not directly extend to 3D image reconstruction problems, such as in Computed Tomography (CT). To bridge this gap, we propose NEtwork-Regularized diffusion sampling for 3D CT (NERD) by incorporating an L1 regularization into the optimization objective. This regularizer encourages spatial continuity across adjacent slices, reducing inter-slice artifacts and promoting coherent volumetric reconstructions. Additionally, we introduce two efficient optimization strategies to solve the resulting objective: one based on the Alternating Direction Method of Multipliers (ADMM) and another based on the Primal-Dual Hybrid Gradient (PDHG) method. Experiments on medical 3D CT data demonstrate that our approach achieves either state-of-the-art or highly competitive results.