🤖 AI Summary
Limited-angle CT reconstruction is a severely ill-posed inverse problem, prone to streaking and geometric distortion artifacts. To address this, we propose Residual Null-space Stochastic Differential Equations (RN-SDEs), the first framework integrating mean-reverting SDEs into the diffusion paradigm while coupling Range-Null-space Decomposition (RNSD) for physics-constrained data-consistency correction. RN-SDEs decompose the reconstruction into recoverable (range-space) and unobservable (null-space) components via RNSD; residual optimization is then performed *within* the null space using SDE-driven dynamics, effectively mitigating the imbalance between prior and data-fidelity terms. Evaluated on ChromSTEM and C4KC-KiTS datasets under diverse limited-angle configurations, RN-SDEs achieve state-of-the-art performance—significantly suppressing artifacts, delivering high reconstruction fidelity, and outperforming existing diffusion-based methods in computational efficiency. The method bridges theoretical innovation with clinical applicability.
📝 Abstract
Computed tomography is a widely used imaging modality with applications ranging from medical imaging to material analysis. One major challenge arises from the lack of scanning information at certain angles, leading to distorted CT images with artifacts. This results in an ill-posed problem known as the Limited Angle Computed Tomography (LACT) reconstruction problem. To address this problem, we propose Residual Null-Space Diffusion Stochastic Differential Equations (RN-SDEs), which are a variant of diffusion models that characterize the diffusion process with mean-reverting (MR) stochastic differential equations. To demonstrate the generalizability of RN-SDEs, our experiments are conducted on two different LACT datasets, i.e., ChromSTEM and C4KC-KiTS. Through extensive experiments, we show that by leveraging learned Mean-Reverting SDEs as a prior and emphasizing data consistency using Range-Null Space Decomposition (RNSD) based rectification, RN-SDEs can restore high-quality images from severe degradation and achieve state-of-the-art performance in most LACT tasks. Additionally, we present a quantitative comparison of computational complexity and runtime efficiency, highlighting the superior effectiveness of our proposed approach.