RN-SDEs: Limited-Angle CT Reconstruction with Residual Null-Space Diffusion Stochastic Differential Equations

TL;DR

This paper introduces RN-SDEs, a novel diffusion model variant that improves limited-angle CT image reconstruction by effectively recovering high-quality images from severely degraded data, outperforming existing methods.

Contribution

The paper proposes Residual Null-Space Diffusion SDEs (RN-SDEs) for LACT reconstruction, combining mean-reverting SDEs with data consistency techniques, demonstrating superior performance and efficiency.

Findings

RN-SDEs achieve state-of-the-art results in LACT tasks.

RN-SDEs outperform other networks in computational efficiency.

Effective recovery of high-quality images from limited-angle data.

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, resulting in distortion or artifacts in the reconstructed images. This is referred to as the Limited Angle Computed Tomography (LACT) reconstruction problem. To address this problem, we propose the use of 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, we conducted experiments with two different LACT datasets, ChromSTEM and C4KC-KiTS. Through extensive experiments, we demonstrate that by leveraging learned MR-SDEs as a prior and emphasizing data consistency using Range-Null Space Decomposition (RNSD) based rectification, we can recover high-quality images from severely degraded ones and achieve state-of-the-art performance in most LACT tasks. Additionally, we present a quantitative comparison of RN-SDE with other networks, in terms of computational complexity and runtime efficiency, highlighting the superior effectiveness of our proposed approach.