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

arXiv: https://arxiv.org/abs/2409.13930 · HTML: https://mlsanity.com/paper/2409.13930/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 30 of 37)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 Challenge](https://mlsanity.com/paper/1912.01054/) (2019)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)

## Built on by (most cited first, 4 of 4)

- [Advancing Limited-Angle CT Reconstruction Through Diffusion-Based Sinogram Completion](https://mlsanity.com/paper/2505.19385/) (2025)
- [Diffusion-Based Limited-Angle CT Reconstruction under Noisy Conditions](https://mlsanity.com/paper/2507.05647/) (2025)
- [Limited-Angle Tomography Reconstruction via Projector Guided 3D Diffusion](https://mlsanity.com/paper/2510.06516/) (2025)
- [Geometry-Aware Diffusion Approximate Posterior Sampling for Sparse-View and Limited-Angle CT](https://mlsanity.com/paper/2610.08866/) (2026)

## Abstract (arXiv)

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.