# Stage-by-stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstruction

arXiv: https://arxiv.org/abs/2308.15942 · HTML: https://mlsanity.com/paper/2308.15942/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [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)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction](https://mlsanity.com/paper/1803.00694/) (2018)
- [Non Gaussian Denoising Diffusion Models](https://mlsanity.com/paper/2106.07582/) (2021)
- [Maximum Likelihood Training of Implicit Nonlinear Diffusion Models](https://mlsanity.com/paper/2205.13699/) (2022)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification](https://mlsanity.com/paper/1611.06345/) (2016)
- [Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis](https://mlsanity.com/paper/1611.06391/) (2016)
- [Heavy-tailed denoising score matching](https://mlsanity.com/paper/2112.09788/) (2021)
- [Patch-Based Denoising Diffusion Probabilistic Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2211.10388/) (2022)
- [Wavelet Transform-assisted Adaptive Generative Modeling for Colorization](https://mlsanity.com/paper/2107.04261/) (2021)
- [Parallel Diffusion Model-based Sparse-view Cone-beam Breast CT](https://mlsanity.com/paper/2303.12861/) (2023)

## Built on by (most cited first, 18 of 18)

- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [Discretized Gaussian Representation for Tomographic Reconstruction](https://mlsanity.com/paper/2411.04844/) (2024)
- [Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2508.10313/) (2025)
- [MSDiff: Multi-Scale Diffusion Model for Ultra-Sparse View CT Reconstruction](https://mlsanity.com/paper/2405.05814/) (2024)
- [Early Lung Cancer Diagnosis from Virtual Follow-up LDCT Generation via Correlational Autoencoder and Latent Flow Matching](https://mlsanity.com/paper/2511.18185/) (2025)
- [Prompting Lipschitz-constrained network for multiple-in-one sparse-view CT reconstruction](https://mlsanity.com/paper/2511.20296/) (2025)
- [Physics-informed DeepCT: Sinogram Wavelet Decomposition Meets Masked Diffusion](https://mlsanity.com/paper/2501.09935/) (2025)
- [Virtual-mask Informed Prior for Sparse-view Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2504.07753/) (2025)
- [Computationally Efficient Diffusion Models in Medical Imaging: A Comprehensive Review](https://mlsanity.com/paper/2505.07866/) (2025)
- [PRO: Projection Domain Synthesis for CT Imaging](https://mlsanity.com/paper/2506.13443/) (2025)
- [Deep Inertia Lp Half-Quadratic Splitting Unrolling Network for Sparse View CT Reconstruction](https://mlsanity.com/paper/2408.06600/) (2024)
- [Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2505.09985/) (2025)
- [Physics-Guided Null-Space Diffusion with Sparse Masking for Corrective Sparse-View CT Reconstruction](https://mlsanity.com/paper/2509.05992/) (2025)
- [MORE: Multi-Organ Medical Image REconstruction Dataset](https://mlsanity.com/paper/2510.26759/) (2025)
- [Iterative Diffusion-Refined Neural Attenuation Fields for Multi-Source Stationary CT Reconstruction: NAF Meets Diffusion Model](https://mlsanity.com/paper/2511.14310/) (2025)
- [Residual Gaussian Splatting for Ultra Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2604.27552/) (2026)
- [LUCID: Learned Undersampling-Adaptive Consistency-Guided Inference with Deterministic Flow Matching for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2606.16212/) (2026)
- [SCMA: Structure-Conditioned and Metal-Aware Flow Matching for CT Metal Artifact Reduction](https://mlsanity.com/paper/2607.28759/) (2026)

## Abstract (arXiv)

Diffusion models have emerged as potential tools to tackle the challenge of sparse-view CT reconstruction, displaying superior performance compared to conventional methods. Nevertheless, these prevailing diffusion models predominantly focus on the sinogram or image domains, which can lead to instability during model training, potentially culminating in convergence towards local minimal solutions. The wavelet trans-form serves to disentangle image contents and features into distinct frequency-component bands at varying scales, adeptly capturing diverse directional structures. Employing the Wavelet transform as a guiding sparsity prior significantly enhances the robustness of diffusion models. In this study, we present an innovative approach named the Stage-by-stage Wavelet Optimization Refinement Diffusion (SWORD) model for sparse-view CT reconstruction. Specifically, we establish a unified mathematical model integrating low-frequency and high-frequency generative models, achieving the solution with optimization procedure. Furthermore, we perform the low-frequency and high-frequency generative models on wavelet's decomposed components rather than sinogram or image domains, ensuring the stability of model training. Our method rooted in established optimization theory, comprising three distinct stages, including low-frequency generation, high-frequency refinement and domain transform. Our experimental results demonstrate that the proposed method outperforms existing state-of-the-art methods both quantitatively and qualitatively.