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.

翻译：扩散模型已成为应对稀疏视角CT重建挑战的潜在工具，展现出优于传统方法的性能。然而，现有扩散模型主要关注正弦图域或图像域，这可能导致模型训练不稳定，甚至收敛至局部最优解。小波变换能够将图像内容与特征分解为不同尺度下的频率分量带，有效捕捉多样化的方向性结构。以小波变换作为引导稀疏先验，可显著增强扩散模型的鲁棒性。本研究提出一种创新方法——逐级小波优化精炼扩散（SWORD）模型，用于稀疏视角CT重建。具体而言，我们构建了集成低频与高频生成模型的统一数学模型，通过优化流程实现求解。此外，我们在小波分解分量上执行低频与高频生成模型，而非正弦图域或图像域，从而确保模型训练的稳定性。该方法根植于成熟的优化理论，包含三个不同阶段：低频生成、高频精炼以及域变换。实验结果表明，本方法在定量与定性性能上均优于现有最优方法。