应用扩散模型进行部分傅里叶重建

Partial Fourier Reconstruction Using Diffusion Models

摘要: 部分傅立叶(PF) MRI重建在准确恢复缺失的k空间数据的同时保持图像细节和相位一致性方面面临挑战。为此，我们提出了一种基于随机微分方程(SDE)的扩散模型，该模型结合物理约束以提升重建质量。该方法利用SDE训练神经网络的分数函数，并通过去噪分数匹配学习数据分布的先验信息。此外，基于k空间的共轭对称性，我们在逆扩散过程中引入虚拟线圈概念(VCC)，扩展k空间数据，从而提供额外的相位编码信息和物理共轭对称性约束。这一设计有效限制了扩散模型在未采样区域的生成能力，实现更加精准且符合物理规律的重建。实验结果表明，与传统算法和深度监督方法相比，该方法在细节保留、相位图像重建表现更优。

Abstract: Partial Fourier (PF) MRI reconstruction faces challenges in accurately recovering missing k-space data while preserving image details and phase consistency. To address this, we propose a score-based Stochastic Differential Equation (SDE) diffusion model that integrates physical constraints to enhance reconstruction quality. This method employs score-based SDE to train a neural network score function using denoising score matching, serving as a prior for the data distribution. Additionally, leveraging the conjugate symmetry of k-space, we introduce the Virtual Coil Concept (VCC) during the inverse diffusion process, which extends k-space to provide additional phase encoding and physical conjugate symmetry constraints. This effectively restricts the generative capability of the Diffusion Model (DM) in non-sampled regions, leading to more accurate and physically consistent reconstructions. Experimental results demonstrate that, compared to traditional algorithms and deep supervision methods, our approach achieves superior performance in detail preservation and phase image reconstruction.