Recently, diffusion models have shown considerable promise for MRI reconstruction. However, extensive experimentation has revealed that these models are prone to generating artifacts due to the inherent randomness involved in generating images from pure noise. To achieve more controlled image reconstruction, we reexamine the concept of interpolatable physical priors in k-space data, focusing specifically on the interpolation of high-frequency (HF) k-space data from low-frequency (LF) k-space data. Broadly, this insight drives a shift in the generation paradigm from random noise to a more deterministic approach grounded in the existing LF k-space data. Building on this, we first establish a relationship between the interpolation of HF k-space data from LF k-space data and the reverse heat diffusion process, providing a fundamental framework for designing diffusion models that generate missing HF data. To further improve reconstruction accuracy, we integrate a traditional physics-informed k-space interpolation model into our diffusion framework as a data fidelity term. Experimental validation using publicly available datasets demonstrates that our approach significantly surpasses traditional k-space interpolation methods, deep learning-based k-space interpolation techniques, and conventional diffusion models, particularly in HF regions. Finally, we assess the generalization performance of our model across various out-of-distribution datasets. Our code are available at https://github.com/ZhuoxuCui/Heat-Diffusion .

中文翻译：

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基于物理学的 DeepMRI：k-Space 插值与热扩散相遇


最近，弥散模型在 MRI 重建方面显示出相当大的前景。然而，广泛的实验表明，由于从纯噪声生成图像所涉及的固有随机性，这些模型容易产生伪影。为了实现更可控的图像重建，我们重新研究了 k 空间数据中可插值物理先验的概念，特别关注高频 （HF） k-空间数据与低频 （LF） k-空间数据的插值。从广义上讲，这种洞察力推动了生成范式的转变，从随机噪声到基于现有 LF k 空间数据的更具确定性的方法。在此基础上，我们首先建立了 LF k-space 数据中 HF k-space 数据的插值与反向热扩散过程之间的关系，为设计生成缺失 HF 数据的扩散模型提供了基本框架。为了进一步提高重建精度，我们将传统的物理学信息型 k 空间插值模型作为数据保真度项集成到我们的扩散框架中。使用公开可用的数据集进行的实验验证表明，我们的方法明显优于传统的 k 空间插值方法、基于深度学习的 k 空间插值技术和传统的扩散模型，尤其是在 HF 区域。最后，我们评估了模型在各种分布外数据集中的泛化性能。我们的代码可在 https://github.com/ZhuoxuCui/Heat-Diffusion 上找到。