In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring k-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both k-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel k-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in k-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional k-space interpolation methods, deep learning-based k-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.
@article{arxiv.2308.15918,
title = {Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation},
author = {Zhuo-Xu Cui and Congcong Liu and Xiaohong Fan and Chentao Cao and Jing Cheng and Qingyong Zhu and Yuanyuan Liu and Sen Jia and Yihang Zhou and Haifeng Wang and Yanjie Zhu and Jianping Zhang and Qiegen Liu and Dong Liang},
journal= {arXiv preprint arXiv:2308.15918},
year = {2023}
}