Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation

• URL: http://arxiv.org/abs/2308.15918v1
• Date: Wed, 30 Aug 2023 09:45:14 GMT
• Title: Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation
• Authors: Zhuo-Xu Cui, Congcong Liu, Xiaohong Fan, Chentao Cao, Jing Cheng, Qingyong Zhu, Yuanyuan Liu, Sen Jia, Yihang Zhou, Haifeng Wang, Yanjie Zhu, Jianping Zhang, Qiegen Liu, Dong Liang
• Abstract summary: This paper introduces an interpretable framework that unifies both $k$-space techniques and image-domain methods. 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. 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.
• Score: 27.081130793389285
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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