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In the field of parallel imaging (PI), alongside image-domain regularizationmethods, substantial research has been dedicated to exploring $k$-spaceinterpolation. However, the interpretability of these methods remains anunresolved issue. Furthermore, these approaches currently face accelerationlimitations 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 $k$-spaceinterpolation techniques and image-domain methods, grounded in the physicalprinciples of heat diffusion equations. Building upon this foundationalframework, a novel $k$-space interpolation method is proposed. Specifically, wemodel the process of high-frequency information attenuation in $k$-space as aheat diffusion equation, while the effort to reconstruct high-frequencyinformation from low-frequency regions can be conceptualized as a reverse heatequation. However, solving the reverse heat equation poses a challenginginverse problem. To tackle this challenge, we modify the heat equation to alignwith the principles of magnetic resonance PI physics and employ the score-basedgenerative method to precisely execute the modified reverse heat diffusion.Finally, experimental validation conducted on publicly available datasetsdemonstrates the superiority of the proposed approach over traditional$k$-space interpolation methods, deep learning-based $k$-space interpolationmethods, and conventional diffusion models in terms of reconstruction accuracy,particularly in high-frequency regions.

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