k-t Self-consistency Diffusion: A Physics-Informed Model for Dynamic MR Imaging

Diffusion models exhibit promising prospects in magnetic resonance (MR) image reconstruction due to their robust image generation and generalization capabilities. However, current diffusion models are predominantly customized for 2D image reconstruction tasks. When addressing dynamic MR imaging (dMRI), the challenge lies in accurately generating 2D images while simultaneously adhering to the temporal direction and matching the motion patterns of the scanned regions. In dynamic parallel imaging, motion patterns can be characterized through the self-consistency of k-t data. Motivated by this observation, we propose to design a diffusion model that aligns with k-t self-consistency. Specifically, following a discrete iterative algorithm to optimize k-t self-consistency, we extend it to a continuous formulation, thereby designing a stochastic diffusion equation in line with k-t self-consistency. Finally, by incorporating the score-matching method to estimate prior terms, we construct a diffusion model for dMRI. Experimental results on a cardiac dMRI dataset showcase the superiority of our method over current state-of-the-art techniques. Our approach exhibits remarkable reconstruction potential even at extremely high acceleration factors, reaching up to 24X, and demonstrates robust generalization for dynamic data with temporally shuffled frames.