SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI

Diffusion models are a leading method for image generation and have been successfully applied in magnetic resonance imaging (MRI) reconstruction. Current diffusion-based reconstruction methods rely on coil sensitivity maps (CSM) to reconstruct multi-coil data. However, it is difficult to accurately estimate CSMs in practice use, resulting in degradation of the reconstruction quality. To address this issue, we propose a self-consistency-driven diffusion model inspired by the iterative self-consistent parallel imaging (SPIRiT), namely SPIRiT-Diffusion. Specifically, the iterative solver of the self-consistent term in SPIRiT is utilized to design a novel stochastic differential equation (SDE) for diffusion process. Then $\textit{k}$-space data can be interpolated directly during the reverse diffusion process, instead of using CSM to separate and combine individual coil images. This method indicates that the optimization model can be used to design SDE in diffusion models, driving the diffusion process strongly conforming with the physics involved in the optimization model, dubbed model-driven diffusion. The proposed SPIRiT-Diffusion method was evaluated on a 3D joint Intracranial and Carotid Vessel Wall imaging dataset. The results demonstrate that it outperforms the CSM-based reconstruction methods, and achieves high reconstruction quality at a high acceleration rate of 10.