Diffusion model based on generalized map for accelerated MRI

In recent years, diffusion models have made significant progress in accelerating magnetic resonance imaging. Nevertheless, it still has inherent limitations, such as prolonged iteration times and sluggish convergence rates. In this work, we present a novel generalized map generation model based on mean-reverting SDE, called GM-SDE, to alleviate these shortcomings. Notably, the core idea of GM-SDE is optimizing the initial values of the iterative algorithm. Specifically, the training process of GM-SDE diffuses the original k-space data to an intermediary degraded state with fixed Gaussian noise, while the reconstruction process generates the data by reversing this process. Based on the generalized map, three variants of GM-SDE are proposed to learn k-space data with different structural characteristics to improve the effectiveness of model training. GM-SDE also exhibits flexibility, as it can be integrated with traditional constraints, thereby further enhancing its overall performance. Experimental results showed that the proposed method can reduce reconstruction time and deliver excellent image reconstruction capabilities compared to the complete diffusion-based method.