High-Frequency Space Diffusion Models for Accelerated MRI

Denoising diffusion probabilistic models (DDPMs) have been shown to have superior performances in MRI reconstruction. From the perspective of continuous stochastic differential equations (SDEs), the reverse process of DDPM can be seen as maximizing the energy of the reconstructed MR image, leading to SDE sequence divergence. For this reason, a modified high-frequency DDPM model is proposed for MRI reconstruction. From its continuous SDE viewpoint, termed high-frequency space SDE (HFS-SDE), the energy concentrated low-frequency part of the MR image is no longer amplified, and the diffusion process focuses more on acquiring high-frequency prior information. It not only improves the stability of the diffusion model but also provides the possibility of better recovery of high-frequency details. Experiments on the publicly fastMRI dataset show that our proposed HFS-SDE outperforms the DDPM-driven VP-SDE, supervised deep learning methods and traditional parallel imaging methods in terms of stability and reconstruction accuracy.