Accelerating multi-echo MRI in k-space with complex-valued diffusion probabilistic model

Compressed sensing (CS) is an interesting technique for effectively accelerating multi-echo gradient-recalled-echo (ME-GRE) magnetic resonance imaging (MRI). However, how to reconstruct high-quality MRI from undersampled k-space data is still a challenge issue. Considering the superiority of complex-valued convolutional neural network and the image generation ability of denoising diffusion probabilistic model (DDPM), in this work, we proposed a complex diffusion probabilistic model (CDPM) to realize the CS-MRI reconstruction in k-space. Specifically, we randomly generated a mask to under-sample the k-space data; those k-space data not acquired were taken as the input of forward diffusion model. We recover these unobserved k-space data through an inverse diffusion process, which was realized by a complex-valued UNet-like network. By comparing the complexvalued CDPM and real-valued DDPM models on the reconstruction of ME-GRE MRI, we validated that our proposed CDPM model outperforms the real-valued DDPM methods. It can effectively restore the image details with a sampling ratio of 25%.