Denoising Diffusion Probabilistic Model with Dual-domain Entropy and Stochastic Differential Equations on High Undersampling Reconstruction

Motivation: Using denoising diffusion probabilistic models (DDPM) for MRI reconstruction remains challenging on high-fold under-sampling. Goal(s): To improve the reconstruction performance of 8-fold under-sampled data by a modified DDPM. Approach: A composite loss function based on information entropy, dual-domain difference, and uniform-static-SDE (stochastic differential equations) is proposed, called EDU-DDPM. Our algorithm has been tested on fastMRI and compared to compressed sensing (CS) TOF-MRA data acquired at 7T. Results: Compared to previous DDPM, our method performs better in single-channel knee and multi-channel brain datasets on fastMRI with 8-fold under-sampling. Additionally, it outperforms CS reconstruction in Time-of-flight (TOF-MRA) acquired in variable density Poisson sampling pattern. Impact: The proposed EDU-DDPM significantly improves MRI reconstruction at high subsampling factors, outperforming DDPM on fastMRI and compressive sensing on 7T TOF-MRA data. This advancement enhances fidelity of reconstruction.