MRI Reconstruction with Regularized 3D Diffusion Model (R3DM)

TL;DR

R3DM tackles fast 3D MRI reconstruction from undersampled k-space data by integrating a pre-trained 3D diffusion prior with an optimization framework that enforces k-space fidelity and 3D consistency through Fourier-slice relations. The approach uses a 2D+A diffusion model to form a volumetric prior and couples it with proximal-regularized optimization to promote sparsity and smoothness during diffusion sampling. Experiments across knee, BRATS brain, and plant-root datasets show superior performance to established baselines under in-distribution and out-of-distribution conditions, highlighting the importance of true 3D representation and diffusion priors for high-fidelity reconstructions. The work suggests promising directions for scalable, robust 3D MRI reconstruction and motivates further exploration of diffusion-based priors and real-time inference.

Abstract

Magnetic Resonance Imaging (MRI) is a powerful imaging technique widely used for visualizing structures within the human body and in other fields such as plant sciences. However, there is a demand to develop fast 3D-MRI reconstruction algorithms to show the fine structure of objects from under-sampled acquisition data, i.e., k-space data. This emphasizes the need for efficient solutions that can handle limited input while maintaining high-quality imaging. In contrast to previous methods only using 2D, we propose a 3D MRI reconstruction method that leverages a regularized 3D diffusion model combined with optimization method. By incorporating diffusion based priors, our method improves image quality, reduces noise, and enhances the overall fidelity of 3D MRI reconstructions. We conduct comprehensive experiments analysis on clinical and plant science MRI datasets. To evaluate the algorithm effectiveness for under-sampled k-space data, we also demonstrate its reconstruction performance with several undersampling patterns, as well as with in- and out-of-distribution pre-trained data. In experiments, we show that our method improves upon tested competitors.

Figures (8)

• Figure 1: Workflow of the proposed algorithm generating volumetric data from a random distribution and guiding the reconstruction for specific k-space data to have a unique reconstruction. The reverse diffusion process is performed using a pre-trained diffusion model.
• Figure 2: Relation between the projected image and a slice of k-space from plant roots data
• Figure 3: Single slice from the volume reconstruction of file1000758 (top) and file1001862 (bottom) from fastMRI knee data. The numbers on the top right corner represent the PSNR/SSIM of the slice. The subplots on the lower left corner represent the difference map between the reconstruction and ground truth. The color range is between $-0.02$ (bluish) and $0.02$ (reddish). Note that the volumetric ground truth data has been normalized. The subplots on the lower right are a zoomed-in view.
• Figure 4: Ablation study to investigate the effect of regularization for reconstruction in terms of SSIM $(\uparrow)$ metric for uniform mask. The optimization iteration $m=10$ and the learning rate $0.01$.
• Figure 5: Hyperparameters search for uniform mask (left) and Gaussian mask (right), where the maximum is given in the configuration at index = $23$ with combination parameters: $(m=10, \alpha = 0.02, \eta = 0.01,$tv=1$)$