Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem

Abstract

Three-Dimensional Gaussian Splatting (3DGS) has shown substantial promise in the field of computer vision, but remains unexplored in the field of magnetic resonance imaging (MRI). This study explores its potential for the reconstruction of isotropic resolution 3D MRI from undersampled k-space data. We introduce a novel framework termed 3D Gaussian MRI (3DGSMR), which employs 3D Gaussian distributions as an explicit representation for MR volumes. Experimental evaluations indicate that this method can effectively reconstruct voxelized MR images, achieving a quality on par with that of well-established 3D MRI reconstruction techniques found in the literature. Notably, the 3DGSMR scheme operates under a self-supervised framework, obviating the need for extensive training datasets or prior model training. This approach introduces significant innovations to the domain, notably the adaptation of 3DGS to MRI reconstruction and the novel application of the existing 3DGS methodology to decompose MR signals, which are presented in a complex-valued format.

Figures (13)

• Figure 1: Cloning method in adaptive control. The cloned Gaussian point will be further optimized to fit into unreconstructed region.
• Figure 2: (a) Original splitting method in adaptive control. (b) The long-axis splitting approach. A large Gaussian point splits into two small identical Gaussian points along the longest axis which are then further optimized to fit into unreconstructed region.
• Figure 3: Training pipeline and components of 3DGSMR. (a) End-to-end pipeline showing data and gradient flow from initialization to output, comprising initialization, voxelization, TV regularization, Fourier transform, and adaptive control. (b) Voxelizer schematic: sparse 3DGS points are aggregated onto grid locations via weighted summation to form a voxelized volume. (c) Original 3DGS adaptive control: cloning (duplicate at the same location), splitting (one Gaussian into two with positions drawn from normal distributions), and pruning (removing low-amplitude Gaussians). (d) Our modified adaptive control for high acceleration factors: cloning is removed; splitting proceeds along the longest axis without overlap, preserving the original shape.
• Figure 4: Visual comparison with SSIM, PSNR, and LPIPS of the reconstructed results from the original optimization method versus the new optimization method that introduces long-axis splitting and abandoning cloning along with initializing using only 500 Gaussian points.
• Figure 5: The progression of reconstruction loss and evaluation metrics (SSIM, PSNR, and LPIPS) is shown for one subject, with an acceleration factor of 8 for the original optimization method and 10 for the long-axis splitting strategy under high acceleration. (a) Curves corresponding to an acceleration factor of 8. (b) Curves corresponding to an acceleration factor of 10.