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

TL;DR

This paper introduces 3D Gaussian MRI (3DGSMR), a self-supervised framework using 3D Gaussian representations for reconstructing high-quality 3D MRI images from undersampled data, without extensive training datasets.

Contribution

It adapts 3D Gaussian Splatting to MRI reconstruction and applies it in a novel, self-supervised manner for the first time.

Findings

Achieves MRI reconstruction quality comparable to existing methods.

Operates effectively without large training datasets.

Successfully reconstructs complex-valued MR signals.

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.