Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem
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.
三维高斯溅射（3DGS）在计算机视觉领域展示了巨大的潜力，但在磁共振成像（MRI）领域仍未得到探索。本研究探讨了其在从欠采样的k空间数据重建各向同性分辨率3D MRI中的潜力。我们提出了一种新颖的框架，称为3D高斯MRI（3DGSMR），该框架使用3D高斯分布作为MRI体积的显式表示。实验评估表明，该方法能够有效重建体素化的MRI图像，质量与文献中已建立的3D MRI重建技术相当。值得注意的是，3DGSMR方案在自监督框架下运行，无需大量训练数据集或先验模型训练。这一方法为该领域带来了重要创新，特别是将3DGS适应于MRI重建，并创新性地应用现有的3DGS方法来分解以复数格式呈现的MRI信号。