Hussain Uzair, Khan Ali R
Centre for Functional and Metabolic Mapping, Robarts Research Institute, Western University, 100 Perth Dr, London, ON N6A 5K8, Canada.
Department of Medical Biophysics, Schulich School of Medicine and Dentistry, Western University, London, Canada.
Sci Rep. 2025 Mar 20;15(1):9631. doi: 10.1038/s41598-025-93033-1.
Diffusion MRI (dMRI) is an imaging technique widely used in neuroimaging research, where the signal carries directional information of underlying neuronal fibres based on the diffusivity of water molecules. One of the shortcomings of dMRI is that numerous images, sampled at gradient directions on a sphere, must be acquired to achieve a reliable angular resolution for model-fitting, which translates to longer scan times, higher costs, and barriers to clinical adoption. In this work we introduce gauge equivariant convolutional neural network (gCNN) layers for dMRI that overcome the challenges associated with the signal being acquired on a sphere with antipodal points identified. This is done by noting that the domain is equivalent to the real projective plane, [Formula: see text], which is a non-euclidean and a non-orientable manifold. This is in stark contrast to a rectangular grid which typical convolutional neural networks (CNNs) are designed for. We apply our method to upsample angular resolution for predicting diffusion tensor imaging (DTI) parameters from just six diffusion gradient directions. The symmetries introduced allow gCNNs the ability to train with fewer subjects as compared to a baseline model that involves only 3D convolutions.
扩散磁共振成像（dMRI）是一种在神经成像研究中广泛应用的成像技术，其中信号基于水分子的扩散率携带潜在神经纤维的方向信息。dMRI的缺点之一是，必须获取在球体上的梯度方向采样的大量图像，以实现用于模型拟合的可靠角分辨率，这意味着扫描时间更长、成本更高，并且阻碍了其在临床上的应用。在这项工作中，我们为dMRI引入了规范等变卷积神经网络（gCNN）层，克服了与在具有对映点识别的球体上采集信号相关的挑战。这是通过注意到该域等同于实射影平面[公式：见正文]来实现的，实射影平面是一个非欧几里得且不可定向的流形。这与典型卷积神经网络（CNN）所设计的矩形网格形成鲜明对比。我们应用我们的方法来提高角分辨率，以便仅从六个扩散梯度方向预测扩散张量成像（DTI）参数。所引入的对称性使gCNN能够与仅涉及3D卷积的基线模型相比，用更少的受试者进行训练。
