The physical and clinical constraints surrounding diffusion-weighted imaging (DWI) often limit the spatial resolution of the produced images to voxels up to 8 times larger than those of T1w images. Thus, the detailed information contained in T1w imagescould help in the synthesis of diffusion images in higher resolution. However, the non-Euclidean nature of diffusion imaging hinders current deep generative models from synthesizing physically plausible images. In this work, we propose the first Riemannian network architecture for the direct generation of diffusion tensors (DT) and diffusion orientation distribution functions (dODFs) from high-resolution T1w images. Our integration of the Log-Euclidean Metric into a learning objective guarantees, unlike standard Euclidean networks, the mathematically-valid synthesis of diffusion. Furthermore, our approach improves the fractional anisotropy mean squared error (FA MSE) between the synthesized diffusion and the ground-truth by more than 23% and the cosine similarity between principal directions by almost 5% when compared to our baselines. We validate our generated diffusion by comparing the resulting tractograms to our expected real data. We observe similar fiber bundles with streamlines having less than 3% difference in length, less than 1% difference in volume, and a visually close shape. While our method is able to generate high-resolution diffusion images from structural inputs in less than 15 seconds, we acknowledge and discuss the limits of diffusion inference solely relying on T1w images. Our results nonetheless suggest a relationship between the high-level geometry of the brain and the overall white matter architecture.

翻译：围绕扩散加权成像(DWI)的物理和临床限制往往将生成的图像的空间分辨率限制在高分辨率 T1w 图像的8倍以上。 因此, T1w 图像中包含的详细信息有助于合成高分辨率的传播图像。 然而, 扩散成像的非欧洲语言性质阻碍了当前从物理上看可信的图像合成的深度变异模型。 在这项工作中, 我们提议了第一个里曼尼网络架构, 用于直接生成高分辨率 T1w 图像的散变声器和扩散方向分布函数(dODFs ) 的空间分辨率。 我们将日志- 欧克利德 元 Metic 整合到学习目标保障中, 不同于标准的 Euclidean 网络, 以数学价值合成合成的合成。 此外, 我们的方法改进了合成散变异图和地面图的偏差(FA MESE) 之间的分数, 超过 23 %, 表明与我们基线相比主要方向的近5 % 。 我们用直径图像的分解比, 我们用直径比直径的平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方。