Geometric deep learning for diffusion MRI signal reconstruction with continuous samplings (DISCUS)

Diffusion-weighted magnetic resonance imaging (dMRI) permits a detailed in-vivo analysis of neuroanatomical microstructure, invaluable for clinical and population studies. However, many measurements with different diffusion-encoding directions and possibly b-values are necessary to infer the underlying tissue microstructure within different imaging voxels accurately. Two challenges particularly limit the utility of dMRI: long acquisition times limit feasible scans to only a few directional measurements, and the heterogeneity of acquisition schemes across studies makes it difficult to combine datasets. Left unaddressed by previous learning-based methods that only accept dMRI data adhering to the specific acquisition scheme used for training, there is a need for methods that accept and predict signals for arbitrary diffusion encodings. Addressing these challenges, we describe the first geometric deep learning method for continuous dMRI signal reconstruction for arbitrary diffusion sampling schemes for both the input and output. Our method combines the reconstruction accuracy and robustness of previous learning-based methods with the flexibility of model-based methods, for example, spherical harmonics or SHORE. We demonstrate that our method outperforms model-based methods and performs on par with discrete learning-based methods on single-, multi-shell, and grid-based diffusion MRI datasets. Relevant for dMRI-derived analyses, we show that our reconstruction translates to higher-quality estimates of frequently used microstructure models compared to other reconstruction methods, enabling high-quality analyses even from very short dMRI acquisitions.