  Diffusion MRI is a modern neuroimaging modality with a unique ability to
acquire microstructural information by measuring water self-diffusion at the
voxel level. However, it generates huge amounts of data, resulting from a large
number of repeated 3D scans. Each volume samples a location in q-space,
indicating the direction and strength of a diffusion sensitizing gradient
during the measurement. This captures detailed information about the
self-diffusion, and the tissue microstructure that restricts it. Lossless
compression with GZIP is widely used to reduce the memory requirements. We
introduce a novel lossless codec for diffusion MRI data. It reduces file sizes
by more than 30% compared to GZIP, and also beats lossless codecs from the JPEG
family. Our codec builds on recent work on lossless PDE-based compression of 3D
medical images, but additionally exploits smoothness in q-space. We demonstrate
that, compared to using only image space PDEs, q-space PDEs further improve
compression rates. Moreover, implementing them with Finite Element Methods and
a custom acceleration significantly reduces computational expense. Finally, we
show that our codec clearly benefits from integrating subject motion
correction, and slightly from optimizing the order in which the 3D volumes are
coded.
