Enhancing the spatial resolution requires sampling of higher frequencies in k-space which is very challenging to accomplish with high SNR and short acquisition duration time. Instead of acquiring high frequencies along all the axes simultaneously, [8] demonstrated that high-resolution (HR) k-space sampling for a diffusion gradient can be achieved by imaging this diffusion gradient with a series of anisotropically oversampled acquisitions (so-called “snapshots”) that each densely samples more frequencies along a limited number of axes (one or two). Compared to full, dense HR sampling, this multi-snapshot non-Cartesian sampling reduces the spatial encoding burden and provides substantially increased SNR for each snapshot due to the larger voxel size. In [8], an image generation model was then employed to describe how the anisotropic low resolution (LR) snapshots are observations of the unknown, underlying HR isotropic DW images we aim to recover (forward model), and the corresponding HR DW images recovered by inversing this forward model. A similar technique was later employed in [6]. A particular strength of this approach is that it only requires a conventional DW-MRI sequence and is therefore straightforward to implement. When using three orthogonal snapshots for each diffusion gradient, this effectively enhances spatial resolution along all the axes (x,y,z) while providing an 8x theoretical reduction in imaging time compared to conventional sampling at equal SNR [8].

A major limitation in [6, 8] is that each DW image was reconstructed separately. First, the fact that the DWIs constitute different views of the same anatomy was ignored. DW images are coupled and this correlation of information can be leveraged by introducing in the reconstruction the knowledge of the local tissue microstructure. Second, an isotropic HR gradient image could not be recovered if one of its snapshots was missing, for example because of intra-scan motion, even if other snapshots for this gradient were successfully acquired.

Tobisch et al. [12] built upon the work in [6, 8] and proposed to introduce an ad-hoc coupling between HR reconstruction and tissue model estimation to capture the coupling between DW images. They considered the ball-and-stick tissue model at each voxel, thereby assuming (1) the presence of a single fascicle in each voxel; (2) the absence of radial diffusivity; and (3) a prefixed axial diffusivity value constant for the entire brain. This model, however, poorly represents in vivo brain tissues. This is critical because, when HR reconstruction and tissue model estimation are coupled, the ability of the tissue model to accurately predict the DW signal for a diffusion gradient conditions the ultimate HR reconstruction accuracy. In [12], only results with synthetic simulations were reported, but no evidence of the technical efficacy of the technique was reported with in vivo data. More importantly, and similarly to [6, 8], this technique required the successful acquisition of all the snapshots for a diffusion gradient to reconstruct the corresponding HR gradient image.

In this work, we propose a novel multi-snapshot DWI reconstruction technique that simultaneously achieves HR reconstruction and tissue model estimation while enabling reconstruction with missing snapshots. Instead of an ad-hoc coupling [12], our approach is formalized as a joint probabilistic model with missing observations, from which interactions between missing snapshots, HR reconstruction and a generic tissue model naturally emerge. We describe the tissue microstructure at a voxel with a diffusion compartment imaging (DCI) tissue model that reflects the presence of tissue compartments in each voxel, providing a model-based description of the signal attenuation for any diffusion gradient orientation and strength. Our novel Simultaneous multi-snapsHot highresOlution ReconsTruCtion and diffUsion comparTment imaging (SHORTCUT) approach enables reconstruction from snapshots with different subsets of gradients, providing increased robustness to patient motion and potential for acceleration. We evaluate SHORTCUT with synthetic simulations, simulated multi-snapshot scenario and in vivo multi-snapshot imaging. We investigate the robustness to missing snapshots. We show that SHORTCUT enables both better reconstruction of each DW image and better estimation of the tissue parameters.