  Purpose: The expanded encoding model incorporates spatially- and time-varying
field perturbations for correction during reconstruction. So far, these
reconstructions have used the conjugate gradient method with early stopping
used as implicit regularization. However, this approach is likely suboptimal
for low-SNR cases like diffusion or high-resolution MRI. Here, we investigate
the extent that l1-wavelet regularization, or equivalently compressed sensing
(CS), combined with expanded encoding improves trade-offs between spatial
resolution, readout time and SNR for single-shot spiral diffusion-weighted
imaging at 7T. The reconstructions were performed using our open-source
GPU-enabled reconstruction toolbox, MatMRI, that allows inclusion of the
different components of the expanded encoding model, with or without CS.
Methods: In vivo accelerated single-shot spirals were acquired with five
acceleration factors (2-6) and three in-plane spatial resolutions (1.5, 1.3,
and 1.1 mm). From the in vivo reconstructions, we estimated diffusion tensors
and computed fractional anisotropy maps. Then, simulations were used to
quantitatively investigate and validate the impact of CS-based regularization
on image quality when compared to a known ground truth. Results: In vivo
reconstructions revealed improved image quality with retainment of small
features when CS was used. Simulations showed that the joint use of the
expanded encoding model and CS improves accuracy of image reconstructions
(reduced mean-squared error) over the range of acceleration factors
investigated. Conclusion: The expanded encoding model and CS regularization are
complementary tools for single-shot spiral diffusion MRI, which enables both
higher spatial resolutions and higher acceleration factors.
