  MR images scanned at low magnetic field ($<1$T) have lower resolution in the
slice direction and lower contrast, due to a relatively small signal-to-noise
ratio (SNR) than those from high field (typically 1.5T and 3T). We adapt the
recent idea of Image Quality Transfer (IQT) to enhance very low-field
structural images aiming to estimate the resolution, spatial coverage, and
contrast of high-field images. Analogous to many learning-based image
enhancement techniques, IQT generates training data from high-field scans alone
by simulating low-field images through a pre-defined decimation model. However,
the ground truth decimation model is not well-known in practice, and lack of
its specification can bias the trained model, aggravating performance on the
real low-field scans. In this paper we propose a probabilistic decimation
simulator to improve robustness of model training. It is used to generate and
augment various low-field images whose parameters are random variables and
sampled from an empirical distribution related to tissue-specific SNR on a
0.36T scanner. The probabilistic decimation simulator is model-agnostic, that
is, it can be used with any super-resolution networks. Furthermore we propose a
variant of U-Net architecture to improve its learning performance. We show
promising qualitative results from clinical low-field images confirming the
strong efficacy of IQT in an important new application area: epilepsy diagnosis
in sub-Saharan Africa where only low-field scanners are normally available.
