  High resolution magnetic resonance (MR) images are desired for accurate
diagnostics. In practice, image resolution is restricted by factors like
hardware, cost and processing constraints. Recently, deep learning methods have
been shown to produce compelling state of the art results for image
super-resolution. Paying particular attention to desired hi-resolution MR image
structure, we propose a new regularized network that exploits image priors,
namely a low-rank structure and a sharpness prior to enhance deep MR image
superresolution. Our contributions are then incorporating these priors in an
analytically tractable fashion in the learning of a convolutional neural
network (CNN) that accomplishes the super-resolution task. This is particularly
challenging for the low rank prior, since the rank is not a differentiable
function of the image matrix (and hence the network parameters), an issue we
address by pursuing differentiable approximations of the rank. Sharpness is
emphasized by the variance of the Laplacian which we show can be implemented by
a fixed {\em feedback} layer at the output of the network. Experiments
performed on two publicly available MR brain image databases exhibit promising
results particularly when training imagery is limited.
