  Improving the image resolution and acquisition speed of magnetic resonance
imaging (MRI) is a challenging problem. There are mainly two strategies dealing
with the speed-resolution trade-off: (1) $k$-space undersampling with
high-resolution acquisition, and (2) a pipeline of lower resolution image
reconstruction and image super-resolution. However, these approaches either
have limited performance at certain high acceleration factor or suffer from the
error accumulation of two-step structure. In this paper, we combine the idea of
MR reconstruction and image super-resolution, and work on recovering HR images
from low-resolution under-sampled $k$-space data directly. Particularly, the
SR-involved reconstruction can be formulated as a variational problem, and a
learnable network unrolled from its solution algorithm is proposed. A
discriminator was introduced to enhance the detail refining performance.
Experiment results using in-vivo HR multi-coil brain data indicate that the
proposed SRR-Net is capable of recovering high-resolution brain images with
both good visual quality and perceptual quality.
