  Image reconstruction from undersampled k-space data plays an important role
in accelerating the acquisition of MR data, and a lot of deep learning-based
methods have been exploited recently. Despite the achieved inspiring results,
the optimization of these methods commonly relies on the fully-sampled
reference data, which are time-consuming and difficult to collect. To address
this issue, we propose a novel self-supervised learning method. Specifically,
during model optimization, two subsets are constructed by randomly selecting
part of k-space data from the undersampled data and then fed into two parallel
reconstruction networks to perform information recovery. Two reconstruction
losses are defined on all the scanned data points to enhance the network's
capability of recovering the frequency information. Meanwhile, to constrain the
learned unscanned data points of the network, a difference loss is designed to
enforce consistency between the two parallel networks. In this way, the
reconstruction model can be properly trained with only the undersampled data.
During the model evaluation, the undersampled data are treated as the inputs
and either of the two trained networks is expected to reconstruct the
high-quality results. The proposed method is flexible and can be employed in
any existing deep learning-based method. The effectiveness of the method is
evaluated on an open brain MRI dataset. Experimental results demonstrate that
the proposed self-supervised method can achieve competitive reconstruction
performance compared to the corresponding supervised learning method at high
acceleration rates (4 and 8). The code is publicly available at
\url{https://github.com/chenhu96/Self-Supervised-MRI-Reconstruction}.
