  Purpose: To introduce a novel deep learning based approach for fast and
high-quality dynamic multi-coil MR reconstruction by learning a complementary
time-frequency domain network that exploits spatio-temporal correlations
simultaneously from complementary domains.
  Theory and Methods: Dynamic parallel MR image reconstruction is formulated as
a multi-variable minimisation problem, where the data is regularised in
combined temporal Fourier and spatial (x-f) domain as well as in
spatio-temporal image (x-t) domain. An iterative algorithm based on variable
splitting technique is derived, which alternates among signal de-aliasing steps
in x-f and x-t spaces, a closed-form point-wise data consistency step and a
weighted coupling step. The iterative model is embedded into a deep recurrent
neural network which learns to recover the image via exploiting spatio-temporal
redundancies in complementary domains.
  Results: Experiments were performed on two datasets of highly undersampled
multi-coil short-axis cardiac cine MRI scans. Results demonstrate that our
proposed method outperforms the current state-of-the-art approaches both
quantitatively and qualitatively. The proposed model can also generalise well
to data acquired from a different scanner and data with pathologies that were
not seen in the training set.
  Conclusion: The work shows the benefit of reconstructing dynamic parallel MRI
in complementary time-frequency domains with deep neural networks. The method
can effectively and robustly reconstruct high-quality images from highly
undersampled dynamic multi-coil data ($16 \times$ and $24 \times$ yielding 15s
and 10s scan times respectively) with fast reconstruction speed (2.8s). This
could potentially facilitate achieving fast single-breath-hold clinical 2D
cardiac cine imaging.
