  Time-of-flight magnetic resonance angiography (TOF-MRA) is one of the most
widely used non-contrast MR imaging methods to visualize blood vessels, but due
to the 3-D volume acquisition highly accelerated acquisition is necessary.
Accordingly, high quality reconstruction from undersampled TOF-MRA is an
important research topic for deep learning. However, most existing deep
learning works require matched reference data for supervised training, which
are often difficult to obtain. By extending the recent theoretical
understanding of cycleGAN from the optimal transport theory, here we propose a
novel two-stage unsupervised deep learning approach, which is composed of the
multi-coil reconstruction network along the coronal plane followed by a
multi-planar refinement network along the axial plane. Specifically, the first
network is trained in the square-root of sum of squares (SSoS) domain to
achieve high quality parallel image reconstruction, whereas the second
refinement network is designed to efficiently learn the characteristics of
highly-activated blood flow using double-headed max-pool discriminator.
Extensive experiments demonstrate that the proposed learning process without
matched reference exceeds performance of state-of-the-art compressed sensing
(CS)-based method and provides comparable or even better results than
supervised learning approaches.
