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Time-of-flight magnetic resonance angiography (TOF-MRA) is one of the mostwidely used non-contrast MR imaging methods to visualize blood vessels, but dueto the 3-D volume acquisition highly accelerated acquisition is necessary.Accordingly, high quality reconstruction from undersampled TOF-MRA is animportant research topic for deep learning. However, most existing deeplearning works require matched reference data for supervised training, whichare often difficult to obtain. By extending the recent theoreticalunderstanding of cycleGAN from the optimal transport theory, here we propose anovel two-stage unsupervised deep learning approach, which is composed of themulti-coil reconstruction network along the coronal plane followed by amulti-planar refinement network along the axial plane. Specifically, the firstnetwork is trained in the square-root of sum of squares (SSoS) domain toachieve high quality parallel image reconstruction, whereas the secondrefinement network is designed to efficiently learn the characteristics ofhighly-activated blood flow using double-headed max-pool discriminator.Extensive experiments demonstrate that the proposed learning process withoutmatched reference exceeds performance of state-of-the-art compressed sensing(CS)-based method and provides comparable or even better results thansupervised learning approaches.

Two-Stage Deep Learning for Accelerated 3D Time-of-Flight MRA without Matched Training Data