The U-net is a deep-learning network model that has been used to solve a number of inverse problems. In this work, the concatenation of two-element U-nets, termed the W-net, operating in k-space (K) and image (I) domains, were evaluated for multi-channel magnetic resonance (MR) image reconstruction. The two-element network combinations were evaluated for the four possible image-k-space domain configurations: a) W-net II, b) W-net KK, c) W-net IK, and d) W-net KI. Selected four element (WW-nets) and six element (WWW-nets) networks were also examined. Two configurations of each network were compared: 1) each coil channel was processed independently, and 2) all channels were processed simultaneously. One hundred and eleven volumetric, T1-weighted, 12-channel coil k-space datasets were used in the experiments. Normalized root mean squared error, peak signal-to-noise ratio and visual information fidelity were used to assess the reconstructed images against the fully sampled reference images. Our results indicated that networks that operate solely in the image domain were better when independently processing individual channels of multi-channel data. Dual-domain methods were better when simultaneously reconstructing all channels of multi-channel data. In addition, the best cascade of U-nets performed better (p < 0.01) than the previously published, state-of-the-art Deep Cascade and Hybrid Cascade models in three out of four experiments.

Keywords: Brain imaging; Compressed sensing (CS); Image reconstruction; Inverse problems; Machine learning; Magnetic resonance imaging; Multi-channel (coil); Parallel imaging (PI).

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