  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 were evaluated. Selected promising four element networks (WW-nets)
were also examined. Two configurations of each network were compared: 1) Each
coil channel processed independently, and 2) all channels 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, visual information fidelity and visual
inspection 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 are better suited when processing individual
channels of multi-channel data independently. Dual domain methods are more
advantageous when simultaneously reconstructing all channels of multi-channel
data. Also, the appropriate cascade of U-nets compared favorably (p < 0.01) to
the previously published, state-of-the-art Deep Cascade model in in three out
of four experiments.
