  Purpose: To use a deep neural network (DNN) for solving the optimization
problem of water/fat separation and to compare supervised and unsupervised
training.
  Methods: The current T2*-IDEAL algorithm for solving fat/water separation is
dependent on initialization. Recently, deep neural networks (DNN) have been
proposed to solve fat/water separation without the need for suitable
initialization. However, this approach requires supervised training of DNN
(STD) using the reference fat/water separation images. Here we propose two
novel DNN water/fat separation methods 1) unsupervised training of DNN (UTD)
using the physical forward problem as the cost function during training, and 2)
no-training of DNN (NTD) using physical cost and backpropagation to directly
reconstruct a single dataset. The STD, UTD and NTD methods were compared with
the reference T2*-IDEAL.
  Results: All DNN methods generated consistent water/fat separation results
that agreed well with T2*-IDEAL under proper initialization.
  Conclusion: The water/fat separation problem can be solved using unsupervised
deep neural networks.
