  The task of MRI fingerprinting is to identify tissue parameters from
complex-valued MRI signals. The prevalent approach is dictionary based, where a
test MRI signal is compared to stored MRI signals with known tissue parameters
and the most similar signals and tissue parameters retrieved. Such an approach
does not scale with the number of parameters and is rather slow when the tissue
parameter space is large.
  Our first novel contribution is to use deep learning as an efficient
nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data
from an MRI simulator, and use them to train a deep net to map the MRI signal
to the tissue parameters directly.
  Our second novel contribution is to develop a complex-valued neural network
with new cardioid activation functions. Our results demonstrate that
complex-valued neural nets could be much more accurate than real-valued neural
nets at complex-valued MRI fingerprinting.
