  Consistency of the predictions with respect to the physical forward model is
pivotal for reliably solving inverse problems. This consistency is mostly
un-controlled in the current end-to-end deep learning methodologies proposed
for the Magnetic Resonance Fingerprinting (MRF) problem. To address this, we
propose ProxNet, a learned proximal gradient descent framework that directly
incorporates the forward acquisition and Bloch dynamic models within a
recurrent learning mechanism. The ProxNet adopts a compact neural proximal
model for de-aliasing and quantitative inference, that can be flexibly trained
on scarce MRF training datasets. Our numerical experiments show that the
ProxNet can achieve a superior quantitative inference accuracy, much smaller
storage requirement, and a comparable runtime to the recent deep learning MRF
baselines, while being much faster than the dictionary matching schemes. Code
has been released at https://github.com/edongdongchen/PGD-Net.
