  Deep neural networks (DNN) have an impressive ability to invert very complex
models, i.e. to learn the generative parameters from a model's output. Once
trained, the forward pass of a DNN is often much faster than traditional,
optimization-based methods used to solve inverse problems. This is however done
at the cost of lower interpretability, a fundamental limitation in most medical
applications. We propose an approach for solving general inverse problems which
combines the efficiency of DNN and the interpretability of traditional
analytical methods. The measurements are first projected onto a dense
dictionary of model-based responses. The resulting sparse representation is
then fed to a DNN with an architecture driven by the problem's physics for fast
parameter learning. Our method can handle generative forward models that are
costly to evaluate and exhibits similar performance in accuracy and computation
time as a fully-learned DNN, while maintaining high interpretability and being
easier to train. Concrete results are shown on an example of model-based brain
parameter estimation from magnetic resonance imaging (MRI).
