  Terahertz (THz) sensing is a promising imaging technology for a wide variety
of different applications. Extracting the interpretable and physically
meaningful parameters for such applications, however, requires solving an
inverse problem in which a model function determined by these parameters needs
to be fitted to the measured data. Since the underlying optimization problem is
nonconvex and very costly to solve, we propose learning the prediction of
suitable parameters from the measured data directly. More precisely, we develop
a model-based autoencoder in which the encoder network predicts suitable
parameters and the decoder is fixed to a physically meaningful model function,
such that we can train the encoding network in an unsupervised way. We
illustrate numerically that the resulting network is more than 140 times faster
than classical optimization techniques while making predictions with only
slightly higher objective values. Using such predictions as starting points of
local optimization techniques allows us to converge to better local minima
about twice as fast as optimization without the network-based initialization.
