  In this work, we describe a new approach that uses deep neural networks (DNN)
to obtain regularization parameters for solving inverse problems. We consider a
supervised learning approach, where a network is trained to approximate the
mapping from observation data to regularization parameters. Once the network is
trained, regularization parameters for newly obtained data can be computed by
efficient forward propagation of the DNN. We show that a wide variety of
regularization functionals, forward models, and noise models may be considered.
The network-obtained regularization parameters can be computed more efficiently
and may even lead to more accurate solutions compared to existing
regularization parameter selection methods. We emphasize that the key advantage
of using DNNs for learning regularization parameters, compared to previous
works on learning via optimal experimental design or empirical Bayes risk
minimization, is greater generalizability. That is, rather than computing one
set of parameters that is optimal with respect to one particular design
objective, DNN-computed regularization parameters are tailored to the specific
features or properties of the newly observed data. Thus, our approach may
better handle cases where the observation is not a close representation of the
training set. Furthermore, we avoid the need for expensive and challenging
bilevel optimization methods as utilized in other existing training approaches.
Numerical results demonstrate the potential of using DNNs to learn
regularization parameters.
