  Inverse Problems in medical imaging and computer vision are traditionally
solved using purely model-based methods. Among those variational regularization
models are one of the most popular approaches. We propose a new framework for
applying data-driven approaches to inverse problems, using a neural network as
a regularization functional. The network learns to discriminate between the
distribution of ground truth images and the distribution of unregularized
reconstructions. Once trained, the network is applied to the inverse problem by
solving the corresponding variational problem. Unlike other data-based
approaches for inverse problems, the algorithm can be applied even if only
unsupervised training data is available. Experiments demonstrate the potential
of the framework for denoising on the BSDS dataset and for computed tomography
reconstruction on the LIDC dataset.
