We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a Learned Primal-Dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We give theoretical results and demonstrate the method for a problem in computerized tomography.

This is poster number 55 in Poster Session

Authors:

Jonas Adler (KTH Royal Institute of Technology)

Ozan Öktem (KTH - Royal Institute of Technology)

Axel Ringh (KTH - Royal Institute of Technology)

Johan Karlsson (KTH - Royal Institute of Technology)

Keywords:

computed tomography, deep learning, image reconstruction, inverse problems, machine learning, optimal transport, wasserstein