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arXiv · 1710.10898

Learning to solve inverse problems using Wasserstein loss

Jonas Adler·Axel Ringh·Ozan Öktem·Johan Karlsson
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Abstract

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 prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

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Jonas Adler, Axel Ringh, Ozan Öktem, Johan Karlsson. 2017-10-30. Learning to solve inverse problems using Wasserstein loss. https://arxiv.org/abs/1710.10898

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