Learning to solve inverse problems using Wasserstein loss
This addresses reconstruction quality issues in inverse problems like medical imaging, though it is incremental as it adapts an existing loss to a specific bottleneck.
The paper tackles the problem of degraded reconstruction quality in ill-posed inverse problems due to misalignments in training data by proposing the use of Wasserstein loss instead of mean squared error, demonstrating that it yields correct compensation and reduces smearing in computerized tomography.
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.