  Image-to-image translation is an ill-posed problem as unique one-to-one
mapping may not exist between the source and target images. Learning-based
methods proposed in this context often evaluate the performance on test data
that is similar to the training data, which may be impractical. This demands
robust methods that can quantify uncertainty in the prediction for making
informed decisions, especially for critical areas such as medical imaging.
Recent works that employ conditional generative adversarial networks (GANs)
have shown improved performance in learning photo-realistic image-to-image
mappings between the source and the target images. However, these methods do
not focus on (i)~robustness of the models to out-of-distribution (OOD)-noisy
data and (ii)~uncertainty quantification. This paper proposes a GAN-based
framework that (i)~models an adaptive loss function for robustness to OOD-noisy
data that automatically tunes the spatially varying norm for penalizing the
residuals and (ii)~estimates the per-voxel uncertainty in the predictions. We
demonstrate our method on two key applications in medical imaging:
(i)~undersampled magnetic resonance imaging (MRI) reconstruction (ii)~MRI
modality propagation. Our experiments with two different real-world datasets
show that the proposed method (i)~is robust to OOD-noisy test data and provides
improved accuracy and (ii)~quantifies voxel-level uncertainty in the
predictions.
