Solving inverse problems with autoencoders on learnt graphs

Solutions to inverse problems with dictionary learning and transform learning are well known. In recent years, their graph regularized versions have also been proposed. Graph regularization introduces non local smoothness to spatially diverse but structurally similar patches. A new approach to solve inverse problems, based on the autoencoder has been introduced lately. In this work, we propose graph regularization on autoencoder and show how it can be used for solving inverse problems. We evaluate different approaches to MRI reconstruction. Results show that our method improves over existing generic representation learning based inversion techniques and several state-of-the-art techniques that are tailored for this particular problem. (c) 2021 Published by Elsevier B.V.