Transductive Inversion via Deep Transform Learning

This work addresses the problem of solving a linear inverse problem. Conventional inversion techniques are model based (transductive). The advent of deep learning led the way for data-driven (inductive) inversion techniques. The main issue with inductive inversion is that unless the unseen signal (to be inverted) is similar to the training data, the learnt model fails to generalize rendering poor inversion results. A recent study on deep dictionary learning has shown how it can combine the best of both worlds – deep learning with transductive inversion. In this work, we show how the analysis counterpart of dictionary learning, called transform learning, can be extended deeper for transductive inversion. Results on dynamic MRI reconstruction, show that the proposed technique improves over the state-of-the-art.