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End-to-end deep neural networks (DNNs) have become the state-of-the-art(SOTA) for solving inverse problems. Despite their outstanding performance,during deployment, such networks are sensitive to minor variations in thetesting pipeline and often fail to reconstruct small but important details, afeature critical in medical imaging, astronomy, or defence. Such instabilitiesin DNNs can be explained by the fact that they ignore the forward measurementmodel during deployment, and thus fail to enforce consistency between theiroutput and the input measurements. To overcome this, we propose a frameworkthat transforms any DNN for inverse problems into a measurement-consistent one.This is done by appending to it an implicit layer (or deep equilibrium network)designed to solve a model-based optimization problem. The implicit layerconsists of a shallow learnable network that can be integrated into theend-to-end training while keeping the SOTA DNN fixed. Experiments onsingle-image super-resolution show that the proposed framework leads tosignificant improvements in reconstruction quality and robustness over the SOTADNNs.

Measurement-Consistent Networks via a Deep Implicit Layer for Solving Inverse Problems