  Deep learning has gained great popularity due to its widespread success on
many inference problems. We consider the application of deep learning to the
sparse linear inverse problem encountered in compressive sensing, where one
seeks to recover a sparse signal from a small number of noisy linear
measurements. In this paper, we propose a novel neural-network architecture
that decouples prediction errors across layers in the same way that the
approximate message passing (AMP) algorithm decouples them across iterations:
through Onsager correction. Numerical experiments suggest that our "learned
AMP" network significantly improves upon Gregor and LeCun's "learned ISTA"
network in both accuracy and complexity.
