Onsager-corrected deep learning for sparse linear inverse problems
Information Theory
2016-07-21 v1 Machine Learning
math.IT
Machine Learning
Abstract
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.
Cite
@article{arxiv.1607.05966,
title = {Onsager-corrected deep learning for sparse linear inverse problems},
author = {Mark Borgerding and Philip Schniter},
journal= {arXiv preprint arXiv:1607.05966},
year = {2016}
}