# Onsager-corrected deep learning for sparse linear inverse problems

arXiv: https://arxiv.org/abs/1607.05966 · HTML: https://mlsanity.com/paper/1607.05966/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2016.

## Built on by (most cited first, 8 of 8)

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## Abstract (arXiv)

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.