AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

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, where one seeks to recover a sparse signal from a few noisy linear measurements. In this paper, we propose two novel...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 65; no. 16; pp. 4293 - 4308
Main Authors: Borgerding, Mark, Schniter, Philip, Rangan, Sundeep
Format: Journal Article
Language:English
Published: IEEE 15.08.2017
Subjects:
approximate message passing
Approximation algorithms
compressive sensing
Deep learning
Inverse problems
Machine learning
massive MIMO
Message passing
Probability density function
random access
Signal processing algorithms
Transforms
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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, where one seeks to recover a sparse signal from a few noisy linear measurements. In this paper, we propose two novel neural-network architectures that decouple prediction errors across layers in the same way that the approximate message passing (AMP) algorithms decouple them across iterations: through Onsager correction. First, we propose a "learned AMP" network that significantly improves upon Gregor and LeCun's "learned ISTA." Second, inspired by the recently proposed "vector AMP" (VAMP) algorithm, we propose a "learned VAMP" network that offers increased robustness to deviations in the measurement matrix from i.i.d. Gaussian. In both cases, we jointly learn the linear transforms and scalar nonlinearities of the network. Interestingly, with i.i.d. signals, the linear transforms and scalar nonlinearities prescribed by the VAMP algorithm coincide with the values learned through back-propagation, leading to an intuitive interpretation of learned VAMP. Finally, we apply our methods to two problems from 5G wireless communications: compressive random access and massive-MIMO channel estimation.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2708040