AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

Mark Borgerding, Philip Schniter, Sundeep Rangan

Research output: Contribution to journalArticlepeer-review

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, 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.

Original languageEnglish (US)
Article number7934066
Pages (from-to)4293-4308
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume65
Issue number16
DOIs
StatePublished - Aug 15 2017

Keywords

  • Deep learning
  • approximate message passing
  • compressive sensing
  • massive MIMO
  • random access

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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