Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing

Gabor Hannak, Alessandro Perelli, Norbert Goertz, Gerald Matz, Mike E. Davies

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple vectors with identical support and accounts for correlations in the signal of interest and in the noise. In this paper, we show how to reduce the complexity of vector BAMP via a simple joint decorrelation diagonalization) transform of the signal and noise vectors, which also facilitates the subsequent performance analysis. We prove that BAMP and the corresponding state evolution (SE) are equivariant with respect to the joint decorrelation transform and preserve diagonality of the residual noise covariance for the Bernoulli-Gauss (BG) prior. We use these results to analyze the dynamics and the mean squared error (MSE) performance of BAMP via the replica method, and thereby understand the impact of signal correlation and number of jointly sparse signals.
Original languageEnglish
JournalIEEE Journal of Selected Topics in Signal Processing
Early online date26 Jun 2018
Publication statusPublished - 2018

Keywords / Materials (for Non-textual outputs)

  • cs.IT
  • cs.DC
  • math.IT


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