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G. Hannak, A. Perelli, G. Matz, M. E. Davies, N. Görtz:
"Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing";
Poster: international Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques, Marseille, France; 21.11.2018 - 23.11.2018; in: "Proceedings iTWIST: international Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques", (2018).

Bayesian approximate message passing (BAMP) is
an efficient method in compressed sensing that is nearly optimal
in the minimum mean squared error (MMSE) sense. Multiple
measurement vector (MMV)-BAMP performs joint recovery of
multiple vectors with identical support and accounts for correla-
tions in the signal of interest and in the noise. In this paper, we
show how to reduce the complexity of vector BAMP via a sim-
ple joint decorrelation (diagonalization) transform of the signal
and noise vectors, which also facilitates the subsequent perfor-
mance analysis. We prove that the corresponding state evolution
(SE) is equivariant with respect to the joint decorrelation trans-
form and preserves 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.

Bayesian approximate message passing (BAMP) is
an efficient method in compressed sensing that is nearly optimal
in the minimum mean squared error (MMSE) sense. Multiple
measurement vector (MMV)-BAMP performs joint recovery of
multiple vectors with identical support and accounts for correla-
tions in the signal of interest and in the noise. In this paper, we
show how to reduce the complexity of vector BAMP via a sim-
ple joint decorrelation (diagonalization) transform of the signal
and noise vectors, which also facilitates the subsequent perfor-
mance analysis. We prove that the corresponding state evolution
(SE) is equivariant with respect to the joint decorrelation trans-
form and preserves 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.

Approximate Message Passing, Compressed Sensing

https://publik.tuwien.ac.at/files/publik_274256.pdf