An Approximate Message Passing Framework for Side Information

TL;DR

This paper introduces an AMP-based framework that leverages side information to improve sparse signal recovery, demonstrating its effectiveness through applications to Bernoulli-Gaussian and birth-death-drift models with empirical validation.

Contribution

The work develops a versatile AMP framework that incorporates side information for separable distributions, with specific algorithms and denoisers for BG and BDD models.

Findings

AMP-SI algorithms outperform traditional methods in simulations.

State evolution accurately predicts algorithm performance.

Framework is applicable to channel estimation and related tasks.

Abstract

Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This work presents an AMP-based framework that exploits SI and can be readily implemented in various settings for which the SI results in separable distributions. To illustrate the simplicity and applicability of our approach, this framework is applied to a Bernoulli-Gaussian (BG) model and a time-varying birth-death-drift (BDD) signal model, motivated by applications in channel estimation. We develop a suite of algorithms, called AMP-SI, and derive denoisers for the BDD and BG models. Numerical evidence demonstrating the advantages of our approach are presented alongside empirical evidence of the accuracy of a proposed state evolution.