An Approximate Message Passing Framework for Side Information
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Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or side information (SI), is commonly available and can aid in efficient signal recovery. In this work, we present an AMP-based framework that exploits SI and can be readily implemented in various settings. To illustrate the simplicity and wide applicability of our approach, we apply this framework 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. We also present numerical evidence demonstrating the advantages of our approach, and empirical evidence of the accuracy of a proposed state evolution.
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