Rigorous State Evolution Analysis for Approximate Message Passing with Side Information

• URL: http://arxiv.org/abs/2003.11964v1
• Date: Wed, 25 Mar 2020 16:11:18 GMT
• Title: Rigorous State Evolution Analysis for Approximate Message Passing with Side Information
• Authors: Hangjin Liu and Cynthia Rush and Dror Baron
• Abstract summary: A novel framework that incorporates side information into Approximate Message Passing with Side Information (AMP-SI) has been introduced. We provide rigorous performance guarantees for AMP-SI when there are statistical dependencies between the signal and SI pairs. We show that the AMP-SI can predict the AMP-SI mean square error accurately.
• Score: 15.90775344965397
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A common goal in many research areas is to reconstruct an unknown signal x from noisy linear measurements. Approximate message passing (AMP) is a class of low-complexity algorithms that can be used for efficiently solving such high-dimensional regression tasks. Often, it is the case that side information (SI) is available during reconstruction. For this reason, a novel algorithmic framework that incorporates SI into AMP, referred to as approximate message passing with side information (AMP-SI), has been recently introduced. In this work, we provide rigorous performance guarantees for AMP-SI when there are statistical dependencies between the signal and SI pairs and the entries of the measurement matrix are independent and identically distributed Gaussian. The AMP-SI performance is shown to be provably tracked by a scalar iteration referred to as state evolution. Moreover, we provide numerical examples that demonstrate empirically that the SE can predict the AMP-SI mean square error accurately.

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