Bayes-Optimal Convolutional AMP

TL;DR

This paper introduces Bayes-optimal convolutional AMP, which enhances convergence and achieves Bayes-optimal performance in certain sensing matrix scenarios by deriving state evolution equations for optimal denoising.

Contribution

It derives SE equations for CAMP and demonstrates that Bayes-optimal CAMP attains Bayes-optimal performance under specific matrix conditions.

Findings

Achieves Bayes-optimal performance with right-orthogonally invariant matrices.

Improves convergence properties of AMP through convolutional modifications.

Demonstrates effectiveness with low-to-moderate condition number matrices.

Abstract

To improve the convergence property of approximate message-passing (AMP), convolutional AMP (CAMP) has been proposed. CAMP replaces the Onsager correction in AMP with a convolution of messages in all preceding iterations while it uses the same low-complexity matched filter (MF) as AMP. This paper derives state evolution (SE) equations to design the Bayes-optimal denoiser in CAMP. Numerical results imply that CAMP with the Bayes-optimal denoiser--called Bayes-optimal CAMP--can achieve the Bayes-optimal performance for right-orthogonally invariant sensing matrices with low-to-moderate condition numbers.