Bayes-Optimal Convolutional AMP

Keigo Takeuchi

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arXiv · 2101.11185

Bayes-Optimal Convolutional AMP

Keigo Takeuchi

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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.

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Keigo Takeuchi. 2021-01-27. Bayes-Optimal Convolutional AMP. https://arxiv.org/abs/2101.11185

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