  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.
