  A signal recovery scheme is developed for linear observation systems based on
expectation consistent (EC) mean field approximation. Approximate message
passing (AMP) is known to be consistent with the results obtained using the
replica theory, which is supposed to be exact in the large system limit, when
each entry of the observation matrix is independently generated from an
identical distribution. However, this is not necessarily the case for general
matrices. We show that EC recovery exhibits consistency with the replica theory
for a wider class of random observation matrices. This is numerically confirmed
by experiments for the Bayesian optimal signal recovery of compressed sensing
using random row-orthogonal matrices.
