In this work we propose a novel iterative estimation algorithm for linear
observation systems called S-AMP whose fixed points are the stationary points
of the exact Gibbs free energy under a set of (first- and second-) moment
consistency constraints in the large system limit. S-AMP extends the
approximate message-passing (AMP) algorithm to general matrix ensembles. The
generalization is based on the S-transform (in free probability) of the
spectrum of the measurement matrix. Furthermore, we show that the optimality of
S-AMP follows directly from its design rather than from solving a separate
optimization problem as done for AMP.Comment: 5 pages, 1 figur
