  In a recent paper, the authors proposed a new class of low-complexity
iterative thresholding algorithms for reconstructing sparse signals from a
small set of linear measurements \cite{DMM}. The new algorithms are broadly
referred to as AMP, for approximate message passing. This is the second of two
conference papers describing the derivation of these algorithms, connection
with related literature, extensions of original framework, and new empirical
evidence.
  This paper describes the state evolution formalism for analyzing these
algorithms, and some of the conclusions that can be drawn from this formalism.
We carried out extensive numerical simulations to confirm these predictions. We
present here a few representative results.
