  Approximate message-passing (AMP) method is a simple and efficient framework
for the linear inverse problems. In this letter, we propose a faster AMP to
solve the \emph{$L_1$-Split-Analysis} for the 2D sparsity separation, which is
referred to as \emph{MixAMP}. We develop the MixAMP based on the factor
graphical modeling and the min-sum message-passing. Then, we examine MixAMP for
two types of the sparsity separation: separation of the direct-and-group
sparsity, and that of the direct-and-finite-difference sparsity. This case
study shows that the MixAMP method offers computational advantages over the
conventional first-order method, TFOCS.
