  In cosparse analysis compressive sensing (CS), one seeks to estimate a
non-sparse signal vector from noisy sub-Nyquist linear measurements by
exploiting the knowledge that a given linear transform of the signal is
cosparse, i.e., has sufficiently many zeros. We propose a novel approach to
cosparse analysis CS based on the generalized approximate message passing
(GAMP) algorithm. Unlike other AMP-based approaches to this problem, ours works
with a wide range of analysis operators and regularizers. In addition, we
propose a novel $\ell_0$-like soft-thresholder based on MMSE denoising for a
spike-and-slab distribution with an infinite-variance slab. Numerical
demonstrations on synthetic and practical datasets demonstrate advantages over
existing AMP-based, greedy, and reweighted-$\ell_1$ approaches.
