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 ℓ0-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-ℓ1 approaches.
@article{arxiv.1312.3968,
title = {Generalized Approximate Message Passing for Cosparse Analysis Compressive Sensing},
author = {Mark Borgerding and Philip Schniter and Sundeep Rangan},
journal= {arXiv preprint arXiv:1312.3968},
year = {2014}
}