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arXiv · 1412.2005

Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm

Jeremy Vila·Philip Schniter·Sundeep Rangan·Florent Krzakala·Lenka Zdeborova
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Abstract

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d sub-Gaussian $A$, GAMP is characterized by a state evolution whose fixed points, when unique, are optimal. For generic $A$, however, GAMP may diverge. In this paper, we propose adaptive damping and mean-removal strategies that aim to prevent divergence. Numerical results demonstrate significantly enhanced robustness to non-zero-mean, rank-deficient, column-correlated, and ill-conditioned $A$.

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Jeremy Vila, Philip Schniter, Sundeep Rangan, Florent Krzakala, Lenka Zdeborova. 2014-12-05. Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm. https://doi.org/10.1109/icassp.2015.7178325

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