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

TL;DR

This paper introduces adaptive damping and mean-removal techniques to improve the robustness of the GAMP algorithm, enabling it to handle non-ideal matrices that cause divergence.

Contribution

The paper proposes novel adaptive damping and mean-removal strategies that prevent divergence of GAMP for a wider class of matrices.

Findings

Enhanced robustness of GAMP to non-zero-mean matrices

Successful handling of rank-deficient and ill-conditioned matrices

Significant improvement in convergence stability

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 $A$.