Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm - Vila, Jeremy; Schniter, Philip; Rangan, Sundeep; Krzakala, Florent; Zdeborova, Lenka (arXiv.org, 2014)
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 \(A\).