A Unitary Transform Based Generalized Approximate Message Passing

TL;DR

This paper introduces GUAMP, a novel algorithm based on unitary transforms and expectation propagation, for signal recovery in nonlinear measurement models, especially effective with correlated measurement matrices.

Contribution

The paper proposes GUAMP, a new generalized approximate message passing algorithm that handles correlated measurement matrices using a unitary transform approach.

Findings

GUAMP outperforms GAMP and GVAMP in correlated matrix scenarios.

Experimental results show significant improvement in quantized compressed sensing.

GUAMP effectively handles highly correlated measurement matrices.

Abstract

We consider the problem of recovering an unknown signal ${\mathbf x}\in {\mathbb R}^n$ from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., ${\mathbf y}= f\left({\mathbf A}{\mathbf x}+{\mathbf w}\right)$, where $f(\cdot)$ is a componentwise nonlinear function. Based on the unitary transform approximate message passing (UAMP) and expectation propagation, a unitary transform based generalized approximate message passing (GUAMP) algorithm is proposed for general measurement matrices $\bf{A}$, in particular highly correlated matrices. Experimental results on quantized compressed sensing demonstrate that the proposed GUAMP significantly outperforms state-of-the-art GAMP and GVAMP under correlated matrices $\bf{A}$.