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arXiv · 2210.08861

A Unitary Transform Based Generalized Approximate Message Passing

Jiang Zhu·Xiangming Meng·Xupeng Lei·Qinghua Guo
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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 $\bf{A}$.

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Jiang Zhu, Xiangming Meng, Xupeng Lei, Qinghua Guo. 2022-10-17. A Unitary Transform Based Generalized Approximate Message Passing. https://arxiv.org/abs/2210.08861

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