A Unitary Transform Based Generalized Approximate Message Passing

10/17/2022

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by   Jiang Zhu, et al.

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We consider the problem of recovering an unknown signal 𝐱∈ℝ^n from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., 𝐲= f(𝐀𝐱+𝐰), where f(·) 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 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 A.