A Unitary Transform Based Generalized Approximate Message Passing
This work addresses signal recovery challenges in compressed sensing for applications like imaging or communications, but it is incremental as it builds on existing UAMP and expectation propagation methods.
The paper tackles the problem of recovering an unknown signal from nonlinear measurements in generalized linear models, particularly under highly correlated measurement matrices, and shows that the proposed GUAMP algorithm significantly outperforms state-of-the-art methods like GAMP and GVAMP in quantized compressed sensing experiments.
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 $\bf{A}$.