A Unitary Transform Based Generalized Approximate Message Passing

We consider the problem of recovering an unknown signal mathbf x∈ mathbb Rn from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., mathbf y= fleft(mathbf Amathbf x+mathbf wright), 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 bfA, 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 bfA.