Extended AMP algorithm for correlated distributed compressed sensing model

We study the correlated distributed compressed sensing (C-DCS) scenarios where the measurement matrices and the signals at different sensors can be correlated. It is assumed that the measurement matrices are Gaussian random matrices and the signals share a common sparse support. Our model is a generalization of the commonly used DCS model where the measurement matrices are independent and the standard multiple measurement vector (MMV) model where the measurement matrices are identical. Based on the famous approximate message passing (AMP) framework, an algorithm is developed to address the correlated matrices and the correlated signals. Simulations show that the empirical results almost perfectly match the theoretical performance prediction. According to the authors' knowledge, such a match is achieved for the first time.