Deep Network for Parametric Bilinear Generalized Approximate Message Passing and Its Application in Compressive Sensing under Matrix Uncertainty

Deep learning is playing an increasingly important role in signal processing field due to its excellent performance on many inference problems. Parametric bilinear generalized approximate message passing (P-BiG-AMP) is a new approximate message passing based approach to a general class of structure-matrix bilinear estimation problems. In this letter, we propose a novel feed-forward neural network architecture to realize P-BiG-AMP methodology with deep learning for the inference problem of compressive sensing under matrix uncertainty. Linear transforms utilized in the recovery process and parameters involved in the input and output channels of measurement are jointly learned from training data. Simulation results show that the trained P-BiG-AMP network can achieve higher reconstruction performance than the P-BiG-AMP algorithm with parameters tuned via the expectation-maximization method.