Efficient recovery from noisy quantized compressed sensing using generalized approximate message passing

Compressed sensing (CS) is a novel technique that allows for stable reconstruction with sampling rate lower than Nyquist rate if the unknown vector is sparse. In many practical applications CS measurements are first scalar quantized and later corrupted in different ways. Reconstruction by conventional techniques on such highly distorted measurements will result in poor accuracy. To address this problem, we use the well established generalized approximate message passing (GAMP) algorithm and tailor it for quantized CS measurements corrupted with noise. We provide the necessary expressions for the nonlinear updates for different noise models, namely the symmetric discrete memoryless channel (SDMC) and the additive white Gaussian noise (AWGN) channel. Numerical results show superiority of the GAMP algorithm compared to conventional reconstruction algorithms in both SDMC and AWGN channels.