A GEM hard thresholding method for reconstructing sparse signals from quantized noisy measurements

We develop a generalized expectation-maximization (GEM) algorithm for sparse signal reconstruction from quantized noisy measurements. The measurements follow an underdetermined linear model with sparse regression coefficients, corrupted by additive white Gaussian noise having unknown variance. These measurements are quantized into bins and only the bin indices are used for reconstruction. We treat the unquantized measurements as the missing data and propose a GEM iteration that aims at maximizing the likelihood function with respect to the unknown parameters. Under certain mild conditions, our GEM iteration converges monotonically to its fixed point. We compare the proposed scheme with the state-of-the-art convex relaxation method for quantized compressed sensing via numerical simulations.