On quantized compressed sensing with saturated measurements via convex optimization

In this paper, we address the problem of sparse signal recovery, from multi-bit scalar quantized compressed sensing measurements, where the saturation issue is taken into account. We propose a convex optimization approach, where saturation errors are jointly estimated with the sparse signal to be recovered. In the proposed approach, saturated measurements, even though over-identified, are considered as outliers and the associated errors are handled as non-negative sparse corruptions with partial support information. We highlight the theoretical recovery guarantee of the proposed approach and we demonstrate, via simulation results, its reliability in cancelling out the effect of the outlying saturated measurements.