  We consider the problem of sparse signal reconstruction from noisy one-bit
compressed measurements when the receiver has access to side-information (SI).
We assume that compressed measurements are corrupted by additive white Gaussian
noise before quantization and sign-flip error after quantization. A generalized
approximate message passing-based method for signal reconstruction from noisy
one-bit compressed measurements is proposed, which is then extended for the
case where the receiver has access to a signal that aids signal reconstruction,
i.e., side-information. Two different scenarios of side-information are
considered-a) side-information consisting of support information only, and b)
side information consisting of support and amplitude information. SI is either
a noisy version of the signal or a noisy estimate of the support of the signal.
We develop reconstruction algorithms from one-bit measurements using noisy SI
available at the receiver. Laplacian distribution and Bernoulli distribution
are used to model the two types of noises which, when applied to the signal and
the support, yields the SI for the above two cases, respectively. The
Expectation-Maximization algorithm is used to estimate the noise parameters
using noisy one-bit compressed measurements and the SI. We show that one-bit
compressed measurement-based signal reconstruction is quite sensitive to noise,
and the reconstruction performance can be significantly improved by exploiting
available side-information at the receiver.
