Efficient estimation of line spectral from quantized samples is of vital
importance in information theory and signal processing, e.g., channel
estimation in energy efficient massive MIMO systems and direction of arrival
estimation. The goal of this paper is to recover the line spectral as well as
its corresponding parameters such as model order, frequency and amplitudes from
heavily quantized samples. To this end, we propose an efficient grid-less
Bayesian algorithm named VALSE-EP, which is based on the variational line
spectral estimation (VALSE) and expectation propagation (EP). The basic idea of
VALSE-EP is to iteratively approximate the challenging quantized model of line
spectral estimation as a sequence of simple pseudo unquantized models, so that
the VALSE algorithm can be applied. Note that since the noise in the pseudo
linear model is heteroscedastic (different components having different
variance), a variant of the VALSE is re-derived to obtain the final VALSE-EP.
Moreover, to obtain a benchmark performance of the proposed algorithm, the
Cram\'{e}r Rao bound (CRB) is derived. Finally, numerical results show that the
performance of VALSE-EP is close to the CRB, demonstrating effectiveness of
VALSE-EP for line spectral estimation from quantized samples.