  In this paper, we present a novel Bayesian approach for estimating spectral
and range profiles from single-photon Lidar waveforms associated with single
surfaces in the photon-limited regime. In contrast to classical multispectral
Lidar signals, we consider a single Lidar waveform per pixel, whereby a single
detector is used to acquire information simultaneously at multiple wavelengths.
A new observation model based on a mixture of distributions is developed. It
relates the unknown parameters of interest to the observed waveforms containing
information from multiple wavelengths. Adopting a Bayesian approach, several
prior models are investigated and a stochastic Expectation-Maximization
algorithm is proposed to estimate the spectral and depth profiles. The
reconstruction performance and computational complexity of our approach are
assessed, for different prior models, through a series of experiments using
synthetic and real data under different observation scenarios. The results
obtained demonstrate a significant speed-up without significant degradation of
the reconstruction performance when compared to existing methods in the
photon-starved regime.
