  This paper presents a new Bayesian spectral unmixing algorithm to analyse
remote scenes sensed via sparse multispectral Lidar measurements. To a first
approximation, in the presence of a target, each Lidar waveform consists of a
main peak, whose position depends on the target distance and whose amplitude
depends on the wavelength of the laser source considered (i.e, on the target
reflectivity). Besides, these temporal responses are usually assumed to be
corrupted by Poisson noise in the low photon count regime. When considering
multiple wavelengths, it becomes possible to use spectral information in order
to identify and quantify the main materials in the scene, in addition to
estimation of the Lidar-based range profiles. Due to its anomaly detection
capability, the proposed hierarchical Bayesian model, coupled with an efficient
Markov chain Monte Carlo algorithm, allows robust estimation of depth images
together with abundance and outlier maps associated with the observed 3D scene.
The proposed methodology is illustrated via experiments conducted with real
multispectral Lidar data acquired in a controlled environment. The results
demonstrate the possibility to unmix spectral responses constructed from
extremely sparse photon counts (less than 10 photons per pixel and band).
