Efficient Range Estimation and Material Quantification from Multispectral Lidar Waveforms

This paper describes a new Bayesian range estimation and spectral unmixing algorithm to analyse remote scenes sensed via multispectral Lidar measurements. To a first approximation, each Lidar waveform consists of the temporal signature of the observed target, which depends on the wavelength of the laser source considered and which is corrupted by Poisson noise. When the number of spectral bands considered is large enough, it becomes possible to identify and quantify the main materials in the scene, in addition to estimating classical Lidar-based range profiles. In this work, we adopt a Bayesian approach and the unknown model parameters are assigned prior distributions translating prior knowledge available (e.g., positivity, sparsity and/or smoothness). This prior model is then combined with the observation model (likelihood) to derive the joint posterior distribution of the unknown parameters which are inferred via maximum a posteriori estimation. Under mild assumptions often true in practice, we show that it is possible to find a global optimizer of the posterior by splitting the problem into two sequential steps estimating the unknown spectral quantities and the target ranges, respectively. The proposed methodology is illustrated via experiments conducted with real multispectral Lidar data aquired under controlled observation conditions.