Robust spectral unmixing of sparse multispectral Lidar waveforms using gamma Markov random fields

TL;DR

This paper introduces a Bayesian spectral unmixing method for sparse multispectral Lidar data, enabling robust material identification and depth estimation even with very low photon counts, using a gamma Markov random field model.

Contribution

It proposes a novel hierarchical Bayesian model with an efficient MCMC algorithm for robust spectral unmixing and depth estimation in sparse multispectral Lidar data, improving over existing methods.

Findings

Effective unmixing with less than 10 photons per pixel and band.

Robust depth and material estimation demonstrated on real data.

Enhanced anomaly detection capabilities.

Abstract

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).