Spectral unmixing of Multispectral Lidar signals

TL;DR

This paper introduces a Bayesian method utilizing Markov chain Monte Carlo for spectral unmixing of multispectral Lidar data, estimating material distribution and positions with performance bounds to aid future instrument design.

Contribution

It presents a novel Bayesian framework with MCMC sampling for spectral unmixing of MSL data, including derivation of Cramer-Rao bounds for performance evaluation.

Findings

Algorithm accurately estimates material distributions in synthetic data.

Derived Cramer-Rao bounds provide theoretical performance limits.

Experimental results align with theoretical bounds, guiding instrument development.

Abstract

In this paper, we present a Bayesian approach for spectral unmixing of multispectral Lidar (MSL) data associated with surface reflection from targeted surfaces composed of several known materials. The problem addressed is the estimation of the positions and area distribution of each material. In the Bayesian framework, appropriate prior distributions are assigned to the unknown model parameters and a Markov chain Monte Carlo method is used to sample the resulting posterior distribution. The performance of the proposed algorithm is evaluated using synthetic MSL signals, for which single and multi-layered models are derived. To evaluate the expected estimation performance associated with MSL signal analysis, a Cramer-Rao lower bound associated with model considered is also derived, and compared with the experimental data. Both the theoretical lower bound and the experimental analysis will be of primary assistance in future instrument design.