Expectation Maximization and the retrieval of the atmospheric extinction coefficients by inversion of Raman lidar data

TL;DR

This paper introduces an Expectation-Maximization algorithm for stable retrieval of aerosol extinction coefficients from Raman lidar data, addressing the ill-posed inverse problem with regularization and validation on synthetic and real data.

Contribution

It proposes a novel EM-based method with a stopping criterion for regularization in aerosol extinction retrieval from Raman lidar measurements.

Findings

EM method provides stable solutions with positivity constraints.

Compared favorably to Tikhonov and Levenberg-Marquardt methods.

Effective on both synthetic and experimental data.

Abstract

We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill--posed inverse problem that needs regularization, and we propose to use the Expectation--Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation.