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

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