A new solution is presented for the reconstruction of profiles of aerosol volume extinction coefficients from the noisy backscattered returns of a monostatic single-wavelength lidar system. This inverse problem is solved by utilizing an information-theoretic method based on the principle of minimum cross-entropy (MCE), which represents an objective and rational approach for the effective incorporation, into the inversion procedure, of both prior information in the form of an initial estimate of the extinction coefficient and additional information in the form of the observed lidar data. A simple and robust numerical procedure, based on the ellipsoid algorithm, is developed to compute the MCE reconstruction of the extinction function. A number of numerical examples, based on noisy synthetic lidar data, are employed to demonstrate and evaluate the utility and efficacy of the inversion method.
Eugene Yee, "Information-theoretic method for the inversion of the lidar equation," Appl. Opt. 28, 1628-1637 (1989)