A New Approach to Inverting Backscatter and Extinction from   Photon-Limited Lidar Observations
  Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar background noise, however, hinder the ability of lidar systems to provide reliable backscatter and extinction cross-section estimates. Standard methods for solving this inverse problem are most effective with high signal-to-noise ratio observations that are only available at low-resolution in uniform scenes. This paper describes a novel method for solving the inverse problem with high-resolution, lower signal-to-noise ratio observations that are effective in non-uniform scenes. The novelty is twofold. First, the inference of the backscatter and extinction are done on images, whereas current lidar algorithms only use the information content of single profiles. Hence, the latent spatial and temporal information in the noisy images are utilized to infer the cross-sections. Second, the noise associated with photon-counting lidar observations can be modeled using a Poisson distribution, and state-of-the-art tools for solving Poisson inverse problems are adapted to the atmospheric lidar problem. It is demonstrated through photon-counting High Spectral Resolution Lidar (HSRL) simulations that the proposed algorithm yield inverted backscatter and extinction cross-sections (per unit volume) with smaller Mean Squared Error (MSE) values at higher spatial and temporal resolutions, compared to the standard approach. Two case studies of real experimental data are also provided where the proposed algorithm is applied on HSRL observations and the inverted backscatter and extinction cross-sections are compared against the standard approach. 
Willem J. Marais, Robert E. Holz, Yu Hen Hu, Ralph E. Kuehn, Edwin E.   Eloranta, Rebecca M. Willett
math.OC