  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.
