# American Institute of Mathematical Sciences

April  2018, 12(2): 261-280. doi: 10.3934/ipi.2018011

## Reconstruction of cloud geometry from high-resolution multi-angle images

 1 Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637, USA 2 Department of Mathematical Sciences, Rensselear Polytechnic Institute, Troy, NY 12180, USA 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Received  November 2015 Revised  October 2016 Published  February 2018

We consider the reconstruction of the interface of compact, connected "clouds" from satellite or airborne light intensity measurements. In a two-dimensional setting, the cloud is modeled by an interface, locally represented as a graph, and an outgoing radiation intensity that is consistent with a diffusion model for light propagation in the cloud. Light scattering inside the cloud and the internal optical parameters of the cloud are not modeled explicitly. The main objective is to understand what can or cannot be reconstructed in such a setting from intensity measurements in a finite (on the order of 10) number of directions along the path of a satellite or an aircraft. Numerical simulations illustrate the theoretical predictions. Finally, we explore a kinematic extension of the algorithm for retrieving cloud motion (wind) along with its geometry.

Citation: Guillaume Bal, Jiaming Chen, Anthony B. Davis. Reconstruction of cloud geometry from high-resolution multi-angle images. Inverse Problems & Imaging, 2018, 12 (2) : 261-280. doi: 10.3934/ipi.2018011
##### References:

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##### References:
Geometry of cloud interface
Left: A cloud model. Right: Simulated radiances $u_j(X) : = u(X,Z,\theta_j)$ for that cloud using (7) with $j = 1,\dots,J = 5$ (specifically, $\theta \in \{90,90\pm26.1,90\pm45.6\}$ in degrees clockwise from the positive $x$ axis) for a uniform $\alpha$ and $\beta = \sin\phi$.
True angular radiation function $\beta(\phi) = \sin\phi$ (in green), reconstructed function (in blue), and initial guess (in red).
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