Article Contents

2018, Volume 12, Issue 2: 261-280. Doi: 10.3934/ipi.2018011

This issue Previous Article Next Article On recovery of an inhomogeneous cavity in inverse acoustic scattering

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: April 2018

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Abstract

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.

Keywords:

Mathematics Subject Classification: 35R30, 35Q86, 85A25.

Citation:

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Figure 1. Geometry of cloud interface

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Figure 2. 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 $\beta = \sin\phi$.

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Figure 3. True angular radiation function $\beta(\phi) = \sin\phi$ (in green), reconstructed function (in blue), and initial guess (in red).

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