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Inverse Problems and Imaging (IPI)
 

Video stabilization of atmospheric turbulence distortion

Pages: 839 - 861, Volume 7, Issue 3, August 2013      doi:10.3934/ipi.2013.7.839

 
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Yifei Lou - Department of Mathematics, University of California Los Angeles, Los Angeles, CA, 90095, United States (email)
Sung Ha Kang - School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States (email)
Stefano Soatto - Computer Science Department, University of California Los Angeles, Los Angeles, CA, 90095, United States (email)
Andrea L. Bertozzi - Department of Mathematics, University of California Los Angeles, Los Angeles, CA, 90095, United States (email)

Abstract: We present a method to enhance the quality of a video sequence captured through a turbulent atmospheric medium, and give an estimate of the radiance of the distant scene, represented as a ``latent image,'' which is assumed to be static throughout the video. Due to atmospheric turbulence, temporal averaging produces a blurred version of the scene's radiance. We propose a method combining Sobolev gradient and Laplacian to stabilize the video sequence, and a latent image is further found utilizing the ``lucky region" method. The video sequence is stabilized while keeping sharp details, and the latent image shows more consistent straight edges. We analyze the well-posedness for the stabilizing PDE and the linear stability of the numerical scheme.

Keywords:  Imaging through turbulence, Sobolev gradient sharpening, anisotropic diffusion, spectral methods, image fusion.
Mathematics Subject Classification:  Primary: 68U10; Secondary: 35B65, 35B35.

Received: April 2012;      Revised: March 2013;      Available Online: September 2013.

 References