American Institute of Mathematical Sciences

Advanced
August  2012, 6(3): 531-546. doi: 10.3934/ipi.2012.6.531

Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization

Yu Mao 1, and  Jérôme Gilles 2,

1. 

Institute for Mathematics and Its Applications, University of Minnesota, 425 Lind Hall 207 Church Street SE, Minneapolis, MN 55455-0134, United States
2. 

Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095-1555, United States

Received  July 2011 Revised  January 2012 Published  September 2012

A novel approach is presented to recover an image degraded by atmospheric turbulence. Given a sequence of frames affected by turbulence, we construct a variational model to characterize the static image. The optimization problem is solved by Bregman Iteration and the operator splitting method. Our algorithm is simple, efficient, and can be easily generalized for different scenarios.
Keywords: optical flow, Bregman iterations., Turbulence restoration, nonlocal total variation.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Yu Mao, Jérôme Gilles. Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization. Inverse Problems & Imaging, 2012, 6 (3) : 531-546. doi: 10.3934/ipi.2012.6.531
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IEEE Transactions on Image Processing, 19 (2010), 1259-1268. doi: 10.1109/TIP.2009.2039660.  Google Scholar

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Multiscale Model Sim., 4 (2005), 460-489.  Google Scholar

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show all references

References:
[1]

IEEE Transactions on Image Processing, 19 (2010), 36-52. doi: 10.1109/TIP.2009.2031231.  Google Scholar

[2]

Proceedings of SPIE, 7463 (2009). Google Scholar

[3]

Comput Vision and Image Understanding, 63 (1996), 75-104. doi: 10.1006/cviu.1996.0006.  Google Scholar

[4]

J. Y. Bouguet, "Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the Algorithm," Intel Corporation Microprocessor Research Labs,, 2000. Available from: , ().   Google Scholar

[5]

Multiscale Model Sim, 4 (2005), 490-530.  Google Scholar

[6]

SIAM Journal on Imaging Sciences, 2 (2009), 226-252.  Google Scholar

[7]

Multiscale Modeling and Simulation, 8 (2009), 337-369.  Google Scholar

[8]

Linear Algebra Appl., 316 (2000), 259-285. doi: 10.1016/S0024-3795(00)00141-5.  Google Scholar

[9]

International Journal of Imaging Systems and Technology, 15 (2005), 92-102. doi: 10.1002/ima.20041.  Google Scholar

[10]

Multiscale Model Sim., 4 (2005), 1168-1200.  Google Scholar

[11]

Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2001. Google Scholar

[12]

Proceedings of the Eusipco, 2004. Google Scholar

[13]

Multiscale Model Sim., 7 (2008), 1005-1028.  Google Scholar

[14]

in "Proceedings of Advanced Concepts for Intelligent Vision Systems,'' 2008. Google Scholar

[15]

SIAM J. Sci. Comput., 31 (2009), 3712-3743. doi: 10.1137/070706318.  Google Scholar

[16]

SIAM Journal on Imaging Sciences, 2 (2009), 323-343.  Google Scholar

[17]

International Journal of Imaging Systems and Technology, 15 (2005), 74-83. doi: 10.1002/ima.20040.  Google Scholar

[18]

Computer Vision and Pattern Recognition Conference, 2010. Google Scholar

[19]

Ph. D Thesis, Université de Bourgogne, 2007. Google Scholar

[20]

IEEE Geoscience and Remote Sensing Letters, 4 (2007), 340-344. Google Scholar

[21]

SIAM Journal on Numerical Analysis, 16 (1979), 964-979. doi: 10.1137/0716071.  Google Scholar

[22]

IEEE Transactions on Image Processing, 19 (2010), 1259-1268. doi: 10.1109/TIP.2009.2039660.  Google Scholar

[23]

Multiscale Model Sim., 4 (2005), 460-489.  Google Scholar

[24]

J. Math. Anal. Appl., 72 (1979), 383-390. doi: 10.1016/0022-247X(79)90234-8.  Google Scholar

[25]

Physica D: Nonlinear Phenomena, 60 (1992), 259-268. doi: 10.1016/0167-2789(92)90242-F.  Google Scholar

[26]

Computer Vision-ECCV, 2008. Google Scholar

[27]

Proceedings of SPIE, 2008. Google Scholar

[28]

SIAM Journal on Imaging Sciences, 3 (2010), 253-276.  Google Scholar

[29]

Journal of Scientific Computing, 46 (2010), 1-27. Google Scholar

[30]

SPIE Electronic Imaging, Conference 7543 on Visual Information Processing and Communication, 2010. Google Scholar

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