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Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging

Part of: Miscellaneous topics - Partial differential equations Optics, electromagnetic theory - General Hyperbolic equations and systems

Published online by Cambridge University Press:  17 May 2016

Lingdi Wang ,
Wenbin Chen  and
Jin Cheng
Lingdi Wang*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
Wenbin Chen*
Affiliation:
Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
Jin Cheng*
Affiliation:
Key Laboratory for Information Science of Electromagnetic Waves and School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
*
*Corresponding author. Email addresses:10110180010@fudan.edu.cn (L. Wang), wbchen@fudan.edu.cn (W. Chen), jcheng@fudan.edu.cn (J. Cheng)
*Corresponding author. Email addresses:10110180010@fudan.edu.cn (L. Wang), wbchen@fudan.edu.cn (W. Chen), jcheng@fudan.edu.cn (J. Cheng)
*Corresponding author. Email addresses:10110180010@fudan.edu.cn (L. Wang), wbchen@fudan.edu.cn (W. Chen), jcheng@fudan.edu.cn (J. Cheng)
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Abstract

The first-order cross correlation and corresponding applications in the passive imaging are deeply studied by Garnier and Papanicolaou in their pioneer works. In this paper, the results of the first-order cross correlation are generalized to the second-order cross correlation. The second-order cross correlation is proven to be a statistically stable quantity, with respective to the random ambient noise sources. Specially, with proper time scales, the stochastic fluctuation for the second-order cross correlation converges much faster than the first-order one. Indeed, the convergent rate is of order , with 0 < α < 1. Besides, by using the stationary phase method in both homogeneous and scattering medium, similar behaviors of the singular components for the second-order cross correlation are obtained. Finally, two imaging methods are proposed to search for a target point reflector: One method is based on the imaging function, and has a better signal-to-noise rate; Another method is based on the geometric property, and can improve the bad range resolution of the imaging results.

Keywords

Second-order cross correlationambient noise sourcesstationary phase methodpassive imaging

MSC classification

Secondary: 35L10: Second-order hyperbolic equations 35R30: Inverse problems 35R60: Partial differential equations with randomness, stochastic partial differential equations 78A46: Inverse scattering problems
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1191 - 1220
Copyright
Copyright © Global-Science Press 2016 

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