Volume 19, Issue 5
Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging

Lingdi Wang, Wenbin Chen & Jin Cheng

Commun. Comput. Phys., 19 (2016), pp. 1191-1220.

Published online: 2018-04

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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 $\mathcal{O}$($T^{−1+α}$), 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; the other method is based on the geometric property, and can improve the bad range resolution of the imaging results.

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@Article{CiCP-19-1191, author = {}, title = {Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1191--1220}, 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 $\mathcal{O}$($T^{−1+α}$), 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; the other method is based on the geometric property, and can improve the bad range resolution of the imaging results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.26s}, url = {http://global-sci.org/intro/article_detail/cicp/11125.html} }
TY - JOUR T1 - Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging JO - Communications in Computational Physics VL - 5 SP - 1191 EP - 1220 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.scpde14.26s UR - https://global-sci.org/intro/article_detail/cicp/11125.html KW - AB -

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 $\mathcal{O}$($T^{−1+α}$), 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; the other method is based on the geometric property, and can improve the bad range resolution of the imaging results.

Lingdi Wang, Wenbin Chen & Jin Cheng. (2020). Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging. Communications in Computational Physics. 19 (5). 1191-1220. doi:10.4208/cicp.scpde14.26s
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