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Passive Array Correlation-Based Imaging in a Random Waveguide

Habib Ammari D ́epartement de Math ́ematiques et Applications, ́Ecole Normale Sup ́erieure, 75230 Paris Cedex05, France Josselin Garnier Laboratoire de Probabilit ́es et Mod`eles Al ́eatoires & Laboratoire Jacques-Louis Lions, Universit ́eParis VII, 75205 Paris Cedex 13, France Wenjia Jing D ́epartement de Math ́ematiques et Applications, ́Ecole Normale Sup ́erieure, 75230 Paris Cedex05, France

Analysis of PDEs Probability mathscidoc:2206.03009

Multiscale Modeling & Simulation, 11, (2), 656-681, 2013.6
We consider reflector imaging in a weakly random waveguide. We address the situation in which the source is farther from the reflector to be imaged than the energy equipartition distance, but the receiver array is closer to the reflector to be imaged than the energy equipartition distance. As a consequence, the reflector is illuminated by a partially coherent field and the signals recorded by the receiver array are noisy. This paper shows that migration of the recorded signals cannot give a good image, but an appropriate migration of the cross correlations of the recorded signals can give a very good image. The resolution and stability analysis of this original functional shows that the reflector can be localized with an accuracy of the order of the wavelength even when the receiver array has small aperture, and that broadband sources are necessary to ensure statistical stability, whatever the aperture of the array.
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@inproceedings{habib2013passive,
  title={Passive Array Correlation-Based Imaging in a Random Waveguide},
  author={Habib Ammari, Josselin Garnier, and Wenjia Jing},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163219862594458},
  booktitle={Multiscale Modeling & Simulation},
  volume={11},
  number={2},
  pages={656-681},
  year={2013},
}
Habib Ammari, Josselin Garnier, and Wenjia Jing. Passive Array Correlation-Based Imaging in a Random Waveguide. 2013. Vol. 11. In Multiscale Modeling & Simulation. pp.656-681. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163219862594458.
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