Resolution enhancement from scattering in passive sensor imaging with cross correlations

Josselin Garnier; George Papanicolaou

doi:10.3934/ipi.2014.8.645

Article Contents

2014, Volume 8, Issue 3: 645-683. Doi: 10.3934/ipi.2014.8.645

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Resolution enhancement from scattering in passive sensor imaging with cross correlations

Josselin Garnier^1, and
George Papanicolaou^2,

1.
Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13
2.
Mathematics Department, Stanford University, Stanford, CA 94305

Received: January 31, 2012

Revised: May 31, 2013

Published: July 2014

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Abstract

It was shown in [Garnier et al., SIAM J. Imaging Sciences 2 (2009), 396] that it is possible to image reflectors by backpropagating cross correlations of signals generated by ambient noise sources and recorded at passive sensor arrays. The resolution of the image depends on the directional diversity of the noise signals relative to the locations of the sensor array and the reflector. When directional diversity is limited it is possible to enhance it by exploiting the scattering properties of the medium since scatterers will act as secondary noise sources. However, scattering increases the fluctuation level of the cross correlations and therefore tends to destabilize the image by reducing its signal-to-noise ratio. In this paper we study the trade-off in passive, correlation-based imaging between resolution enhancement and signal-to-noise ratio reduction that is due to scattering.

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Mathematics Subject Classification: Primary: 35R30, 35R60; Secondary: 86A15, 78A46.

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