# American Institute of Mathematical Sciences

August  2014, 8(3): 645-683. doi: 10.3934/ipi.2014.8.645

## Resolution enhancement from scattering in passive sensor imaging with cross correlations

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

Received  February 2012 Revised  June 2013 Published  August 2014

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.
Citation: Josselin Garnier, George Papanicolaou. Resolution enhancement from scattering in passive sensor imaging with cross correlations. Inverse Problems & Imaging, 2014, 8 (3) : 645-683. doi: 10.3934/ipi.2014.8.645
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