Signal-to-Noise Ratio Estimation in Passive Correlation-Based Imaging

Garnier, Josselin; Papanicolaou, George; Semin, Adrien; Tsogka, Chrysoula

doi:10.1137/120875533

Cited by 12 publications

(10 citation statements)

References 18 publications

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“…For the noise-free case, (17) can be solved via semi-definite programming after discretizing the problem. However, semi-definite programming does not scale well with respect to the number of dimensions.…”

Section: B Optimization Methods For Image Reconstructionmentioning

confidence: 99%

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Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

Mason

Son

Yazıcı

2015

IEEE J. Sel. Top. Signal Process.

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We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used Time Difference of Arrival (TDOA) or correlation-based backprojection method. These methods backprojection work under the assumption that the scene is composed of a single or a few widely separated point targets.The new method overcomes this limitation and can reconstruct heterogeneous scenes with extended targets.We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semidefinite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges and better noise suppression.1932-4553 (c)

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Section: B Optimization Methods For Image Reconstructionmentioning

confidence: 99%

“…The solution to(17) will be the Kronecker product of the reconstructed scene. (a) The original Kroneker product scene.…”

mentioning

confidence: 99%

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

Mason

Son

Yazıcı

2015

IEEE J. Sel. Top. Signal Process.

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“…We note, however, that a large physical source array (and/or braodband sources) is necessary to ensure the statistical stability of the imaging function. This has been already addressed in detail in different contexts in [7,23].…”

mentioning

confidence: 96%

Role of Scattering in Virtual Source Array Imaging

Garnier¹,

Papanicolaou²

2014

SIAM J. Imaging Sci.

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International audienceWe consider imaging in a scattering medium where the illumination goes through this medium but there is also an auxiliary, passive receiver array that is near the object to be imaged. Instead of imaging with the source-receiver array on the far side of the object, we image with the data of the passive array on the near side of the object. The imaging is done with travel time migration using the cross correlations of the passive array data. We showed in [J. Garnier and G. Papanicolaou, Inverse Problems, 28 (2012), 075002] that if (i) the source array is infinite, (ii) the scattering medium is modeled by either an isotropic random medium in the paraxial regime or a randomly layered medium, and (iii) the medium between the auxiliary array and the object to be imaged is homogeneous, then imaging with cross correlations completely eliminates the effects of the random medium. It is as if we imaged with an active array, instead of a passive one, near the object. The purpose of this paper is to analyze the resolution of the image when both the source array and the passive receiver array are finite. We show with a detailed analysis that for isotropic random media in the paraxial regime, not only is imaging not affected by the inhomogeneities, but the resolution can in fact be enhanced. This is because the random medium can increase the diversity of the illumination. We also show analytically that this will not happen in a randomly layered medium, and there may be some loss of resolution in this case

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“…To avoid problems with circular correlation in numerics, we transform this signal to the time domain, appropriately zero-pad the result and then transform the padded time signal back to the frequency domain (see e.g., [30,Appendix B]). Finally, the empirical correlations in (77) are generated for each x r ∈ A as…”

Section: Stochastic Experimentmentioning

confidence: 99%

Imaging small polarizable scatterers with polarization data

Bardsley¹,

Cassier²,

Vasquez³

2018

Inverse Problems

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We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency matrix or Stokes parameters of the electric field at the array. We introduce a simple preprocessing of the coherency matrix data that partially recovers the ideal data where all the components of the electric field are known for different source dipole moments. We prove that the images obtained using an electromagnetic version of Kirchhoff migration applied to the partial data are, for high frequencies, asymptotically identical to the images obtained from ideal data. We analyze the image resolution and show that polarizability tensor components in an appropriate basis can be recovered from the Kirchhoff images, which are tensor fields. A time domain interpretation of this imaging problem is provided and numerical experiments are used to illustrate the theory.

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Signal-to-Noise Ratio Estimation in Passive Correlation-Based Imaging

Cited by 12 publications

References 18 publications

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

Role of Scattering in Virtual Source Array Imaging

Imaging small polarizable scatterers with polarization data

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