# A class of singular Fourier integral operators in Synthetic Aperture Radar imaging

@article{Ambartsoumian2011ACO,
title={A class of singular Fourier integral operators in Synthetic Aperture Radar imaging},
author={Gaik Ambartsoumian and Raluca Felea and Venkateswaran P. Krishnan and Clifford J. Nolan and Eric Todd Quinto},
journal={Journal of Functional Analysis},
year={2011},
volume={264},
pages={246-269}
}
• Published 6 October 2011
• Mathematics
• Journal of Functional Analysis
30 Citations

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## References

SHOWING 1-10 OF 29 REFERENCES
MICROLOCAL ASPECTS OF COMMON OFFSET SYNTHETIC APERTURE RADAR IMAGING
• Mathematics
• 2011
In this article, we analyze the microlocal properties of the lin- earized forward scattering operator F and the reconstruction operator F F appearing in bistatic synthetic aperture radar imaging. In
MICROLOCAL ASPECTS OF BISTATIC SYNTHETIC APERTURE RADAR IMAGING
• Mathematics
• 2010
In this article, we analyze the microlocal properties of the linearized forward scattering operator $F$ and the reconstruction operator $F^{*}F$ appearing in bistatic synthetic aperture radar
Microlocal Analysis of Synthetic Aperture Radar Imaging
• Mathematics, Environmental Science
• 2004
AbstractWe consider Synthetic Aperture Radar (SAR) in which backscattered waves are measured from locations along a single flight path of an aircraft. Emphasis is on the case where it is not possible
Displacement of artefacts in inverse scattering
We analyse further inverse problems related to synthetic aperture radar imaging considered by Nolan and Cheney (2002 Inverse Problems 18 221). Under a nonzero curvature assumption, it is proved that
Enhanced angular resolution from multiply scattered waves
• Mathematics
• 2006
Multiply scattered waves are often neglected in imaging methods, largely because of the inability of standard algorithms to deal with the associated non-linear models. This paper shows that by
Composition of Fourier Integral Operators with Fold and Blowdown Singularities
ABSTRACT The purpose of this work is to present results about the composition of Fourier integral operators with certain singularities, for which the composition is not again a Fourier integral
An FIO calculus for marine seismic imaging, II: Sobolev estimates
• Mathematics
• 2009
We establish sharp L2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [Guillemin and Uhlmann (Duke Math J 48:251–267, 1981), Melrose and Uhlmann (Commun Pure Appl
Fourier integral operators. I
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value
Fourier integral operators with cusp singularities
• Art, Mathematics
• 1998
<abstract abstract-type="TeX"><p>We study the boundedness properties, on Lebesgue and Sobolev spaces, of Fourier integral operators associated with canonical relations such that at least one of the