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

Gaik Ambartsoumian; Raluca Felea; Venkateswaran P. Krishnan; Clifford Nolan; Eric Todd Quinto

doi:10.1016/j.jfa.2012.10.008

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

Gaik Ambartsoumian
, Raluca Felea
, Venkateswaran P. Krishnan
, Clifford Nolan
, Eric Todd Quinto

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we analyze the microlocal properties of the linearized forward scattering operator F and the normal operator F ^*F (where F ^* is the L ² adjoint of F) which arises in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry. When F ^* is applied to the scattered data, artifacts appear. We show that F ^*F can be decomposed as a sum of four operators, each belonging to a class of distributions associated to two cleanly intersecting Lagrangians, I ^p,l(Λ ₀, Λ ₁), thereby explaining the latter artifacts.

Original language	English
Pages (from-to)	246-269
Number of pages	24
Journal	Journal of Functional Analysis
Volume	264
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2012.10.008
Publication status	Published - 1 Jan 2013

Keywords

Elliptical Radon transforms
Fold and Blowdown singularities
Singular Fourier integral operators
Synthetic Aperture Radar

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10.1016/j.jfa.2012.10.008

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title = "A class of singular Fourier integral operators in Synthetic Aperture Radar imaging",

abstract = "In this article, we analyze the microlocal properties of the linearized forward scattering operator F and the normal operator F *F (where F * is the L 2 adjoint of F) which arises in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry. When F * is applied to the scattered data, artifacts appear. We show that F *F can be decomposed as a sum of four operators, each belonging to a class of distributions associated to two cleanly intersecting Lagrangians, I p,l(Λ 0, Λ 1), thereby explaining the latter artifacts.",

keywords = "Elliptical Radon transforms, Fold and Blowdown singularities, Singular Fourier integral operators, Synthetic Aperture Radar",

author = "Gaik Ambartsoumian and Raluca Felea and Krishnan, \{Venkateswaran P.\} and Clifford Nolan and Quinto, \{Eric Todd\}",

year = "2013",

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AU - Ambartsoumian, Gaik

AU - Felea, Raluca

AU - Krishnan, Venkateswaran P.

AU - Nolan, Clifford

AU - Quinto, Eric Todd

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this article, we analyze the microlocal properties of the linearized forward scattering operator F and the normal operator F *F (where F * is the L 2 adjoint of F) which arises in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry. When F * is applied to the scattered data, artifacts appear. We show that F *F can be decomposed as a sum of four operators, each belonging to a class of distributions associated to two cleanly intersecting Lagrangians, I p,l(Λ 0, Λ 1), thereby explaining the latter artifacts.

AB - In this article, we analyze the microlocal properties of the linearized forward scattering operator F and the normal operator F *F (where F * is the L 2 adjoint of F) which arises in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry. When F * is applied to the scattered data, artifacts appear. We show that F *F can be decomposed as a sum of four operators, each belonging to a class of distributions associated to two cleanly intersecting Lagrangians, I p,l(Λ 0, Λ 1), thereby explaining the latter artifacts.

KW - Elliptical Radon transforms

KW - Fold and Blowdown singularities

KW - Singular Fourier integral operators

KW - Synthetic Aperture Radar

UR - https://www.scopus.com/pages/publications/84869494313

U2 - 10.1016/j.jfa.2012.10.008

DO - 10.1016/j.jfa.2012.10.008

M3 - Article

AN - SCOPUS:84869494313

SN - 0022-1236

VL - 264

SP - 246

EP - 269

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

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

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Keywords

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