Communications in Partial Differential Equations · 2005 · 36 citations · 15 references
Natural SciencesPhysicsAcousticsComputational AcousticsTheoretical PhysicsAcoustic Inverse ProblemsAcoustic ScatteringFourier AnalysisIntegral GeometryOperator TheoryScattering TheoryAcoustic Inverse ScatteringFourier IntegralInverse ScatteringInversion TheoremsOperatorsSingularitiesSynthetic Aperture RadarSynthetic Aperture Radar Imaging
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 operator. The singularities considered here are folds and blowdowns. We prove that for such operators, the Schwartz kernel of F*F belongs to a class of distributions associated to two cleanly intersection Lagrangians. Such Fourier integral operators appear in integral geometry, inverse acoustic scattering theory and Synthetic Aperture Radar imaging, where the composition calculus can be used as a tool for finding approximate inversion formulas and for recovering images.
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