A support theorem for the geodesic ray transform of symmetric tensor fields
Venkateswaran P. Krishnan Plamen Stefanov
Inverse Problems & Imaging 2009, 3(3): 453-464 doi: 10.3934/ipi.2009.3.453
Let $(M,g)$ be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of such a field $f$ along maximal geodesics vanish on an appropriate open subset of the space of geodesics in $M$. Under the assumption that the metric $g$ is real-analytic, it is shown that there exists a vector field $v$ satisfying $f=dv$ on the set of points lying on these geodesics and $v=0$ on the intersection of this set with the boundary ∂$ M$ of the manifold $M$. Using this result, a Helgason's type of a support theorem for the geodesic ray transform is proven. The approach is based on analytic microlocal techniques.
keywords: integral geometry support theorem. X ray transform tensors
Microlocal aspects of common offset synthetic aperture radar imaging
Venkateswaran P. Krishnan Eric Todd Quinto
Inverse Problems & Imaging 2011, 5(3): 659-674 doi: 10.3934/ipi.2011.5.659
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 imaging. In our model, the radar source and detector travel along a line a fixed distance apart. We show that $F$ is a Fourier integral operator, and we give the mapping properties of the projections from the canonical relation of $F$, showing that the right projection is a blow-down and the left projection is a fold. We then show that $F^{*}F$ is a singular FIO belonging to the class $I^{3,0}$.
keywords: Fourier Integral Operators Microlocal Analysis SAR Imaging Scattering. Radar

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