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### Open Access Journals

IPI

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 $I^{3,0}$.

IPI

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.

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