Reconstruction of a Function from its Elliptical Radon Transform
AbstractThe talk discusses the fundamental question of image
reconstruction in bistatic regime in which the measurements
represent line integrals over a family of ellipses with foci at the
source and receiver locations. An integral transform, the elliptical
Radon transform is introduced and used to model the data. This
talk presents some new numerical results about the inversion of
the elliptical Radon in 2D. A new approximate inversion formula
is presented in the case of circular acquisition geometry when
the source and the receiver are rotating around the origin at a
fixed distance from each other. We demonstrate the efficiency of
the suggested algorithm by presenting a computational implementation
of the method on a numerical phantom. This novel
algorithm can be efficiently implemented as a numerical method
in several bistatic imaging modalities e.g. in biomedical imaging.
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