INVERSION OF A CLASS OF CIRCULAR AND ELLIPTICAL RADON TRANSFORMS

The paper considers a class of elliptical and circular Radon transforms appearing in problems of ultrasound imaging. These transforms put into correspondence to an unknown image function f in 2D its integrals Rf along a family of ellipses (or circles) . From the imaging point of view, of particular interest is the circular geometry of data acquisition. Here the generalized Radon transform R integrates f along ellipses (circles) with their foci (centers) located on a fixed circle C. We prove that such transforms can be uniquely inverted from radially incomplete data to recover the image function in annular regions. Our results hold for cases when f is supported inside and/or outside of the data acquisition circle C.

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