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 in 2-dimensional space, the integrals 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 integrates the function 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 annularregions. Our results hold for cases when f is supported inside and/or outside of the data acquisition circle C.

People: Gaik Ambartsoumian and Venkateswaran P. Krishnan
Status: Paper to appear in Contemporary Mathematics, American Mathematical Society.