On the determination of a function from an elliptical Radon transform
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- On the determination of a function from an elliptical Radon transform
- Moon, Sunghwan
- Issue Date
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.416, no.2, pp.724 - 734
- In recent years, Radon-type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in synthetic aperture radar, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in Rn over a set of solid ellipses (when n = 2) or solid ellipsoids of rotation (when n ≥ 3) with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates and local uniqueness results are also provided.
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