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On the determination of a function from an elliptical Radon transform

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Title
On the determination of a function from an elliptical Radon transform
Author
Moon, Sunghwan
Keywords
Ellipsoid; Radar; Radio; Radon; Tomography; Ultrasound
Issue Date
201408
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.416, no.2, pp.724 - 734
Abstract
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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DOI
http://dx.doi.org/10.1016/j.jmaa.2014.02.058
ISSN
0022-247X
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