On the Determination of a Function from an Elliptical Radon Transform

2013/02/18 by Moon, Sunghwan
#44A12 #92C55 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1302.4396

Abstract

In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in \RRⁿ over a set of solid ellipsoids of rotation 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, range description, and local uniqueness results are also provided.

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