On the determination of a function from an elliptical Radon transform

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Moon, Sunghwan

关键词: Ellipsoid;    Radon;    Radio;    Tomography;    Radar;    Ultrasound;   

DOI  :  10.1016/j.jmaa.2014.02.058

来源: Elsevier

【 摘 要 】

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 R-n over a set of solid ellipses (when n = 2) or solid ellipsoids of rotation (when >= 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free