An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Salman, Yehonatan

关键词: Spherical means;    Radon transform;    Inversion formula;    Inverse problems;   

DOI  :  10.1016/j.jmaa.2014.05.007

来源: Elsevier

【 摘 要 】

In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh, inversion formulas were found in any dimension greater than or equal to 2 for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere. The aim of this article is to show that the methods used in [1,2] can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free