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

2012/08/28 by Yehonatan Salman, Salman, Yehonatan
Earth and Planetary Sciences · Mathematics · #Geophysics and Gravity Measurements #Numerical methods in inverse problems #Statistical and numerical algorithms #math.AP

paper · pdf · doi:10.48550/arxiv.1208.5739

10 pages

arxiv created 2012/08/28 · arxiv updated 2012/08/29

Abstract

In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension n≥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.

Related

• Inversion of the Weighted Spherical Mean
• The Spherical Mean Transform with Data on a Parabola in the Plane
• Recovering Functions from the Spherical Mean Transform with Data on an Ellipse Using Eigenfunction Expansion in Elliptical Coordinates
• Inversion of the Spherical Mean Transform with Sources on a Hyperplane
• Spherical means with centers on a hyperplane in even dimensions