# Recovering finite parametric distributions and functions using the spherical mean transform

Recovering finite parametric distributions and functions using the spherical mean transform The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set \$\$\Gamma \$\$ Γ . For this, we show how the problem of reconstruction can be converted to a Prony’s type system of equations whose regularity is guaranteed by the assumption that the points in the set \$\$\Gamma \$\$ Γ are in general position. By solving the corresponding Prony’s system we can extract the set of parameters which define the corresponding function or distribution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Recovering finite parametric distributions and functions using the spherical mean transform

, Volume 8 (3) – Apr 18, 2017
27 pages

/lp/springer-journals/recovering-finite-parametric-distributions-and-functions-using-the-mWWuAKkfce
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0171-y
Publisher site
See Article on Publisher Site

### Abstract

The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set \$\$\Gamma \$\$ Γ . For this, we show how the problem of reconstruction can be converted to a Prony’s type system of equations whose regularity is guaranteed by the assumption that the points in the set \$\$\Gamma \$\$ Γ are in general position. By solving the corresponding Prony’s system we can extract the set of parameters which define the corresponding function or distribution.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 18, 2017