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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

Analysis and Mathematical Physics , Volume 8 (3) – Apr 18, 2017

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing
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

References