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Analysis and Mathematical Physics

, Volume 8, Issue 3, pp 437–463 | Cite as

Recovering finite parametric distributions and functions using the spherical mean transform

  • Yehonatan Salman
Article
  • 111 Downloads

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 \(\Gamma \). 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 \(\Gamma \) 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.

Notes

Acknowledgements

The author would like to thank Professor Yosef Yomdin from Weizmann Institute of Science for his useful comments and suggestions during the writing of this article.

Compliance with ethical standards

Conflict of interest

The author declare that they have no competing interests.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Weizmann Institute of ScienceRehovotIsrael

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