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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.

Recovering finite parametric distributions and functions using the spherical mean transform