Algebraic–exponential Data Recovery from Moments

What is it about?

It solves an inverse problem. Provides a simple algorithm to compute the coefficients of a polynomial that describes the boundary of a semi-algebraic set when the only knowledge available is the list of moments of the Lebesgue measure on the set.

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Why is it important?

It solves a difficult inverse problem by a simple routine of linear algebra involving the moment matrix of the Lebesgue measure on the set. It also exhibits a new class of probability measures (which is not an exponential family) for which all moments are determined by finitely many of them.