Learning algebraic decompositions using Prony structures (Q2182612)

The recovery of a structured function from sampled data is a fundamental problem in signal processing. The classical Prony method recovers all parameters of a univariate exponential sum from sampled data. Up to now, several variants and multivariate generalizations of the classical Prony method are known. In this paper, the authors analyze the purely algebraic nature of Prony's reconstruction method. Therefore they introduce a general algebraic framework called Prony structures for reconstruction methods. This new approach allows a simultaneous treatment of decomposition problems for multivariate exponential sums, for multivariate polynomials, multivariate Gaussian sums, spherical harmonic sums, and eigenfunction sums.