Recovering a function out of a finite number of moments is generally an ill-posed inverse problem. We focus on two special cases arising from applications to multiphase geometric optics computations where this problem can be carried out in a restricted class of given densities. More precisely, we present a simple algorithm for the inversion of Markov's moment problem which appears in the treatment of Brenier and Corrias' "K-multibranch solutions" and study Stieltje's algorithm in order to process moment systems arising from a Wigner analysis. Numerical results are provided for moderately intricate wave-fields.
"Finite Moment Problems and Applications to Multiphase Computations in Geometric Optics." Commun. Math. Sci. 3 (3) 373 - 392, September 2005.