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Reconstruction of Support of a Measure From Its Moments

In this work, we address the problem of reconstruction of support of a positive finite Borel measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. 


Problem Statement:


Application:




Equivalent Convex Problem
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Example:

                                                                    Polynomial of Order d  obtained by solving SDP of Problem 7



Paper:


  • Reconstruction of Support of a Measure From Its Moments [pdf]
         53rd IEEE Conference on Decision and Control, Los Angeles, California, 2014