Reconstruction of Support of a Measure From Its Moments

Abstract

In this paper, we address the problem of reconstruction of support of a 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. Numerical examples are presented to illustrate the performance of the proposed approach.

This has been submitted to the 53rd IEEE Conference on Decision and Control

References in corpus (3)

• Approximate volume and integration for basic semi-algebraic sets
• The inverse moment problem for convex polytopes
• Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets

Cited by in corpus (2)

• Convex Constrained Semialgebraic Volume Optimization: Application in Systems and Control
• Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems