Decompounding on compact Lie groups

TL;DR

This paper introduces a harmonic analysis-based method for nonparametric decompounding of compound Poisson processes on compact Lie groups, with applications to inverse scattering problems in physics.

Contribution

It generalizes classical decompounding to noncommutative Lie groups using characteristic functions, addressing a complex inverse problem.

Findings

Developed a characteristic function approach for decompounding on Lie groups

Extended classical methods to noncommutative harmonic analysis setting

Applicable to models of multiple scattering in physics

Abstract

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.