Deconvolution on the Euclidean motion group SE(3)

초록

Deconvolution is an important class of inverse problems. The goal of this paper is to develop the optimality properties of deconvolution density estimators on the noncommutative and noncompact six-dimensional Euclidean motion group. The idea is that if the underlying random object is a composition of several independent objects, then the underlying density is a convolution of densities of those independent objects. Therefore, deconvolution allows one to recover the main components of the mixture. We illustrate this with some numerical work.

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