An adaptive wavelet shrinkage approach to the Spektor–Lord–Willis problem

Abstract

The stereological problem of unfolding the sphere size distribution from linear sections is considered. A minimax estimator of the intensity function of a Poisson process that describes the problem is introduced and an adaptive estimator is constructed that achieves the optimal rate of convergence over Besov balls to within logarithmic factors. The construction of these estimators uses Wavelet–Vaguelette Decomposition (WVD) of the operator that defines our inverse problem.