Estimating the intensity of a filtered Poisson point process on Rd
Résumé
Motivated by the preeminence of Poisson point processes in various imaging modalities, we address the problem of recovering the intensity of a filtered Poisson point process on R d . That is, we observe the convolution of the measure µ underlying the point process with a known filter h. We investigate both the case where the full function h⋆µ is of avail, or where the data is given by its evaluation on a grid. Upon choosing an orthornormal basis, we propose two nonparametric estimators of the intensity, either through a model selection approach or a thresholding procedure. We provide convergence rates in all cases based on appropriate concentration inequalities for Poisson processes, with a focus on the Hermite basis for the observation on a grid. Exhaustive numerical experiments show the implementability of our proposed methods and confirm our theoretical results.
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