Pré-Publication, Document De Travail Année : 2025

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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hal-05084273 , version 1 (26-05-2025)

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  • HAL Id : hal-05084273 , version 1

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Rémy Abergel, Fabienne Comte, Céline Duval, Camille Pouchol. Estimating the intensity of a filtered Poisson point process on Rd. 2025. ⟨hal-05084273⟩
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