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arXiv · 2306.15640

Adaptive local density estimation in tomography

Sergio Brenner Miguel·Janine Steck
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Abstract

We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We identify the underlying statistical inverse problem and use a spectral cut-off regularisation to deduce an estimator. A fully data-driven choice of the cut-off parameter m in R+ is proposed and studied. To discuss the bias-variance trade off, we consider Sobolev spaces and show the minimax-optimality of the spectral cut-off density estimator. In a simulation study, we illustrate a reasonable behaviour of the studied fully data-driven estimator.

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Sergio Brenner Miguel, Janine Steck. 2023-06-27. Adaptive local density estimation in tomography. https://arxiv.org/abs/2306.15640

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