Minimax Optimal Estimator in a Stochastic Inverse Problem for Exponential Radon Transform

Abhishek, Anuj

doi:10.1007/s13171-022-00285-4

Published: 06 May 2022

Minimax Optimal Estimator in a Stochastic Inverse Problem for Exponential Radon Transform

Anuj Abhishek ORCID: orcid.org/0000-0002-3440-130X¹

Sankhya A (2022)Cite this article

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Abstract

In this article, we consider the problem of inverting the exponential Radon transform of a function in the presence of noise. We propose a kernel estimator to estimate the true function. Such an estimator is closely related to filtered backprojection type inversion formulas in the noise-less setting. For the estimator proposed in this article, we then show that the convergence to the true function is at a minimax optimal rate.

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Department of Mathematics and Statistics, UNC Charlotte, 9201 University City Blvd., Charlotte, 28213, North Carolina, USA
Anuj Abhishek

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Abhishek, A. Minimax Optimal Estimator in a Stochastic Inverse Problem for Exponential Radon Transform. Sankhya A (2022). https://doi.org/10.1007/s13171-022-00285-4

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Received: 27 September 2021
Accepted: 10 March 2022
Published: 06 May 2022
DOI: https://doi.org/10.1007/s13171-022-00285-4

Keywords and phrases.

Exponential Radon Transform
Non-parametric estimation

AMS (2000) subject classification.

Primary 62G05; Secondary 44A12