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

Anuj Abhishek ()
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Anuj Abhishek: UNC Charlotte

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 40, 980-998

Abstract: 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.

Keywords: Exponential Radon Transform; Non-parametric estimation; Primary 62G05; Secondary 44A12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-022-00285-4

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