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

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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Correspondence to 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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  • 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