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

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  • Anuj Abhishek

    (UNC Charlotte)

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.

Suggested Citation

  • Anuj Abhishek, 2023. "Minimax Optimal Estimator in a Stochastic Inverse Problem for Exponential Radon Transform," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 980-998, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00285-4
    DOI: 10.1007/s13171-022-00285-4
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