Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform

TL;DR

This paper introduces a kernel estimator for the exponential Radon transform inverse problem under noise, demonstrating it achieves the best possible convergence rate in a minimax sense.

Contribution

It proposes a new kernel estimator for noisy exponential Radon transform inversion and proves its minimax optimal convergence rate.

Findings

Estimator converges at minimax optimal rate

Method is analogous to previous tomography estimators

Provides theoretical guarantees for estimator performance

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, analogous to the one proposed by Korostel\"{e}v and Tsybakov in their article `Optimal rates of convergence of estimators in a probabilistic setup of tomography problem', Problems of Information Transmission, 27:73-81,1991. For the estimator proposed in this article, we then show that it converges to the true function at a minimax optimal rate.