论文标题
在随机逆问题中的最小估计量指数ra transform
Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform
论文作者
论文摘要
在本文中，我们考虑了在噪声存在下函数的指数ra换变换的问题。我们提出了一个内核估计器来估计真实功能，类似于Korostelëv和Tsybakov在其文章“在概率的层析成像问题中的最佳收敛速率”，《信息传播问题》，27：73-81,1991。对于本文提出的估计器，我们表明它以最小值最佳速率收敛到真实函数。
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 Korostelëv 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.
