This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications it is ad hoc unrealistic to know the error of a measurement. In practice, the error of a measurement may often be estimated through averaging of multiple measurements. We integrated that in our anlaysis and obtained convergence to the true solution, with the only assumption that the measurements are unbiased, independent and identically distributed according to an unknown distribution.

中文翻译：

---

超越 Bakushinkii 否决：在不知道噪声分布的情况下对线性逆问题进行正则化

本文处理希尔伯特空间中线性不适定方程的解。通常，人们手头只有右手边的损坏测量值，而 Bakushinskii 否决告诉我们，如果我们不知道噪声水平，我们将无法求解方程。但是在应用中，知道测量的误差是不切实际的。在实践中，测量的误差通常可以通过多次测量的平均来估计。我们将其整合到我们的分析中并获得了对真实解的收敛性，唯一的假设是根据未知分布，测量值是无偏的、独立的和同分布的。