Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution

被引：15

作者：

Harrach, Bastian ^{[1
]}

Jahn, Tim ^{[1
]}

Potthast, Roland ^{[2
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, Frankfurt, Germany

[2] Deutsch Wetterdienst, Data Assimilat Unit, Offenbach, Germany

来源：

NUMERISCHE MATHEMATIK | 2020年 / 145卷 / 03期

关键词：

65J22 (Numerical solution to inverse problems in abstract spaces); ILL-POSED PROBLEMS; CONVERGENCE-RATES;

D O I：

10.1007/s00211-020-01122-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：581 / 603

页数：23

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