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

Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution