On parameter choice in the regularization of ill-posed problems with rough estimate of the noise level of the data

We consider linear ill-posed problems in Hilbert space with noisy data. The noise level may be given exactly or approximately or there may be no information about the noise level. We regularize the problem using the Landweber method, the Tikhonov method or the iterated or extrapolated version of the Tikhonov method. For all three cases of noise information we propose rules for the choice of the regularization parameter and give recommendations for preferences of rules depending on the accuracy of noise level information. The main attention is paid for the case if the noise level is under-or overestimated.