We consider the variational regularization for inverse problems in a general form. Based on the discrepancy principle, we propose a heuristic parameter choice rule for choosing the regularization parameter which does not require the information on the noise level and is therefore purely data driven. Under variational source conditions, we obtain a posteriori error estimates. According to the Bakushinskii veto, convergence in the worst case scenario can not be expected in general. However, by imposing certain conditions on the random noise, we establish a convergence result for the heuristic rule. Applications of the results are addressed and numerical simulations are reported.

中文翻译：

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逆问题变分正则化的启发式差异原理

我们以一般形式考虑逆问题的变分正则化。基于差异原理，我们提出了一种启发式参数选择规则，用于选择不需要噪声水平信息的正则化参数，因此纯数据驱动。在变分源条件下，我们获得了后验误差估计。根据 Bakushinskii 否决，一般不能预期最坏情况下的收敛。然而，通过对随机噪声施加一定的条件，我们建立了启发式规则的收敛结果。讨论了结果的应用并报告了数值模拟。