We consider the Landweber iteration for solving linear as well as nonlinear inverse problems in Banach spaces. 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, so it is purely data-driven. According to a famous veto, convergence in the worst-case scenario cannot be expected in general. However, by imposing certain conditions on the noisy data, we establish a new convergence result which, in addition, requires neither the Gâteaux differentiability of the forward operator nor the reflexivity of the image space. Therefore, we also expand the applied range of the Landweber iteration to cover non-smooth ill-posed inverse problems and to handle the situation that the data is contaminated by various types of noise. Numerical simulations are also reported.

我们考虑使用 Landweber 迭代来解决 Banach 空间中的线性和非线性反问题。基于差异原理，我们提出了一种用于选择正则化参数的启发式参数选择规则，该规则不需要噪声水平的信息，因此它是纯数据驱动的。根据著名的否决权，一般情况下不能指望最坏情况下的收敛。然而，通过对噪声数据施加某些条件，我们建立了一个新的收敛结果，此外，该结果既不需要前向算子的 Gâteaux 可微性，也不需要图像空间的自反性。因此，我们还扩大了Landweber迭代的应用范围，以涵盖非光滑不适定反问题以及处理数据被各种类型噪声污染的情况。还报告了数值模拟。