The iteratively regularized Gauss-Newton method (IRGNM) is a prominent method for solving nonlinear inverse problems. Based on a modified discrepancy principle, in this paper we propose for the IRGNM in Banach spaces a heuristic rule which is purely data driven and requires no information on the noise level. Under the tangential cone condition on the forward operator and the variational source conditions on the sought solution, we obtain a posteriori error estimates for this heuristic rule. Under further conditions on the noisy data, we establish a general convergence result without using any source conditions. Numerical simulations are given to test the performance of the heuristic rule.

中文翻译：

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带凸正则化项的 Banach 空间中 IRGNM 的启发式规则分析

迭代正则化高斯-牛顿法 (IRGNM) 是求解非线性逆问题的重要方法。基于修正的差异原则，在本文中，我们为 Banach 空间中的 IRGNM 提出了一种启发式规则，该规则纯粹是数据驱动的，不需要有关噪声水平的信息。在前向算子的切线锥条件和所寻求解的变分源条件下，我们获得了该启发式规则的后验误差估计。在噪声数据的进一步条件下，我们在不使用任何源条件的情况下建立了一般收敛结果。给出了数值模拟来测试启发式规则的性能。