Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms

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.