Generalized Inexact Newton-Landweber Iteration for Possibly Non-Smooth Inverse Problems in Banach Spaces

In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth convex penalty terms, including L1-like and total variation-like functionals, capture special features of solutions such as sparsity piecewise constancy. Furthermore, inaccurate inner solver incorporated into minimization problem each step. Under some assumptions, based on ε-subdifferential, establish convergence analysis proposed method. Finally, numerical simulations are provided illustrate effectiveness for solving both smooth problems.