Inexact Newton-Landweber Iteration in Banach Spaces with NonSmooth Convex Penalty Terms

By making use of tools from convex analysis, we formulate an inexact NewtonLandweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme provides increments by applying Landweber iteration with non-smooth uniformly convex penalty terms to local linearized equations. The outer iteration is then terminated by the discrepancy principle. Detailed convergence analysis is present under standard conditions on the nonlinearity. Finally, numerical simulations are reported to test the performance of the method.