An iteration regularizaion method with general convex penalty for nonlinear inverse problems in Banach spaces
For researchers solving nonlinear inverse problems with sparsity or piecewise constant features, this method offers a computationally efficient alternative.
The paper proposes a novel iterative regularization method with general convex penalty for nonlinear inverse problems in Banach spaces, achieving competitive computational time reduction compared to existing Landweber iteration in numerical simulations.
In this paper, we discuss the construction, analysis and implementation of a novel iterative regularization scheme with general convex penalty term for nonlinear inverse problems in Banach spaces based on the homotopy perturbation technique, in an attempt to detect the special features of the sought solutions such as sparsity or piecewise constant. By using tools from convex analysis in Banach spaces, we provide a detailed convergence and stability results for the presented algorithm. Numerical simulations for one-dimensional and two-dimensional parameter identification problems are performed to validate that our approach is competitive in terms of reducing the overall computational time in comparison with the existing Landweber iteration with general convex penalty.