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

Author

Listed:
  • Ruixue Gu

    (School of Science, Dalian Maritime University, Dalian 116026, China)

  • Hongsun Fu

    (School of Science, Dalian Maritime University, Dalian 116026, China)

  • Zhuoyue Wang

    (School of Science, Dalian Maritime University, Dalian 116026, China)

Abstract

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 L 1 -like and total variation-like penalty functionals, to capture special features of solutions such as sparsity and piecewise constancy. Furthermore, the inaccurate inner solver is incorporated into the minimization problem in each iteration step. Under some assumptions, based on ε -subdifferential, we establish the convergence analysis of the proposed method. Finally, some numerical simulations are provided to illustrate the effectiveness of the method for solving both smooth and non-smooth nonlinear inverse problems.

Suggested Citation

  • Ruixue Gu & Hongsun Fu & Zhuoyue Wang, 2023. "Generalized Inexact Newton-Landweber Iteration for Possibly Non-Smooth Inverse Problems in Banach Spaces," Mathematics, MDPI, vol. 11(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1706-:d:1114398
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