A novel two-point gradient method for regularization of inverse problems in Banach spaces. Issue 18 (12th December 2022)

• Record Type: Journal Article
• Authors: Mittal, Gaurav; Kumar Giri, Ankik
• Is Part Of: Applicable analysis. Volume 101:Issue 18(2022)
• Page Start: 6596
• Page End: 6622
• Publication Date: 2022-12-12
• Subjects: Regularization -- iterative methods -- two point gradient method; 65J15 -- 65J20 -- 47H17; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1939312
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method together with an extrapolation strategy. The general formulation of iteratively regularized Landweber iteration method in Banach spaces excludes the use of certain functions such as total variation like penalty functionals, L 1 functions, etc. The novel scheme presented in this paper allows to use such non-smooth penalty terms that can be helpful in practical applications involving the reconstruction of several important features of solutions such as piecewise constancy and sparsity. We carefully discuss the choices for important parameters, such as combination parameters and step sizes involved in the design of the method. Additionally, we discuss an example to validate our assumptions.