36 research outputs found
A novel two-point gradient method for Regularization of inverse problems in Banach spaces
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,
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.Comment: Submitted in Applicable Analysi