Regularization of inverse problems by two-point gradient methods in Banach spaces
- 157 Downloads
In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms, including the \(L^1\)-like and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications. The design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed. Numerical simulations are presented to illustrate the effectiveness of the proposed method.
Mathematics Subject Classification65J15 65J20 47H17
The work of M. Zhong is supported by the National Natural Science Foundation of China (Nos. 11871149, 11671082) and and supported by Zhishan Youth Scholar Program of SEU. The work of W. Wang is partially supported by the National Natural Science Foundation of China (No. 11871180) and Natural Science Foundation of Zhejiang Province (No. LY19A010009). The work of Q Jin is partially supported by the Future Fellowship of the Australian Research Council (FT170100231).
- 33.Zhu, M., Chan, T.F.: An efficient primaldual hybrid gradient algorithm for total variation image restoration. CAM Report 08-34, UCLA (2008)Google Scholar