On the asymptotical regularization with convex constraints for inverse problems
Numerical Analysis
2022-03-23 v2 Numerical Analysis
Abstract
In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy. Under certain conditions we give convergence properties of the methods. Moreover, we propose Runge-Kutta type methods to discrete the initial value problems to construct new type iterative regularization methods.
Cite
@article{arxiv.2110.03242,
title = {On the asymptotical regularization with convex constraints for inverse problems},
author = {Min Zhong and Wei Wang},
journal= {arXiv preprint arXiv:2110.03242},
year = {2022}
}
Comments
11 pages