Runge-Kutta type total variation regularization for nonlinear inverse problems

- RK type TV regularization for the nonlinear ill-posed problems is constructed.
- This method introduced Bregman distance as regularization functional.
- Under appropriate stopping rule this method with noise is convergent.
- Numerical tests testify the method for problems with discontinuous solutions.

In this paper, we construct a Runge-Kutta type total variation regularization for the nonlinear ill-posed problems. This method resembles Runge-Kutta type iteration with the Bregman distance as a regularization functional. In the presence of noise with noise level δ we prove this method to be convergent under appropriate stopping rule. Furthermore, some numerical experiments are presented to verify this method to be more suitable for problems with discontinuous solutions.