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.