Runge–Kutta type total variation regularization for nonlinear inverse problems

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：Nonlinear ill-posed problems,Runge–Kutta type,Total variation,Regularization,Bregman distance

论文评审过程：Received 6 April 2012, Revised 27 September 2013, Available online 18 December 2013.

论文官网地址：https://doi.org/10.1016/j.cam.2013.12.012