An improved and accelerated non-linear multigrid method for total-variation denoising

Abstract

Fast solution of the non-linear partial differential equations (PDEs) arising from image restoration is of practical importance. The standard multigrid methods do not work well, because of the highly discontinuous coefficients of the underlying non-linear PDEs. We present two related global but linear smoothers that help the convergence of multigrid methods. Furthermore, the Krylov acceleration technique is combined with the proposed multigrid method to improve performance. Numerical experiments are shown.

Keywords:

• Image restoration
• Total variation
• Denoising
• Multigrid methods
• Krylov acceleration
• Smoothers

Acknowledgements

J.S. is grateful for support from a UK EPSRC DTA grant.