A family of modified regularizing circulant preconditioners for image reconstruction problems

摘要

Regularizing iterative methods for image restoration problems with 2D band Toeplitz matrices are examined. They often require the use of suitable preconditioners. Circulant preconditioners, which can be applied with a low cost and can be easily adapted to cope with the noise, are widely used. In this paper three of them are taken into consideration and modified in order to obtain a better convergence rate, still retaining regularizing properties. A large numerical experimentation validates the theoretical results.