Iterative solution of Toeplitz systems by preconditioning with the discrete sine transform

摘要

Abstract: Solving linear systems or least-squares related to Toeplitz matrices is often required in the context of signal and image processing; conjugate-gradient-like methods are well-suited for solving such problems. The recent preconditioning technique involving the discrete sine transform is presented: convergence properties are reported and suitable generalizations to block matrices, nonsymmetric systems, and least-squares problems are discussed. Finally, these techniques are applied to regularized inverse problems arising in image restoration. !14