Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration

The BiCG and QMR methods are well-known Krylov subspace iterative methods for the solution of linear systems of equations with a large nonsymmetric, nonsingular matrix. However, little is known of the performance of these methods when they are applied to the computation of approximate solutions of linear systems of equations with a matrix of ill-determined rank. Such linear systems are known as linear discrete ill-posed problems. We describe an application of the BiCG and QMR methods to the solution of linear discrete ill-posed problems that arise in image restoration, and compare these methods to the conjugate gradient method applied to the associated normal equations and to total variation-penalized Tikhonov regularization.