Preconditioners for image restoration by reblurring techniques

It is well known that iterative algorithms for image deblurring that involve the normal equations show usually a slow convergence. A variant of the normal equations which replaces the conjugate transpose A^H of the system matrix A with a new matrix is proposed. This approach, which is linked with regularization preconditioning theory and reblurring processes, can be applied to a wide set of iterative methods; here we examine Landweber, Steepest descent, Richardson–Lucy and Image Space Reconstruction Algorithm. Several computational tests show that this strategy leads to a significant improvement of the convergence speed of the methods. Moreover it can be naturally combined with other widely used acceleration techniques.