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 re- places 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.

Preconditioners for image restoration by reblurring techniques

DONATELLI, MARCO;
2014-01-01

Abstract

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 re- places 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.
2014
http://www.sciencedirect.com/science/article/pii/S0377042713005918
Image deblurring problem; Iterative methods; Preconditioning; Reblurring
Dell'Acqua, P.; Donatelli, Marco; Estatico, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1965120
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