A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimized convex nonlinear functions subject to non-negativity constraints and, in some cases, toan additional flux conservation constraint. Aspecial gradient projection method is introduced that exploits effective scaling strategies and steplength updating rules, appropriately designed for improving the convergence rate. We give convergence results for this scheme and we evaluate its effectiveness by means of an extensive computational study on the minimization problems arising from the maximum likelihood approach to image deblurring. Comparisons with the standard expectation maximization algorithm and with other iterative regularization schemes are also reported to show the computational gainprovided by the proposed method.

A scaled gradient projection method for constrained image deblurring / Bonettini, Silvia; Zanella, Riccardo; Zanni, Luca. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - STAMPA. - 25:1(2009), pp. 015002-015002. [10.1088/0266-5611/25/1/015002]

A scaled gradient projection method for constrained image deblurring

BONETTINI, Silvia;ZANELLA, RICCARDO;ZANNI, Luca
2009

Abstract

A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimized convex nonlinear functions subject to non-negativity constraints and, in some cases, toan additional flux conservation constraint. Aspecial gradient projection method is introduced that exploits effective scaling strategies and steplength updating rules, appropriately designed for improving the convergence rate. We give convergence results for this scheme and we evaluate its effectiveness by means of an extensive computational study on the minimization problems arising from the maximum likelihood approach to image deblurring. Comparisons with the standard expectation maximization algorithm and with other iterative regularization schemes are also reported to show the computational gainprovided by the proposed method.
2009
25
1
015002
015002
A scaled gradient projection method for constrained image deblurring / Bonettini, Silvia; Zanella, Riccardo; Zanni, Luca. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - STAMPA. - 25:1(2009), pp. 015002-015002. [10.1088/0266-5611/25/1/015002]
Bonettini, Silvia; Zanella, Riccardo; Zanni, Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/593384
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