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An automatic regularization parameter selection algorithm in the total variation model for image deblurring. (English) Zbl 1296.68183
Summary: Image restoration is an inverse problem that has been widely studied in recent years. The total variation based model by Rudin-Osher-Fatemi [L. I. Rudin et al., Physica D 60, No. 1–4, 259–268 (1992; Zbl 0780.49028)] is one of the most effective and well known due to its ability to preserve sharp features in restoration. This paper addresses an important and yet outstanding issue for this model in selection of an optimal regularization parameter, for the case of image deblurring. We propose to compute the optimal regularization parameter along with the restored image in the same variational setting, by considering a Karush Kuhn Tucker (KKT) system. Through establishing analytically the monotonicity result, we can compute this parameter by an iterative algorithm for the KKT system. Such an approach corresponds to solving an equation using discrepancy principle, rather than using discrepancy principle only as a stopping criterion. Numerical experiments show that the algorithm is efficient and effective for image deblurring problems and yet is competitive.

##### MSC:
 68U10 Computing methodologies for image processing 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 49N70 Differential games and control 49N75 Pursuit and evasion games 62H35 Image analysis in multivariate analysis
na28
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