Alessandro Lanza,
Monica Pragliola,
Fiorella Sgallari
S. 329 - 351
doi:
10.1553/etna_vol53s329
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol53s329
Abstract:
Selecting the regularization parameter in the image restoration variational framework is of crucial importance, since it can highly influence the quality of the final restoration. In this paper, we propose a parameter-free approach for automatically selecting the regularization parameter when the blur is space-invariant and known and the noise is additive white Gaussian with unknown standard deviation, based on the so-called residual whiteness principle. More precisely, the regularization parameter is required to minimize the residual whiteness function, namely the normalized auto-correlation of the residual image of the restoration. The proposed method can be applied to a wide class of variational models, such as those including in their formulation regularizers of Tikhonov and Total Variation type. For non-quadratic regularizers, the residual whiteness principle is nested in an iterative optimization scheme based on the alternating direction method of multipliers. The effectiveness of the proposed approach is verified by solving some test examples and performing a comparison with other parameter estimation state-of-the-art strategies, such as the discrepancy principle.
image restoration, variational methods, regularization parameter, additive white Gaussian noise, alternating direction method of multipliers
Published Online:
2020/04/20 13:40:49
Object Identifier:
0xc1aa5576 0x003b715c
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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