Volume 53, pp. 329-351, 2020.

Residual whiteness principle for parameter-free image restoration

Alessandro Lanza, Monica Pragliola, and Fiorella Sgallari


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.

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Key words

image restoration, variational methods, regularization parameter, additive white Gaussian noise, alternating direction method of multipliers

AMS subject classifications

68U10, 94A08, 65K10

ETNA articles which cite this article

Vol. 59 (2023), pp. 202-229 Alessandro Lanza, Monica Pragliola, and Fiorella Sgallari: Parameter-free restoration of piecewise smooth images
Vol. 61 (2024), pp. 66-91 Alessandro Buccini and Lothar Reichel: Software for limited memory restarted $l^p$-$l^q$ minimization methods using generalized Krylov subspaces

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