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Penalized Least Squares are widely used in signal and image processing. Yet,it suffers from a major limitation since it requires fine-tuning of theregularization parameters. Under assumptions on the noise probabilitydistribution, Stein-based approaches provide unbiased estimator of thequadratic risk. The Generalized Stein Unbiased Risk Estimator is revisited tohandle correlated Gaussian noise without requiring to invert the covariancematrix. Then, in order to avoid expansive grid search, it is necessary todesign algorithmic scheme minimizing the quadratic risk with respect toregularization parameters. This work extends the Stein's Unbiased GrAdientestimator of the Risk of Deledalle et al. to the case of correlated Gaussiannoise, deriving a general automatic tuning of regularization parameters. First,the theoretical asymptotic unbiasedness of the gradient estimator isdemonstrated in the case of general correlated Gaussian noise. Then, theproposed parameter selection strategy is particularized to fractal texturesegmentation, where problem formulation naturally entails inter-scale andspatially correlated noise. Numerical assessment is provided, as well asdiscussion of the practical issues.

Automated data-driven selection of the hyperparameters for Total-Variation based texture segmentation