  Penalized Least Squares are widely used in signal and image processing. Yet,
it suffers from a major limitation since it requires fine-tuning of the
regularization parameters. Under assumptions on the noise probability
distribution, Stein-based approaches provide unbiased estimator of the
quadratic risk. The Generalized Stein Unbiased Risk Estimator is revisited to
handle correlated Gaussian noise without requiring to invert the covariance
matrix. Then, in order to avoid expansive grid search, it is necessary to
design algorithmic scheme minimizing the quadratic risk with respect to
regularization parameters. This work extends the Stein's Unbiased GrAdient
estimator of the Risk of Deledalle et al. to the case of correlated Gaussian
noise, deriving a general automatic tuning of regularization parameters. First,
the theoretical asymptotic unbiasedness of the gradient estimator is
demonstrated in the case of general correlated Gaussian noise. Then, the
proposed parameter selection strategy is particularized to fractal texture
segmentation, where problem formulation naturally entails inter-scale and
spatially correlated noise. Numerical assessment is provided, as well as
discussion of the practical issues.
