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We look into the minimax results for the anisotropic two-dimensionalfunctional deconvolution model with the two-parameter fractional Gaussiannoise. We derive the lower bounds for the $L^p$-risk, $1 \leq p < \infty$, andtaking advantage of the Riesz poly-potential, we apply a wavelet-vagueletteexpansion to de-correlate the anisotropic fractional Gaussian noise. Weconstruct an adaptive wavelet hard-thresholding estimator that attainsasymptotically quasi-optimal convergence rates in a wide range of Besov balls.Such convergence rates depend on a delicate balance between the parameters ofthe Besov balls, the degree of ill-posedness of the convolution operator andthe parameters of the fractional Gaussian noise. A limited simulations studyconfirms theoretical claims of the paper. The proposed approach is extended tothe general $r$-dimensional case, with $r> 2$, and the correspondingconvergence rates do not suffer from the curse of dimensionality.

Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet