Residual whiteness principle for automatic parameter selection in $\ell_2$-$\ell_2$ image super-resolution problems

Monica Pragliola (1) , Luca Calatroni (2) , Alessandro Lanza (1) , Fiorella Sgallari (1)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 MORPHEME - Morphologie et Images

We propose an automatic parameter selection strategy for variational image super-resolution of blurred and down-sampled images corrupted by additive white Gaussian noise (AWGN) with unknown standard deviation. By exploiting particular properties of the operators describing the problem in the frequency domain, our strategy selects the optimal parameter as the one optimising a suitable residual whiteness measure. Numerical tests show the effectiveness of the proposed strategy for generalised $\ell_2$-$\ell_2$ Tikhonov problems.

Domaines: Traitement des images [eess.IV]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Monica Pragliola, Luca Calatroni, Alessandro Lanza, Fiorella Sgallari. Residual whiteness principle for automatic parameter selection in $\ell_2$-$\ell_2$ image super-resolution problems. 2021. ⟨hal-03195617⟩