  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.
