Residual Whiteness Principle for Automatic Parameter Selection in $$\ell _2$$-$$\ell _2$$ Image Super-Resolution Problems

Abstract

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.