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

TL;DR

This paper introduces an automatic parameter selection method for $ ext{l}_2$-$ ext{l}_2$ image super-resolution that uses residual whiteness measures to optimize parameters, improving performance on noisy, blurred, and down-sampled images.

Contribution

It presents a novel residual whiteness-based strategy for automatic parameter tuning in $ ext{l}_2$-$ ext{l}_2$ super-resolution, leveraging frequency domain properties.

Findings

Effective parameter selection demonstrated on super-resolution tasks.

Improved image reconstruction quality with the proposed method.

Applicable to generalised $ ext{l}_2$-$ ext{l}_2$ Tikhonov 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.