# ADMM-based residual whiteness principle for automatic parameter selection in super-resolution problems

2 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : We propose an automatic parameter selection strategy for the problem of image super-resolution for images corrupted by blur and additive white Gaussian noise with unknown standard deviation. The proposed approach exploits the structure of both the down-sampling and the blur operators in the frequency domain and computes the optimal regularisation parameter as the one optimising a suitable residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov $\ell_2$-$\ell_2$ problems as proposed in a work from Zhao et al. These problems naturally appear as substeps of the Alternating Direction Method of Multipliers (ADMM) optimisation approach used to solve super-resolution problems with non-quadratic and often non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties defined in the frequency domain which allow to express the whiteness functional in a compact way, we report an exhaustive list of numerical experiments proving the effectiveness of the proposed approach for different type of problems, in comparison with well-known parameter selection strategy such as, e.g., the discrepancy principle.
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https://hal.archives-ouvertes.fr/hal-03341769
Contributor : Luca Calatroni <>
Submitted on : Sunday, September 12, 2021 - 4:30:13 PM
Last modification on : Monday, September 13, 2021 - 11:04:46 AM

### Identifiers

• HAL Id : hal-03341769, version 1
• ARXIV : 2108.13091

### Citation

Monica Pragliola, Luca Calatroni, Alessandro Lanza, Fiorella Sgallari. ADMM-based residual whiteness principle for automatic parameter selection in super-resolution problems. 2021. ⟨hal-03341769⟩

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