We propose an automatic parameter selection strategy for the single image super-resolution problem 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 suitably defined residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov l(2)-l(2) problems as proposed in Zhao et al. (IEEE Trans Image Process 25:3683-3697, 2016). These problems naturally appear as substeps of the Alternating Direction Method of Multipliers used to solve single image super-resolution problems with non-quadratic, non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties allowing 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 strategies such as, e.g., the discrepancy principle.

ADMM-Based Residual Whiteness Principle for Automatic Parameter Selection in Single Image Super-Resolution Problems

Lanza, A
Penultimo
;
Sgallari, F
Ultimo
2022

Abstract

We propose an automatic parameter selection strategy for the single image super-resolution problem 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 suitably defined residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov l(2)-l(2) problems as proposed in Zhao et al. (IEEE Trans Image Process 25:3683-3697, 2016). These problems naturally appear as substeps of the Alternating Direction Method of Multipliers used to solve single image super-resolution problems with non-quadratic, non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties allowing 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 strategies such as, e.g., the discrepancy principle.
2022
Pragliola, M; Calatroni, L; Lanza, A; Sgallari, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/897506
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