Abstract
AbstractWe 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 $$\ell _2$$
ℓ
2
–$$\ell _2$$
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.
Funder
gruppo nazionale per l’analisi matematica, la probabilità e le loro applicazioni
eu h2020 rise nomads
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Computer Vision and Pattern Recognition,Condensed Matter Physics,Modeling and Simulation,Statistics and Probability
Cited by
4 articles.
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