Constrained TV $$_p$$ p - $$\ell _2$$ ℓ 2 Model for Image Restoration

Lanza, Alessandro; Morigi, Serena; Sgallari, Fiorella

doi:10.1007/s10915-015-0129-x

Cited by 55 publications

(50 citation statements)

References 27 publications

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“…We remark that the TVp-L2 model has been introduced in [8], whereas the TVp-L1 model has not been proposed before and can be regarded as a further contribution of this paper, together with the automatic selection procedure for the space-variant p parameters. For what concerns the TV sv p -L1 model in order to have a robust evaluation of the p-map, the image is preliminarily processed by an adaptive filter.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The usefulness of this great flexibility is however conditioned to the existence of effective procedures for the automatic estimation of the pi values. As it will be discussed in the paper, the algorithm used in [8] for estimating a unique, global p value is not sufficiently robust to be used for inferring our local pi values. Hence, in the paper we also propose a new suitable estimation procedure of the pi values based on the statistical inference technique described in [7].…”

Section: Introductionmentioning

confidence: 99%

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Space-Variant TV Regularization for Image Restoration

et al. 2017

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We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L2 and L1 fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer, referred to as TV SV p , where the so-called shape parameter p is automatically and locally estimated by applying a statistical inference technique based on the generalized Gaussian distribution. The restored image is efficiently computed by using an alternating direction method of multipliers procedure. We validated our models on images corrupted by Gaussian blur and two important types of noise, namely the additive white Gaussian noise and the impulsive salt and pepper noise. Numerical examples show that the proposed approach is particularly effective and well suited for images characterized by a wide range of gradient distributions.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Space-Variant TV Regularization for Image Restoration

et al. 2017

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“…Hence, we can alternate a minimisation step with respect to the primal variables t, u, w with a maximisation step with respect to the dual variables ρ t , ρ w , in combination with an iterative update of the space variant parameters α i and µ, which hence will be denoted by α we use the easy ML estimation strategy described next, whereas for µ (k) we will rely on a global discrepancy principle Primal variables update. The three primal sub-problems can be solved efficiently and in closedform by simple shrinkage/projection operators (in both cases p = 1, 2) and linear system solvers -see [13,12]. More in details, the sub-problem with respect to the t primal variable, after some algebraic manipulations, can be written as,…”

Section: Admm Optimisation and Automatic Parameter Selectionmentioning

confidence: 99%

Adaptive parameter selection for weighted-TV image reconstruction problems

Calatroni

Lanza

Pragliola

et al. 2020

J. Phys.: Conf. Ser.

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We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximumlikelihood approach estimating space-variant image scales with a global discrepancy principle related to noise statistics. We verify the effectiveness of the proposed approach solving some exemplar image reconstruction problems and show its outperformance in comparison to state-of-the-art parameter estimation strategies, the former weighting locally the fit with the data [4], the latter relying on a bilevel learning paradigm [8,9].

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“…. , n}, the Gibbs prior in (9) reduces to the TV prior which, plugged into (7), yields the popular TV regularizer. We remark that the TV prior corresponds to choosing…”

Section: Deriving the Model Via Mapmentioning

confidence: 99%

Space-Adaptive Anisotropic Bivariate Laplacian Regularization for Image Restoration

et al. 2019

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In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anistropic extension of the classical Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the unknown target image distribute locally according to space-variant bivariate Laplacian distributions. The high flexibility of the proposed regularizer holds the potential for effectively modelling local image properties, in particular driving in an adaptive manner the strength and direction of non-linear TV-diffusion. The free parameters of the regularizer are automatically set -and, eventually, updated -based on a robust Maximumum Likelihood estimation procedure. A minimization algorithm based on the Alternating Direction Method of Multipliers is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported which demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical TV-regularized models.

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Constrained TV $$_p$$ p - $$\ell _2$$ ℓ 2 Model for Image Restoration

Cited by 55 publications

References 27 publications

Space-Variant TV Regularization for Image Restoration

Space-Variant TV Regularization for Image Restoration

Adaptive parameter selection for weighted-TV image reconstruction problems

Space-Adaptive Anisotropic Bivariate Laplacian Regularization for Image Restoration

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