Color Image Restoration by Saturation-Value Total Variation

Jia, Zhigang; Ng, Michael K.; Wang, Wei

doi:10.1137/18m1230451

Cited by 72 publications

(51 citation statements)

References 26 publications

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“…Despite being relatively simple to calculate, total variation is successfully used in areas such as denoising [21]- [24], image restoration [25]- [28], image super-resolution [29], [30], image enhancement [31], [32], compressive sensing applications [33], [34], computer graphics [35], and others.…”

Section: The Total Variationmentioning

confidence: 99%

“…Applying Eq. (28) and the equality N k=0 q k = 1 leads to the following inequality that holds for each even n > 4:…”

Section: ) Asymptoticsmentioning

confidence: 99%

“…Here n has to be greater than 4 because having n = 4 effectively leads to use of the function F (2, N ) on the right side of the inequality, and as explained earlier, this is inappropriate for Eq. (28). If n = k2 r where k ≥ 3 and r ≥ 0 are integers, then taking the inequality above recursively leads further to…”

Section: ) Asymptoticsmentioning

confidence: 99%

See 2 more Smart Citations

TVOR: Finding Discrete Total Variation Outliers Among Histograms

Banić¹,

Elezović

2021

IEEE Access

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In this paper, we respond to a critique of one of our papers previously published in this journal, entitled "TVOR: Finding Discrete Total Variation Outliers among Histograms". Our paper proposes a method for smoothness outliers detection among histograms by using the relation between their discrete total variations (DTV) and their respective sample sizes. In this response, we demonstrate point by point that, contrary to its claims, the critique has not found any mistakes or problems in our paper, either in the used datasets, methodology, or in the obtained top outlier candidates. On the contrary, the critique's claims can easily be shown to be mathematically unfounded, to directly contradict the common statistical theorems, and to go against well established demographic terms. Exactly this is done in the reply here by providing both theoretical and experimental evidence. Additionally, due to critique's compalint, a more extensive research on top outlier candidate, i.e. the Jasenovac list is conducted and in order to clear any of the critique's doubts, new evidence of its problematic nature unseen in other lists are presented. This reply is accompanied by additional theoretical explanations, simulations, and experimental results that not only confirm the earlier findings, but also present new data. The source code is at https://github.com/DiscreteTotalVariation/TVOR.

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Section: The Total Variationmentioning

confidence: 99%

“…Applying Eq. (28) and the equality N k=0 q k = 1 leads to the following inequality that holds for each even n > 4:…”

Section: ) Asymptoticsmentioning

confidence: 99%

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TVOR: Finding Discrete Total Variation Outliers Among Histograms

Banić¹,

Elezović

2021

IEEE Access

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“…Where B m denotes the closed united ball in R m with a positive integer m. K m = C 1 (Ω, B 2m ) is the set of continuously differentiable and bounded functions from the compact support in Ω to B 2m . Meanwhile, the convexity, lower semi-continuity, approximation and compactness properties can be established [7].…”

Section: 1mentioning

confidence: 99%

“…The rest of this paper is organized as follows. In Section 2, we review Saturation-Value Total Variation (SVTV) regularization [7], PDE based approach [9], and TV CA correction model [20]. In Section 3, we present the proposed SVTV CA correction model.…”

mentioning

confidence: 99%

Saturation-Value Total Variation model for chromatic aberration correction

Wang¹,

Pi²,

Ng³

2020

Inverse Problems &Amp; Imaging

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Chromatic aberration generally occurs in the regions of sharp edges in captured digital color images. The main aim of this paper is to propose and develop a novel Saturation-Value Total Variation (SVTV) model for chromatic aberration correction. In the proposed optimization model, there are three terms for the correction purpose. The SVTV regularization term is to model the target color image in HSV color space instead of RGB color space, and to avoid oscillations in the recovering process. In correction process, the gradient matching terms based on the green component are used to govern both red and blue components, and the intensity terms are employed to fit red, green and blue data components. The existence of the minimizer of the optimization model is analyzed and an efficient optimization algorithm is also developed for solving the resulting variational problem. Experimental results are presented to illustrate the effectiveness of the proposed model and to show that the correction results are better than those by using the other testing methods.

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Structure preserving quaternion full orthogonalization method with applications

Wang

2023

Numerical Linear Algebra App

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This article proposes a structure‐preserving quaternion full orthogonalization method (QFOM) for solving quaternion linear systems arising from color image restoration. The method is based on the quaternion Arnoldi procedure preserving the quaternion Hessenberg form. Combining with the preconditioning techniques, we further derive a variant of the QFOM for solving the linear systems, which can greatly improve the rate of convergence of QFOM. Numerical experiments on randomly generated data and color image restoration problems illustrate the effectiveness of the proposed algorithms in comparison with some existing methods.

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Color Image Restoration by Saturation-Value Total Variation

Cited by 72 publications

References 26 publications

TVOR: Finding Discrete Total Variation Outliers Among Histograms

TVOR: Finding Discrete Total Variation Outliers Among Histograms

Saturation-Value Total Variation model for chromatic aberration correction

Structure preserving quaternion full orthogonalization method with applications

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