Image Restoration by a Mixed High-Order Total Variation and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> Regularization Model

Zhu, Jianguang; Li, Kai; Hao, Bin

doi:10.1155/2018/6538610

Cited by 8 publications

(7 citation statements)

References 64 publications

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“…It is obvious that when θ = , φ θ reduces to the famous CHKS smoothing function, θ = , φ θ reduces to the famous Fischer-Burmeister smoothing function. As we all know, these two smoothing functions and their variants have been widely used in designing smoothing-type methods for solving mathematical programming problems, such as the nonlinear complementarity problems (NCPs) [16][17][18][19][20][21][22], the second-order cone complementarity problems(SOCCPs) [23][24][25][26][27][28][29], the second-order cone programming (SOCP) [30][31][32][33][34][35][36][37][38][39].…”

Section: Smoothing Function and Its Propertiesmentioning

confidence: 99%

A new smoothing method for solving nonlinear complementarity problems

Zhu

Hao

2019

Open Mathematics

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In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

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Section: Smoothing Function and Its Propertiesmentioning

confidence: 99%

A new smoothing method for solving nonlinear complementarity problems

Zhu

Hao

2019

Open Mathematics

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“…To address this issue, blind deconvolution [2] is often used in the literature to estimate the original image and the PSF from the blurred image, g ( x,y ). Several techniques, such as maximum likelihood method [3], simulated annealing [4], Richardson–Lucy algorithm [5], and total variation [6, 7], are proposed to solve this problem. However, many of these algorithms are iterative or recursive thus they are potentially unstable, divergent and time‐consuming.…”

Section: Introductionmentioning

confidence: 99%

Non‐iterative blind deconvolution algorithm based on power‐law distribution

Gao

Yang

et al. 2020

IET image process

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The spectral amplitude of most natural images is approximately isotropic and follows the power law. In this study, the authors propose a new non‐iterative blind image deconvolution algorithm that builds an isosceles curve model to approximate the spectrum amplitude of the real image. In the authors’ proposed algorithm, the optical transfer function (OTF) is obtained by comparing the reconstructed and degraded spectra. Then they employ the integrated multidirectional comprehensive estimation to reduce the OTF estimation error. The restored image is then obtained by applying the estimated OTF and the Wiener filter. Experiments on image deconvolution tasks indicate that the proposed algorithm provides a significant performance gain by obtaining an accurate OTF, reducing ringing artefacts compared with existing algorithms, and realising real‐time image restoration.

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“…Staircase solutions developed false edges that do not exist in the true image. To alleviate this drawback, many improved variation models have been proposed, such as high-order TV regularization methods [29][30][31] and fractional order TV model. [32][33][34][35] Combining the first-order and second-order TV regularizations, Papafitsoros and Schönlieb 36 proposed a hybrid variational model.…”

Section: Introductionmentioning

confidence: 99%

Restoration of remote sensing images based on nonconvex constrained high-order total variation regularization

Zhu

Hao

2019

J. Appl. Rem. Sens.

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Convex total variation (TV) regularization models have been widely used in remote sensing image restoration problems; however, these models tend to produce staircase effects. We consider a nonconvex second-order TV regularization model with linear constraints for remote sensing image restoration. To solve the nonconvex second-order TV regularization model, we propose an efficient alternating minimization algorithm based on generalized iterated shrinkage algorithm and alternating direction method of multipliers. Experimental results demonstrate the effectiveness of the proposed model, which can reduce staircase effects while preserving edges. In terms of signal-to-noise ratio and structural similarity index measure, the experimental results show that our proposed model and algorithm can give better performance compared with some state-of-the-art methods.

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Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

Cited by 8 publications

References 64 publications

A new smoothing method for solving nonlinear complementarity problems

A new smoothing method for solving nonlinear complementarity problems

Non‐iterative blind deconvolution algorithm based on power‐law distribution

Restoration of remote sensing images based on nonconvex constrained high-order total variation regularization

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