Augmented Lagrangian method for TV-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e1094" altimg="si5.gif"><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e1104" altimg="si6.gif"><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> based colo

Padcharoen, Anantachai; Martínez-Moreno, Juan

doi:10.1016/j.cam.2018.09.053

Cited by 24 publications

(8 citation statements)

References 8 publications

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“…To avoid any ringing artifacts close to image boundaries, we should perform valid convolution, for example, the output image is smaller and covers a region where both the convolution kernel and input image are fully defined. The TV regularizer [28] can help to reduce such artifacts. Therefore, the f -step performed with an overall O(N log N ) cost.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

Adaptive Optics Image Restoration via Regularization Priors With Gaussian Statistics

Qiu

Zhang

2020

IEEE Access

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In order to compensate for any failure on the use of point spread function (blur kernel) estimation and image estimation priors, we propose a novel regularization priors scheme with adapting the parameter for image restoration involving adaptive optics (AO) images. Our scheme uses a maximum a posteriori estimation with Gaussian statistics on the image and point spread function (blur kernel). An efficient regularization prior method associated with alternating minimization method is described to obtain the optimal solution recursively. Our method is applied to synthetic and real adaptive optics images. After applying our restoration method, satisfying results are obtained. Experimental results demonstrate that our proposed model and method performs better for restoring images in terms of both subjective results and objective assessments than the current state-of-the-art restoring methods. In addition, our proposed method can be a new way to promote their performances for AO image restoration.

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Section: Computational Complexity Analysismentioning

confidence: 99%

Adaptive Optics Image Restoration via Regularization Priors With Gaussian Statistics

Qiu

Zhang

2020

IEEE Access

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“…Due to the importance and interest of the problem, many researchers have developed iterative methods for solving , see, for example, References 2 and 6‐16 and the references therein. One popular method is the well‐known forward‐backward splitting method (FBM) introduced by Lions and Mercier 11 and Passty 12 .…”

Section: Introductionmentioning

confidence: 99%

Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems

Padcharoen

Kitkuan

Kumam

2020

Comp and Math Methods

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In this article, we offer two modifications of the modified forward‐backward splitting method based on inertial Tseng method and viscosity method for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak and strong convergence of the proposed algorithms. We give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for solving the image deblurring and image recovery problems. Our result extends some related works in the literature and the primary experiments might also suggest their potential applicability.

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“…Tseng proved the sequence {x n } generated by (3) converges weakly to an element of problem (2) in real Hilbert spaces provided that A is Lipschitz continuous and monotone and B is maximal monotone. In recent years, the forward-backward splitting method has received great attention by many authors, who improved it in various ways (, see Attouch et al (2018), Bauschke et al (2005), Bot and Csetnek (2016), Combettes and Wajs (2005), Combettes and Pesquet (2010), Cruz and Nghia (2016), Svaiter (2008, 2009), Gibali and Thong (2018), Huang and Dong (2014), Lions and Mercier (1979), Kitkuan et al (2018), Lorenz and Pock (2015), Moudafi and Oliny (2003), Raguet et al (2013), Padcharoen et al (2018), Tseng (2000), Thong and Hieu (2018a, b, c, d), Thong and Gibali (2018a, b), Zhang and Wang (2018), and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions

Thong

Cholamjiak

2019

Comp. Appl. Math.

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In this paper, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. To solve this problem, we propose a new modified forward-backward splitting method using the viscosity method (Moudafi in J Math Anal Appl 241(527):46-55, 2000). Under some mild conditions, we establish the strong convergence of the iterative sequence generated by the proposed algorithm. The advantage of our algorithm is that it does not require the co-coercivity of the single-valued operator. Our result improves related results in the literature. Finally, the performances of our proposed method are presented through numerical experiments in signal recovery. Keywords Forward-backward splitting method • Tseng's splitting method • Viscosity method • Zero point Mathematics Subject Classification 47H06 • 47H09 • 47H10 • 47J25 • 65K15 0 ∈ T x, (1) Dedicated to Professor Pham Ky Anh on the Occasion of his 70th Birthday. Communicated by F. T. Carlos Conca.

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Augmented Lagrangian method for TV-l1-l2 based colo

Cited by 24 publications

References 8 publications

Adaptive Optics Image Restoration via Regularization Priors With Gaussian Statistics

Adaptive Optics Image Restoration via Regularization Priors With Gaussian Statistics

Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems

Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions

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