Restoration of images based on subspace optimization accelerating augmented Lagrangian approach

Chen, Dai-Qiang; Cheng, Lizhi; Su, Fang

doi:10.1016/j.cam.2010.11.028

Cited by 7 publications

(11 citation statements)

References 29 publications

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“…It is closely related to the DRS (Douglas-Rachford splitting) algorithm [27,32] and the alternating direction method [14,28]. For more details about these algorithms refer to [29].…”

Section: Relationship With Previous Methodsmentioning

confidence: 99%

A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

2011

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In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.

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“…It is closely related to the DRS (Douglas-Rachford splitting) algorithm [27,32] and the alternating direction method [14,28]. For more details about these algorithms refer to [29].…”

Section: Relationship With Previous Methodsmentioning

confidence: 99%

A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

2011

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“…Recently, as a fast and accurate algorithm, the augmented Lagrangian method is widely used for variational models in image processing [25][26][27][28]. It is closely related to the DRS (Douglas-Rachford splitting) algorithm [29] and the alternating direction method.…”

Section: Iterative Algorithm Based On the Augmented Lagrangian Methodsmentioning

confidence: 99%

A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution

Chen

Cheng

2011

J Sci Comput

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Recently, TV-Stokes model has been widely researched for various image processing tasks such as denoising and inpainting. In this paper, we introduce a new TV-Stokes model for image deconvolution, and propose fast and efficient iterative algorithms based on the augmented Lagrangian method. The new TV-Stokes model is a two-step model: in the first step, a smoothed and divergence free tangential field of the observed image is recovered based on total variation (TV) minimization and a new data fidelity term; in the second step, the image is reconstructed by minimizing the distance between the unit image gradient and the regularized unit normal direction. Numerical experiments demonstrate that the proposed model has the potential to outperform popular TV-based restoration methods in preserving texture details and fine structures. As a result, an improvement in signal-to-noise ratio (SNR) is obtained for deconvolution and denoising results.

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“…The main utilization of the collocation scheme used on equation 21is that the suggested meshless method displays the unique solution of (21) due to the MQ-RBF interpolation method employed in the collocation scheme which results in the preservation of the edges. Furthermore, the resultant smooth solution of equation 21is due to the weighted mean determined in equation (15) using the interpolation process which is based on the Euclidian distance between a noisy pixel and other non-noisy pixels obtained from equation (14) in the selected frame. Consequently, the smooth solution of the equation 21is responsible for image restoration, reducing the staircase effect, and preserving edges, textures, and image details.…”

Section: B Proposed Meshless Scheme M2mentioning

confidence: 99%

“…Therefore the classical numerical schemes unsuccessful to solve the PDE equation for the smooth solution, which produces staircase effects, textures, and degrading the fine details during the image denoising process. Some numerical scheme have been utilized by the researchers to minimize the above mentioned issues such as Augmented Lagrangian Method (ALM) [14], [15], Dual Method (DM) [16], Variable Splitting Based Method (VSBM) [17], and Alternating Direction Method of Multipliers (ADMM) [18]. But Still there is a space for improvement.…”

Section: Introductionmentioning

confidence: 99%

Total Variation Filter via Multiquadric Radial Basis Function Approximation Scheme for Additive Noise Removal

Khan¹,

Altamimi

Khan

et al. 2020

IEEE Access

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The Digital Total Variation (DTV) scheme is a digitized energy regularization scheme used for image denoising. This technique takes advantage of being applied to arbitrarily located data points and also has the edge detective property. This article aims to introduce a novel meshless scheme using DTV filtering and Radial Basis Functions (RBFs) to solve the associated equation with the DTV model numerically which results in the image denoising to remove additive noise from image information. This meshless algorithm based on local collocation and Multiquadric Radial Basis Function. These appearances allow this algorithm not only to remove the additive noise from images but also to resolve the discontinuities sharply. It is also noticed that the proposed meshless scheme is simple, fast, computationally effective, requires simply post-processing, and can be easily implemented mathematically. Experimental results confirm that the peak signal-to-noise ratio, the structural similarity, signal-to-noise ratio, the visual effect, and the computational performance of this new meshless scheme are improved compared with state-of-the-art denoising schemes. Furthermore, the proposed scheme can be applied to colour images as well.

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Restoration of images based on subspace optimization accelerating augmented Lagrangian approach

Cited by 7 publications

References 29 publications

A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution

Total Variation Filter via Multiquadric Radial Basis Function Approximation Scheme for Additive Noise Removal

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