Image Denoising Using TV-Stokes Equation with an Orientation-Matching Minimization

Tai, Xue–Cheng; Borok, Sofia; Hahn, Jooyoung

doi:10.1007/978-3-642-02256-2_41

Cited by 11 publications

(8 citation statements)

References 16 publications

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“…We observe that the features of the Cameraman image such as the face of the man and the tripod are sharper in the difference image generated by TVS − L 2 + TVn − L 2 . It justifies the use of the new minimization function in (15).…”

Section: Image Denoisingmentioning

confidence: 95%

“…Next, we compare our regularization method (15) with previous models such as (5)-(6) and (8). The regularization terms in (5) and (6) are related to both |∇u| and the angle θ .…”

Section: Image Reconstruction Based On the Estimated Tangential Vectormentioning

confidence: 99%

“…Authors in [15,20] pointed out that the value of |∇u| influences the angle θ , and it may derive an erroneous effect near edges where |∇u| is large. Therefore, a new regularization term which is only orientation-matching minimization was proposed in the second step…”

mentioning

confidence: 98%

“…Recently, two-step models which reduce a high order problem into two second order problems seem to become one of the most efficient models in image denoising [11][12][13][14][15]. The basic method is to decompose the restoration process into two separate procedures: estimating derivatives of the original image and producing an image whose derivatives fit to the estimated ones.…”

mentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Image Denoisingmentioning

confidence: 95%

“…Next, we compare our regularization method (15) with previous models such as (5)-(6) and (8). The regularization terms in (5) and (6) are related to both |∇u| and the angle θ .…”

Section: Image Reconstruction Based On the Estimated Tangential Vectormentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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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, some variants of the LOT method have also been studied, in [15][16][17]. But all of these models suffer from complicated implementations which are especially obvious in the first step (1.7).…”

Section: Introductionmentioning

confidence: 99%

A two-step model for image denoising using a duality strategy and surface fitting

Pang

Yang

2010

Journal of Computational and Applied Mathematics

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a b s t r a c tIn order to alleviate the staircase effect or the edge blurring in the course of the image denoising, we propose a two-step model based on the duality strategy. In fact, this strategy follows the observation that the dual variable of the restored image can be looked at as the normal vector. So we first obtain the dual variable and then reconstruct the image by fitting the dual variable. Following the augmented Lagrangian strategy, we propose a projection gradient method for solving this two-step model. We also give some convergence analyses of the proposed projection gradient method. Several numerical experiments are tested to compare our proposed model with the ROF model and the LLT model. Crown

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Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

Rahman

Tai

2018

Mathematics and Visualization

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Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured geometries, is considered in this paper. A new model has been proposed which is based on the idea of using normal vector matching combined with a first order and a second order total variation regularizers. A fast algorithm based on the augmented Lagrangian is also proposed. Numerical experiments are provided showing the effectiveness of the model and the algorithm in reconstructing surfaces with detailed features and complex structures for both synthetic and real world digital maps.

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Image Denoising Using TV-Stokes Equation with an Orientation-Matching Minimization

Cited by 11 publications

References 16 publications

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

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

A two-step model for image denoising using a duality strategy and surface fitting

Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

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