Augmented Lagrangian Method for Generalized TV-Stokes Model

Hahn, Jooyoung; Wu, Chunlin

doi:10.1007/s10915-011-9482-6

Cited by 34 publications

(32 citation statements)

References 34 publications

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“…For more detailed description of the discretisation of other high order differential operators, we refer the reader to [3,4]. More advanced discretisation on a staggered grid can be found in [21,33,34]. Finally, we address the implementation problem of the first order derivatives of u σ in (2.7).…”

Section: Discretisation Of Differential Operatorsmentioning

confidence: 99%

Introducing diffusion tensor to high order variational model for image reconstruction

Duan

Ward

Sibbett

et al. 2017

Digital Signal Processing

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The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk JID:YDSPR AID:2153 /FLA [m5G; v1.219; Prn:17/07/2017; 11:02] Second order total variation (SOTV) models have advantages for image restoration over their first order counterparts including their ability to remove the staircase artefact in the restored image. However, such models tend to blur the reconstructed image when discretised for numerical solution [1][2][3][4][5]. To overcome this drawback, we introduce a new tensor weighted second order (TWSO) model for image restoration. Specifically, we develop a novel regulariser for the SOTV model that uses the Frobenius norm of the product of the isotropic SOTV Hessian matrix and an anisotropic tensor. We then adapt the alternating direction method of multipliers (ADMM) to solve the proposed model by breaking down the original problem into several subproblems. All the subproblems have closed-forms and can be solved efficiently. The proposed method is compared with state-of-the-art approaches such as tensor-based anisotropic diffusion, total generalised variation, and Euler's elastica. We validate the proposed TWSO model using extensive experimental results on a large number of images from the Berkeley BSDS500. We also demonstrate that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

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Section: Discretisation Of Differential Operatorsmentioning

confidence: 99%

Introducing diffusion tensor to high order variational model for image reconstruction

Duan

Ward

Sibbett

et al. 2017

Digital Signal Processing

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“…A simultaneous minimization could also be performed efficiently solving a 2×2 linear system of equations for each pixel in the frequency domain, see e.g., [64]. The Euler-Lagrange equations associated with the minimization with respect to d x and d y are…”

Section: E Minimization Wrt Dmentioning

confidence: 99%

Surface Reconstruction From Microscopic Images in Optical Lithography

Estellers

Thiran

Gabrani

2014

IEEE Trans. on Image Process.

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We propose a shape-from-shading method to reconstruct surfaces of silicon wafers from images of printed circuits taken with scanning electron microscope. Our method combines the physical model of the optical acquisition system with prior knowledge about the shapes of the patterns in the circuit. The reconstruction of the surface is formulated as an optimization problem with a combined criterion based on the irradiance equation and a shape prior that constrains the shape of the surface to agree with the expected shape of the pattern. To account for the variability of the manufacturing process, the model allows a non-linear elastic deformation between the expected patterns and the reconstructed surface. Our method provides two outputs: a reconstructed surface and a deformation field. The reconstructed surface is derived from the shading observed in the images and the prior knowledge about circuit patterns, which results in a shape-from-shading technique stable and robust to noise. The deformation field produces a mapping between the expected shape and the reconstructed surface, which provides a measure of deviation between the models and the real manufacturing process.

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“…Note that the difference operators appear in the second term of (13). As a consequence, (13) becomes a problem in the form of the TV-H1 model, which is different from the TV − L 2 model discussed in [12,14,19]. The proposed model is derived from Bayes rule, and hence is more reasonable for the estimation of the tangential vector.…”

Section: And Then We Getmentioning

confidence: 99%

“…2.3 in [19]. Since the incompressible condition is used in the first step, there exists an image u 1 such that…”

Section: Image Reconstruction Based On the Estimated Tangential Vectormentioning

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, 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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Augmented Lagrangian Method for Generalized TV-Stokes Model

Cited by 34 publications

References 34 publications

Introducing diffusion tensor to high order variational model for image reconstruction

Introducing diffusion tensor to high order variational model for image reconstruction

Surface Reconstruction From Microscopic Images in Optical Lithography

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

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