Image decomposition using adaptive second-order total generalized variation

Xu, Jianlou; Feng, Xiaoyi; Hu, Yan; Han, Yu

doi:10.1007/s11760-012-0420-3

Cited by 20 publications

(16 citation statements)

References 20 publications

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“…In Figure 7, we compare our denoising results with those of the TV-TV 2 h model [24] and OSV with TGV 2 h model [49]. The comparison shows that our denoising combined with decomposition denoises the texture part better than the other methods, while successfully preserving textures.…”

Section: Denoising Via Decomposition (A = I)mentioning

confidence: 99%

“…Note that the proposed TGV 2 h,h and TV-TV 2 h,h regularizers are different from the weighted second-order TGV regularizer in [49], which is incorporated with the OSV decomposition model, as…”

Section: 1mentioning

confidence: 99%

“…In [49] and [24], the edge function h is imposed to include both cartoon and texture edges. In our work, the function h is supposed to represent only the cartoon edges, so the regularizer TV-TV 2 h in (3.8) incorporated with our edge function h utilizes only the TV 2 term to extract a cartoon component.…”

Section: 1mentioning

confidence: 99%

“…The following process is similar to the algorithm in [49] proposed for the OSV model integrated with the TGV 2 h regularizer. By introducing dual variables p and q, the primal-dual formulation of the (primal) problem (A.4) is as follows: …”

Section: Appendix a Algorithm For Model (32) With Original Tgv (A =mentioning

confidence: 99%

“…Comparison of denoising results given by our model with TV-TV 2 h,h , and models in[24,49].SNR: (a) 24.60, (b) 24.46, (c) 26.15. (a) λ = 0.05, α0 = 0.5, (b) β = 0.2, α = 1.…”

mentioning

confidence: 99%

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Simultaneous Cartoon and Texture Image Restoration with Higher-Order Regularization

Jung¹,

Kang²

2015

SIAM J. Imaging Sci.

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This article introduces a variational color image decomposition and restoration model. The aim is to recover an image from its degraded version, while simultaneously decomposing the image into its cartoon and texture components. The energy involves adaptive higher-order regularizers, incorporated with an edge indicator function. This not only helps cartoon and texture decomposition, but also provides higher quality image restoration by ameliorating the staircasing effect that arises in total variation regularization methods. To realize the proposed models, we present fast and efficient iterative algorithms based on a variable splitting scheme and an augmented Lagrangian method. A convergence analysis of the proposed algorithms is also presented under certain conditions. Numerical results and comparisons demonstrate that the proposed model is more effective than state-of-the-art methods for both image decomposition and restoration.

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Section: Denoising Via Decomposition (A = I)mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

Section: Appendix a Algorithm For Model (32) With Original Tgv (A =mentioning

confidence: 99%

“…Comparison of denoising results given by our model with TV-TV 2 h,h , and models in[24,49].SNR: (a) 24.60, (b) 24.46, (c) 26.15. (a) λ = 0.05, α0 = 0.5, (b) β = 0.2, α = 1.…”

mentioning

confidence: 99%

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Simultaneous Cartoon and Texture Image Restoration with Higher-Order Regularization

Jung¹,

Kang²

2015

SIAM J. Imaging Sci.

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Gibbs ringing in diffusion MRI

Veraart

Fieremans

Jelescu

et al. 2015

Magnetic Resonance in Med

120

104

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Purpose To study and reduce the effect of Gibbs ringing artifact on computed diffusion parameters. Methods We reduce the ringing by extrapolating the k-space of each diffusion weighted image beyond the measured part by selecting an adequate regularization term. We evaluate several regularization terms and tune the regularization parameter to find the best compromise between anatomical accuracy of the reconstructed image and suppression of the Gibbs artifact. Results We demonstrate empirically and analytically that the Gibbs artifact, which is typically observed near sharp edges in magnetic resonance images, has a significant impact on the quantification of diffusion model parameters, even for infinitesimal diffusion weighting. We find the second order total generalized variation to be a good choice for the penalty term to regularize the extrapolation of the k-space, as it provides a parsimonious representation of images, a practically full suppression of Gibbs ringing, and the absence of staircasing artifacts typical for total variation methods. Conclusions Regularized extrapolation of the k-space data significantly reduces truncation artifacts without compromising spatial resolution in comparison to the default option of window filtering. In particular, accuracy of estimating diffusion tensor imaging and diffusion kurtosis imaging parameters improves so much that unconstrained fits become possible.

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Structure–texture image decomposition via non-convex total generalized variation and convolutional sparse coding

Wang

Liu

2022

Vis Comput

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Image decomposition using adaptive second-order total generalized variation

Cited by 20 publications

References 20 publications

Simultaneous Cartoon and Texture Image Restoration with Higher-Order Regularization

Simultaneous Cartoon and Texture Image Restoration with Higher-Order Regularization

Gibbs ringing in diffusion MRI

Structure–texture image decomposition via non-convex total generalized variation and convolutional sparse coding

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