Directional total generalized variation regularization

Kongskov, Rasmus Dalgas; Dong, Yiqiu; Knudsen, Kim

doi:10.1007/s10543-019-00755-6

Cited by 36 publications

(41 citation statements)

References 38 publications

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“…A very popular algorithm to solve such saddle point problems is the primal-dual hybrid gradient (PDHG) 1 algorithm [36,20,12,35,13,14]. It has been used to solve a vast amount of stateof-the-art problems-to name a few examples in imaging: image denoising with the structure tensor [21], total generalized variation denoising [10], dynamic regularization [6], multi-modal medical imaging [26], multi-spectral medical imaging [42], computation of non-linear eigenfunctions [25], regularization with directional total generalized variation [28]. Its popularity stems from two facts: First, it is very simple and therefore easy to implement.…”

mentioning

confidence: 99%

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Chambolle¹,

Ehrhardt²,

Richtárik³

et al. 2018

SIAM J. Optim.

144

226

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We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.

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mentioning

confidence: 99%

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Chambolle¹,

Ehrhardt²,

Richtárik³

et al. 2018

SIAM J. Optim.

144

226

View full text Add to dashboard Cite

show abstract

“…We note that problem ( 6 ) is a nonsmooth convex optimization problem because of the properties of the KL divergence (see, e.g., [ 11 ]) and the DTGV operator (see, e.g., [ 10 ]).…”

Section: The Kl-dtgv Modelmentioning

confidence: 99%

“…On the other hand, to improve the quality of restoration for directional images, the Directional TV (DTV) regularization has been considered in [ 8 ], in the discrete setting. In [ 9 , 10 ], a regularizer combining DTV and TGV, named Directional TGV (DTGV), has been successfully applied to directional images affected by impulse and Gaussian noise.…”

Section: Introductionmentioning

confidence: 99%

“…In this work we focus on directional images affected by Poisson noise, with the aim of assessing the behaviour of DTGV in this case. Besides extending the use of DTGV to Poisson noise, we introduce a novel technique for estimating the main direction of the image, which appears to be more efficient than the techniques applied in [ 9 , 10 ]. We solve the resulting optimization problem by using a customized version of the Alternating Direction Method of Multipliers (ADMM).…”

Section: Introductionmentioning

confidence: 99%

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Directional TGV-Based Image Restoration under Poisson Noise

2021

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We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.

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“…Those models have been widely adopted to image segmentation, image restoration, image inpainting, etc. Higher order total directional variation (HTDV) [26], [27] and directional TGV: HDTGV [28] are extensions of anisotropic diffusion [29] via Hessian and directions, as…”

Section: Introductionmentioning

confidence: 99%

Two Variational Models for Image Denoising Using Jacobian of Normals

2021

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Variational models with second order regularizers can efficiently overcome the problems of staircasing effects caused by first order models. However, different types of second order regularizers may lead to different properties of feature preserving in restored images. In this paper, we show two variational models with second order regularizers. The first one is bounded Hessian model with Jacobian of normals, which uses bounded Jacobian of image intensity normals as regularizer, it is an extension of classical bounded Hessian (BH) model. The second one is total generalized variation model with Jacobian of normals, which is an extension to total generalized variation (TGV) model by replacing gradients in TGV with normals. The common objective is to improve feature preserving, such as edge, contrast and smoothness preservation. Additionally, their Alternating Direction Method of Multipliers (ADMM) are designed by introducing some proper auxiliary variables, Lagrange multipliers and penalty parameters to decompose the original models into some simple minimization sub-problems to solve. Extensive comparisons demonstrate that the proposed models are superior to the classical models with Hessian and TGV regularizers, especially in edge and corner preservation, smoothness, contrast enhancement. Moreover, the proposed models can be also extended to image inpainting, deblurring, and image enhancement.

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Directional total generalized variation regularization

Cited by 36 publications

References 38 publications

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Directional TGV-Based Image Restoration under Poisson Noise

Two Variational Models for Image Denoising Using Jacobian of Normals

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