A conditional gradient method for primal-dual total variation-based image denoising

The total variation (TV) model has been studied extensively because it is able to preserve sharp attributes and capture some sparsely critical information in images. However, TV denoising problem is usually ill-conditioned that the classical monotone projected gradient method cannot solve the problem efficiently. Therefore, a new strategy based on nonmonotone approach is digged out as accelerated spectral project gradient (ASPG) for solving TV. Furthermore, traditional TV is handled by vectorizing, which makes the scheme far more complicated for designing algorithms. In order to simplify the computing process, a new technique is developed in view of matrix rather than traditional vector. Numerical results proved that our ASPG algorithm is better than some state-of-the-art algorithms in both accuracy and convergence speed.

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A nonmonotone adaptive projected gradient method for primal-dual total variation image restoration

Signal Processing ◽

10.1016/j.sigpro.2014.02.025 ◽

2014 ◽

Vol 103 ◽

pp. 242-249 ◽

Cited By ~ 7

Author(s):

Gaohang Yu ◽

Wei Xue ◽

Yi Zhou

Keyword(s):

Image Restoration ◽

Total Variation ◽

Gradient Method ◽

Projected Gradient Method ◽

Projected Gradient ◽

Primal Dual

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An efficient method for adapting step-size parameters of primal-dual hybrid gradient method in application to total variation regularization

2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC) ◽

10.1109/apsipa.2017.8282164 ◽

2017 ◽

Cited By ~ 2

Author(s):

Tatsuya Yokota ◽

Hidekata Hontani

Keyword(s):

Total Variation ◽

Efficient Method ◽

Gradient Method ◽

Total Variation Regularization ◽

Step Size ◽

Primal Dual

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Total variation regularization for seismic waveform inversion using an adaptive primal dual hybrid gradient method

Inverse Problems ◽

10.1088/1361-6420/aaaf8e ◽

2018 ◽

Vol 34 (4) ◽

pp. 045006 ◽

Cited By ~ 12

Author(s):

Peng Yong ◽

Wenyuan Liao ◽

Jianping Huang ◽

Zhenchuan Li

Keyword(s):

Total Variation ◽

Gradient Method ◽

Waveform Inversion ◽

Total Variation Regularization ◽

Seismic Waveform ◽

Primal Dual

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Primal-dual method to smoothing TV-based model for image denoising

Journal of Algorithms & Computational Technology ◽

10.1177/1748301816656298 ◽

2016 ◽

Vol 10 (4) ◽

pp. 235-243 ◽

Cited By ~ 7

Author(s):

Zhanjiang Zhi ◽

Baoli Shi ◽

Yi Sun

Keyword(s):

Image Processing ◽

Convergence Analysis ◽

Image Denoising ◽

Total Variation ◽

Dual Method ◽

Splitting Scheme ◽

Prior Model ◽

Processing Problem ◽

Proposed Model ◽

Primal Dual

The total variation-based Rudin–Osher–Fatemi model is an effective and popular prior model in the image processing problem. Different to frequently using the splitting scheme to directly solve this model, we propose the primal dual method to solve the smoothing total variation-based Rudin–Osher–Fatemi model and give some convergence analysis of proposed method. Numerical implements show that our proposed model and method can efficiently improve the numerical results compared with the Rudin–Osher–Fatemi model.

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Fractional-Order Total Variation Image Restoration Based on Primal-Dual Algorithm

Abstract and Applied Analysis ◽

10.1155/2013/585310 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 15

Author(s):

Dali Chen ◽

YangQuan Chen ◽

Dingyu Xue

Keyword(s):

Convergence Rate ◽

Saddle Point ◽

Image Denoising ◽

Total Variation ◽

Fractional Order ◽

Numerical Procedure ◽

Saddle Point Problem ◽

Point Problem ◽

Dual Algorithm ◽

Primal Dual

This paper proposes a fractional-order total variation image denoising algorithm based on the primal-dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, convergence rate, and blocky effect. The fractional-order total variation model is introduced by generalizing the first-order model, and the corresponding saddle-point and dual formulation are constructed in theory. In order to guaranteeO1/N2convergence rate, the primal-dual algorithm was used to solve the constructed saddle-point problem, and the final numerical procedure is given for image denoising. Finally, the experimental results demonstrate that the proposed methodology avoids the blocky effect, achieves state-of-the-art performance, and guaranteesO1/N2convergence rate.

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