Image Denoising with Overlapping Group Sparsity and Second Order Total Variation Regularization

2019 ◽  
Author(s):  
Nguyen Minh Hue ◽  
Dang N. H. Thanh ◽  
Le Thi Thanh ◽  
Nguyen Ngoc Hien ◽  
V. B. Surya Prasath
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Second Order ◽  
Total Variation Regularization ◽  
Group Sparsity ◽  
Overlapping Group Sparsity

scholarly journals Seismic impedance inversion using second-order overlapping group sparsity with A-ADMM

2019 ◽  
Vol 17 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Hao Wu ◽  
Shu Li ◽  
Yingpin Chen ◽  
Zhenming Peng
Keyword(s):  
Total Variation ◽  
Second Order ◽  
Inversion Method ◽  
Structured Sparsity ◽  
Group Sparsity ◽  
Order Difference ◽  
Impedance Inversion ◽  
Staircase Effect ◽  
Overlapping Group Sparsity ◽  
Anisotropic Total Variation

Abstract The anisotropic total variation with overlapping group sparsity (ATV_OGS) regularisation term is an improvement on the anisotropic total variation (ATV) regularisation term. It has been employed successfully in seismic impedance inversion as it can enhance the boundary information and relieve the staircase effect by exploring the structured sparsity of seismic impedance. However, because ATV_OGS constrains only the structured sparsity of the impedance's first-order difference and ignores the structured sparsity of the second-order difference, the staircase effect still occurs in an inversion result based on ATV_OGS. To further fit the structured sparsity of the impedance's second-order gradients, we introduce the overlapping group sparsity into the second-order difference of the impedance and propose a novel second-order ATV with overlapping group sparsity (SATV_OGS) seismic impedance inversion method. The proposed method reduces the interference of the large amplitude noise and further mitigates the staircase effect of the ATV_OGS. Furthermore, the accelerated alternating direction method of multipliers (A-ADMM) framework applied to this novel method. It can increase the efficiency of inversion. The experiments are carried out on a general model data and field data. Based on the experimental results, the proposed method can obtain higher resolution impedance than some impedance inversion methods based on total variation.

Total variation with overlapping group sparsity for speckle noise reduction

2016 ◽  
Vol 216 ◽  
pp. 502-513 ◽  
Author(s):  
Jun Liu ◽  
Ting-Zhu Huang ◽  
Gang Liu ◽  
Si Wang ◽  
Xiao-Guang Lv
Keyword(s):  
Noise Reduction ◽  
Total Variation ◽  
Speckle Noise ◽  
Group Sparsity ◽  
Overlapping Group Sparsity ◽  
Speckle Noise Reduction

Total variation with overlapping group sparsity for deblurring images under Cauchy noise

2019 ◽  
Vol 341 ◽  
pp. 128-147 ◽  
Author(s):  
Meng Ding ◽  
Ting-Zhu Huang ◽  
Si Wang ◽  
Jin-Jin Mei ◽  
Xi-Le Zhao
Keyword(s):  
Total Variation ◽  
Group Sparsity ◽  
Overlapping Group Sparsity

Four-directional fractional-order total variation regularization for image denoising

2017 ◽  
Vol 26 (05) ◽  
pp. 1 ◽  
Author(s):  
Linna Wu ◽  
Yingpin Chen ◽  
Jiaquan Jin ◽  
Hongwei Du ◽  
Bensheng Qiu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Fractional Order ◽  
Total Variation Regularization

scholarly journals An Adaptive Image Denoising Model Based on Tikhonov and TV Regularizations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kui Liu ◽  
Jieqing Tan ◽  
Benyue Su
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Tikhonov Regularization ◽  
Experimental Results ◽  
Total Variation Regularization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Gradient Information ◽  
Weighted Combination ◽  
Staircase Artifacts

To avoid the staircase artifacts, an adaptive image denoising model is proposed by the weighted combination of Tikhonov regularization and total variation regularization. In our model, Tikhonov regularization and total variation regularization can be adaptively selected based on the gradient information of the image. When the pixels belong to the smooth regions, Tikhonov regularization is adopted, which can eliminate the staircase artifacts. When the pixels locate at the edges, total variation regularization is selected, which can preserve the edges. We employ the split Bregman method to solve our model. Experimental results demonstrate that our model can obtain better performance than those of other models.

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