Total Variation with Overlapping Group Sparsity for Removing Mixed Noise

2018 ◽  
pp. 223-235
Author(s):  
Jin-Jin Mei ◽  
Ting-Zhu Huang
Keyword(s):  
Total Variation ◽  
Group Sparsity ◽  
Overlapping Group Sparsity ◽  
Mixed Noise

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

Total variation with modified group sparsity for CT reconstruction under low SNR

2021 ◽  
pp. 1-18
Author(s):  
Lingli Zhang
Keyword(s):  
Total Variation ◽  
Signal To Noise Ratio ◽  
Gaussian Kernel ◽  
Reconstruction Technique ◽  
Ct Reconstruction ◽  
Group Sparsity ◽  
Low Snr ◽  
Overlapping Group Sparsity ◽  
Weighted Factor ◽  
Tv Model

BACKGROUND AND OBJECTIVE: Since the stair artifacts may affect non-destructive testing (NDT) and diagnosis in the later stage, an applicable model is desperately needed, which can deal with the stair artifacts and preserve the edges. However, the classical total variation (TV) algorithm only considers the sparsity of the gradient transformed image. The objective of this study is to introduce and test a new method based on group sparsity to address the low signal-to-noise ratio (SNR) problem. METHODS: This study proposes a weighted total variation with overlapping group sparsity model. This model combines the Gaussian kernel and overlapping group sparsity into TV model denoted as GOGS-TV, which considers the structure sparsity of the image to be reconstructed to deal with the stair artifacts. On one hand, TV is the accepted commercial algorithm, and it can work well in many situations. On the other hand, the Gaussian kernel can associate the points around each pixel. Quantitative assessments are implemented to verify this merit. RESULTS: Numerical simulations are performed to validate the presented method, compared with the classical simultaneous algebraic reconstruction technique (SART) and the state-of-the-art TV algorithm. It confirms the significantly improved SNR of the reconstruction images both in suppressing the noise and preserving the edges using new GOGS-TV model. CONCLUSIONS: The proposed GOGS-TV model demonstrates its advantages to reduce stair artifacts especially in low SNR reconstruction because this new model considers both the sparsity of the gradient image and the structured sparsity. Meanwhile, the Gaussian kernel is utilized as a weighted factor that can be adapted to the global distribution.

scholarly journals Impulse Noise Denoising Using Total Variation with Overlapping Group Sparsity and Lp-Pseudo-Norm Shrinkage

2018 ◽  
Vol 8 (11) ◽  
pp. 2317 ◽  
Author(s):  
Lingzhi Wang ◽  
Yingpin Chen ◽  
Fan Lin ◽  
Yuqun Chen ◽  
Fei Yu ◽  
...  
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Random Noise ◽  
Group Sparsity ◽  
L1 Norm ◽  
New Model ◽  
Staircase Effect ◽  
Overlapping Group Sparsity ◽  
The Difference ◽  
Tv Model

Models based on total variation (TV) regularization are proven to be effective in removing random noise. However, the serious staircase effect also exists in the denoised images. In this study, two-dimensional total variation with overlapping group sparsity (OGS-TV) is applied to images with impulse noise, to suppress the staircase effect of the TV model and enhance the dissimilarity between smooth and edge regions. In the traditional TV model, the L1-norm is always used to describe the statistics characteristic of impulse noise. In this paper, the Lp-pseudo-norm regularization term is employed here to replace the L1-norm. The new model introduces another degree of freedom, which better describes the sparsity of the image and improves the denoising result. Under the accelerated alternating direction method of multipliers (ADMM) framework, Fourier transform technology is introduced to transform the matrix operation from the spatial domain to the frequency domain, which improves the efficiency of the algorithm. Our model concerns the sparsity of the difference domain in the image: the neighborhood difference of each point is fully utilized to augment the difference between the smooth and edge regions. Experimental results show that the peak signal-to-noise ratio, the structural similarity, the visual effect, and the computational efficiency of this new model are improved compared with state-of-the-art denoising methods.

scholarly journals Non-Convex High Order Total Variation With Overlapping Group Sparsity Denoising Model Under Cauchy Noise

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 49901-49911
Author(s):  
Jianguang Zhu ◽  
Haijun Lv ◽  
Binbin Hao ◽  
Jianwen Peng
Keyword(s):  
Total Variation ◽  
High Order ◽  
Group Sparsity ◽  
Overlapping Group Sparsity
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