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.

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 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.

scholarly journals Total Variation with Overlapping Group Sparsity for Image Deblurring under Impulse Noise

PLoS ONE ◽  
2015 ◽  
Vol 10 (4) ◽  
pp. e0122562 ◽  
Author(s):  
Gang Liu ◽  
Ting-Zhu Huang ◽  
Jun Liu ◽  
Xiao-Guang Lv
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Image Deblurring ◽  
Group Sparsity ◽  
Overlapping Group Sparsity

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

scholarly journals Image Deblurring under Impulse Noise via Total Generalized Variation and Non-Convex Shrinkage

Algorithms ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 221
Author(s):  
Lin ◽  
Chen ◽  
Chen ◽  
Yu
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Signal To Noise Ratio ◽  
Image Deblurring ◽  
L1 Norm ◽  
Signal To Noise ◽  
Total Generalized Variation ◽  
First Order ◽  
Norm Constraint ◽  
Generalized Variation

Image deblurring under the background of impulse noise is a typically ill-posed inverse problem which attracted great attention in the fields of image processing and computer vision. The fast total variation deconvolution (FTVd) algorithm proved to be an effective way to solve this problem. However, it only considers sparsity of the first-order total variation, resulting in staircase artefacts. The L1 norm is adopted in the FTVd model to depict the sparsity of the impulse noise, while the L1 norm has limited capacity of depicting it. To overcome this limitation, we present a new algorithm based on the Lp-pseudo-norm and total generalized variation (TGV) regularization. The TGV regularization puts sparse constraints on both the first-order and second-order gradients of the image, effectively preserving the image edge while relieving undesirable artefacts. The Lp-pseudo-norm constraint is employed to replace the L1 norm constraint to depict the sparsity of the impulse noise more precisely. The alternating direction method of multipliers is adopted to solve the proposed model. In the numerical experiments, the proposed algorithm is compared with some state-of-the-art algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), signal-to-noise ratio (SNR), operation time, and visual effects to verify its superiority.

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