scholarly journals A New Fast Algorithm for Constrained Four-Directional Total Variation Image Denoising Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Fan Liao ◽  
Jean Louis Coatrieux ◽  
Jiasong Wu ◽  
Huazhong Shu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Signal To Noise Ratio ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Nonlocal Total Variation ◽  
Fast Gradient ◽  
Gradient Projection Methods ◽  
Generalized Variation

A new four-directional total variation (4-TV) model, applicable to isotropic and anisotropic TV functions, is proposed for image denoising. A dual based fast gradient projection algorithm for the constrained 4-TV image denoising problem is also reported which combines the well-known gradient projection and the fast gradient projection methods. Experimental results show that this model provides in most cases a better signal to noise ratio when compared to previous models like the reference TV, the total generalized variation, and the nonlocal total variation.

scholarly journals Variant Gradient Projection Methods for the Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Strong Convergence ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Projection Algorithms ◽  
Infinite Dimensional ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Gradient Projection Methods

The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu’s work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed.

A compensating total variation image denoising model combining L1 and L2 norm

2020 ◽  
pp. 002072092092330
Author(s):  
Liqiong Zhang ◽  
Min Li ◽  
Xiaohua Qiu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Structural Information ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Structural Similarity ◽  
Isotropic Diffusion ◽  
Model Combining ◽  
L2 Norm ◽  
Staircase Effect

To overcome the “staircase effect” while preserving the structural information such as image edges and textures quickly and effectively, we propose a compensating total variation image denoising model combining L1 and L2 norm. A new compensating regular term is designed, which can perform anisotropic and isotropic diffusion in image denoising, thus making up for insufficient diffusion in the total variation model. The algorithm first uses local standard deviation to distinguish neighborhood types. Then, the anisotropic diffusion based on L1 norm plays the role of edge protection in the strong edge region. The anisotropic and the isotropic diffusion simultaneously exist in the smooth region, so that the weak textures can be protected while overcoming the “staircase effect” effectively. The simulation experiments show that this method can effectively improve the peak signal-to-noise ratio and obtain the higher structural similarity index and the shorter running time.

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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