scholarly journals A Nonmonotone Gradient Algorithm for Total Variation Image Denoising Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Peng Wang ◽  
Shifang Yuan ◽  
Xiangyun Xie ◽  
Shengwu Xiong
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Gradient Method ◽  
State Of The Art ◽  
Gradient Algorithm ◽  
Projected Gradient Method ◽  
New Strategy ◽  
A New Technique ◽  
Tv Model ◽  
Better Than

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.

scholarly journals Image Denoising viaL0Gradient Minimization with Effective Fidelity Term

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Wenxue Zhang ◽  
Yongzhen Cao ◽  
Rongxin Zhang ◽  
Lingling Li ◽  
Yunlei Wen
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
State Of The Art ◽  
Least Square Method ◽  
Least Square ◽  
Image Smoothing ◽  
Piecewise Constant ◽  
Moving Least Square ◽  
Fidelity Term ◽  
Tv Model

TheL0gradient minimization (LGM) method has been proposed for image smoothing very recently. As an improvement of the total variation (TV) model which employs theL1norm of the gradient, the LGM model yields much better results for the piecewise constant image. However, just as the TV model, the LGM model also suffers, even more seriously, from the staircasing effect and the inefficiency in preserving the texture in image. In order to overcome these drawbacks, in this paper, we propose to introduce an effective fidelity term into the LGM model. The fidelity term is an exemplar of the moving least square method using steering kernel. Under this framework, these two methods benefit from each other and can produce better results. Experimental results show that the proposed scheme is promising as compared with the state-of-the-art methods.

scholarly journals New hybrid conjugate gradient method as a convex combination of FR and PRP methods

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3083-3100 ◽  
Author(s):  
Snezana Djordjevic
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Numerical Comparisons ◽  
Hybrid Conjugate Gradient Method ◽  
Better Than

We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

scholarly journals Local and Nonlocal Steering Kernel Weighted Total Variation Model for Image Denoising

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 329 ◽  
Author(s):  
Rui Lai ◽  
Yiguo Mo ◽  
Zesheng Liu ◽  
Juntao Guan
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Noise Suppression ◽  
Nonlocal Symmetry ◽  
Visual Appearance ◽  
Quantitative Indices ◽  
Proposed Model ◽  
Total Variation Model ◽  
Weighted Total Variation ◽  
Tv Model

To eliminate heavy noise and retain more scene details, we propose a structure-oriented total variation (TV) model based on data dependent kernel function and TV criterion for image denoising application. The innovative model introduces the weights produced from the local and nonlocal symmetry features involved in the image itself to pick more precise solutions in the TV denoising process. As a result, the proposed local and nonlocal steering kernel weighted TV model yields excellent noise suppression and structure-preserving performance. The experimental results verify the validity of the proposed model in objective quantitative indices and subjective visual appearance.

scholarly journals Algorithmic versatility of SPF-regularization methods

2020 ◽  
Vol 19 (01) ◽  
pp. 43-69
Author(s):  
Lixin Shen ◽  
Bruce W. Suter ◽  
Erin E. Tripp
Keyword(s):  
Recent Work ◽  
Image Denoising ◽  
Total Variation ◽  
Optimization Problems ◽  
Regularization Methods ◽  
Moreau Envelope ◽  
The Difference ◽  
Tv Model

Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are sparse in some basis. For example, the [Formula: see text]-regularized wavelet model and the Rudin–Osher–Fatemi total variation (ROF-TV) model are some of the most well-known models for signal and image denoising, respectively. However, recent work demonstrates that convexity is not always desirable in SPFs. In this paper, we replace convex SPFs with their induced nonconvex SPFs and develop algorithms for the resulting model by exploring the intrinsic structures of the nonconvex SPFs. These functions are defined as the difference of the convex SPF and its Moreau envelope. We also present simulations illustrating the performance of a special SPF and the developed algorithms in image denoising.

scholarly journals Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Liang Ding ◽  
Hui Zhao ◽  
Yixin Dou
Keyword(s):  
Gradient Method ◽  
Numerical Solutions ◽  
Impulsive Noise ◽  
Gradient Algorithm ◽  
Sparse Signal ◽  
Projected Gradient Method ◽  
Projected Gradient ◽  
Regularization Term ◽  
Spectral Projected Gradient ◽  
Signal Inversion

We consider sparse signal inversion with impulsive noise. There are three major ingredients. The first is regularizing properties; we discuss convergence rate of regularized solutions. The second is devoted to the numerical solutions. It is challenging due to the fact that both fidelity and regularization term lack differentiability. Moreover, for ill-conditioned problems, sparsity regularization is often unstable. We propose a novel dual spectral projected gradient (DSPG) method which combines the dual problem of multiparameter regularization with spectral projection gradient method to solve the nonsmooth l1+l1 optimization functional. We show that one can overcome the nondifferentiability and instability by adding a smooth l2 regularization term to the original optimization functional. The advantage of the proposed functional is that its convex duality reduced to a constraint smooth functional. Moreover, it is stable even for ill-conditioned problems. Spectral projected gradient algorithm is used to compute the minimizers and we prove the convergence. The third is numerical simulation. Some experiments are performed, using compressed sensing and image inpainting, to demonstrate the efficiency of the proposed approach.

Block wavelet threshold image denoising on total variation

2013 ◽  
Vol 32 (5) ◽  
pp. 1289-1292
Author(s):  
Yuan-yuan GAO ◽  
Yong-feng DIAO ◽  
Yun BIAN
Keyword(s):  
Image Denoising ◽  
Total Variation

A new technique for guided filter based image denoising using modified cuckoo search optimization

2021 ◽  
Vol 176 ◽  
pp. 114884
Author(s):  
Himanshu Singh ◽  
Sethu Venkata Raghavendra Kommuri ◽  
Anil Kumar ◽  
Varun Bajaj
Keyword(s):  
Image Denoising ◽  
Cuckoo Search ◽  
New Technique ◽  
Guided Filter ◽  
Search Optimization ◽  
Cuckoo Search Optimization ◽  
A New Technique
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