scholarly journals An Iterative Regularization Method for Total Variation-Based Image Restoration

2005 ◽  
Vol 4 (2) ◽  
pp. 460-489 ◽  
Author(s):  
Stanley Osher ◽  
Martin Burger ◽  
Donald Goldfarb ◽  
Jinjun Xu ◽  
Wotao Yin
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Iterative Regularization

scholarly journals Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 258
Author(s):  
Ge Ma ◽  
Ziwei Yan ◽  
Zhifu Li ◽  
Zhijia Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Split Bregman ◽  
Iterative Regularization ◽  
Tv Regularization ◽  
Fidelity Term ◽  
Restoration Effect

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

scholarly journals Iterative Nonlocal Total Variation Regularization Method for Image Restoration

PLoS ONE ◽  
2013 ◽  
Vol 8 (6) ◽  
pp. e65865 ◽  
Author(s):  
Huanyu Xu ◽  
Quansen Sun ◽  
Nan Luo ◽  
Guo Cao ◽  
Deshen Xia
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Total Variation Regularization ◽  
Nonlocal Total Variation

Iterative regularization method in generalized inverse beamforming

2017 ◽  
Vol 396 ◽  
pp. 108-121 ◽  
Author(s):  
Zhifei Zhang ◽  
Si Chen ◽  
Zhongming Xu ◽  
Yansong He ◽  
Shu Li
Keyword(s):  
Regularization Method ◽  
Generalized Inverse ◽  
Iterative Regularization

scholarly journals Heating source localization in a reduced time

2016 ◽  
Vol 26 (3) ◽  
pp. 623-640 ◽  
Author(s):  
Sara Beddiaf ◽  
Laurent Autrique ◽  
Laetitia Perez ◽  
Jean-Claude Jolly
Keyword(s):  
Heat Conduction ◽  
Source Localization ◽  
Conjugate Gradient ◽  
Regularization Method ◽  
Three Dimensional ◽  
Gradient Algorithm ◽  
Iterative Regularization ◽  
Heating Source ◽  
Ill Posed ◽  
Reduced Time

Abstract Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

2D Wavelet Tree Ordering Based Localized Total Variation Model for Efficient Image Restoration

2022 ◽  
Author(s):  
K. Praveen Kumar ◽  
C. Venkata Narasimhulu ◽  
K. Satya Prasad
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Good Condition ◽  
Window Size ◽  
Local Variation ◽  
Image Simulation ◽  
Regularization Algorithm ◽  
Total Variation Model ◽  
Degraded Image ◽  
Adjustment Scheme

The degraded image during the process of image analysis needs more number of iterations to restore it. These iterations take long waiting time and slow scanning, resulting in inefficient image restoration. A few numbers of measurements are enough to recuperate an image with good condition. Due to tree sparsity, a 2D wavelet tree reduces the number of coefficients and iterations to restore the degraded image. All the wavelet coefficients are extracted with overlaps as low and high sub-band space and ordered them such that they are decomposed in the tree ordering structured path. Some articles have addressed the problems with tree sparsity and total variation (TV), but few authors endorsed the benefits of tree sparsity. In this paper, a spatial variation regularization algorithm based on tree order is implemented to change the window size and variation estimators to reduce the loss of image information and to solve the problem of image smoothing operation. The acceptance rate of the tree-structured path relies on local variation estimators to regularize the performance parameters and update them to restore the image. For this, the Localized Total Variation (LTV) method is proposed and implemented on a 2D wavelet tree ordering structured path based on the proposed image smooth adjustment scheme. In the end, a reliable reordering algorithm proposed to reorder the set of pixels and to increase the reliability of the restored image. Simulation results clearly show that the proposed method improved the performance compared to existing methods of image restoration.

Wavelet-based Total Variation Equation Image Restoration

2013 ◽  
Vol 12 (23) ◽  
pp. 7778-7781
Author(s):  
Zhao Dong-Hong ◽  
Wang Chen-Chen
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Variation Equation
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