scholarly journals Combined Energy Minimization for Image Reconstruction from Few Views

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Wei Wei ◽  
Xiao-Lin Yang ◽  
Bin Zhou ◽  
Jun Feng ◽  
Pei-Yi Shen
Keyword(s):  
Image Reconstruction ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Energy Minimization ◽  
Numerical Experiments ◽  
Applied Mathematics ◽  
Image Features ◽  
Density Region ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

Reconstruction from few views is an important problem in medical imaging and applied mathematics. In this paper, a combined energy minimization is proposed for image reconstruction.l2energy of the image gradient is introduced in the lower density region, and it can accelerate the reconstruction speed and improve the results. Total variation of the image is introduced in the higher density region, and the image features can be preserved well. Nonlinear conjugate gradient method is introduced to solve the problem. The efficiency and accuracy of our method are shown in several numerical experiments.

scholarly journals Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

2019 ◽  
Vol 235 ◽  
pp. 179-186 ◽  
Author(s):  
Lukas Exl ◽  
Johann Fischbacher ◽  
Alexander Kovacs ◽  
Harald Oezelt ◽  
Markus Gusenbauer ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Energy Minimization ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

scholarly journals A Modified Nonlinear Conjugate Gradient Method for Engineering Computation

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Tiefeng Zhu ◽  
Zaizai Yan ◽  
Xiuyun Peng
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
General Criterion ◽  
Mild Conditions ◽  
Nonlinear Conjugate Gradient Method ◽  
Engineering Computation ◽  
Nonlinear Conjugate Gradient

A general criterion for the global convergence of the nonlinear conjugate gradient method is established, based on which the global convergence of a new modified three-parameter nonlinear conjugate gradient method is proved under some mild conditions. A large amount of numerical experiments is executed and reported, which show that the proposed method is competitive and alternative. Finally, one engineering example has been analyzed for illustrative purposes.

A Hybrid Nonlinear Conjugate Gradient Method with Sufficient Descent Property

2011 ◽  
Vol 58-60 ◽  
pp. 943-949
Author(s):  
Wan You Cheng ◽  
Xue Jie Liu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
Test Problems ◽  
Sufficient Descent Property ◽  
Nonlinear Conjugate Gradient Method ◽  
Descent Property ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

In this paper, on the basis of the recently developed HZ (Hager-Zhang) method [SIAM J. Optim., 16 (2005), pp. 170-192], we propose a hybrid descent conjugate gradient method which reserves the sufficient descent property of the HZ method. Under suitable conditions, we prove the global convergence of the proposed method. Extensive numerical experiments show that the method is promising for the test problems from the CUTE library.

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Xiwen Lu ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Special Role ◽  
Conjugacy Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

Sign in / Sign up

Export Citation Format

Share Document