Kronecker product approximations for image restoration with anti-reflective boundary conditions

2006 ◽  
Vol 13 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Lisa Perrone
Keyword(s):  
Boundary Conditions ◽  
Image Restoration ◽  
Kronecker Product

Kronecker product approximations for image restoration with whole-sample symmetric boundary conditions

2012 ◽  
Vol 186 (1) ◽  
pp. 150-163 ◽  
Author(s):  
Xiao-Guang Lv ◽  
Ting-Zhu Huang ◽  
Zong-Ben Xu ◽  
Xi-Le Zhao
Keyword(s):  
Boundary Conditions ◽  
Image Restoration ◽  
Kronecker Product

scholarly journals Kronecker product approximations for image restoration with new mean boundary conditions

2012 ◽  
Vol 36 (1) ◽  
pp. 225-237 ◽  
Author(s):  
Xi-Le Zhao ◽  
Ting-Zhu Huang ◽  
Xiao-Guang Lv ◽  
Zong-Ben Xu ◽  
Jie Huang
Keyword(s):  
Boundary Conditions ◽  
Image Restoration ◽  
Kronecker Product

Image restoration with shifting reflective boundary conditions

2011 ◽  
Vol 56 (6) ◽  
pp. 1-15 ◽  
Author(s):  
Jie Huang ◽  
TingZhu Huang ◽  
XiLe Zhao ◽  
ZongBen Xu
Keyword(s):  
Boundary Conditions ◽  
Image Restoration

scholarly journals Global Quasi-Minimal Residual Method for Image Restoration

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Jun Liu ◽  
Ting-Zhu Huang ◽  
Xiao-Guang Lv ◽  
Hao Xu ◽  
Xi-Le Zhao
Keyword(s):  
Iterative Method ◽  
Image Restoration ◽  
Tikhonov Regularization ◽  
Kronecker Product ◽  
Gmres Method ◽  
Regularization Technique ◽  
Minimal Residual Method ◽  
Ill Posed ◽  
Qmr Method ◽  
Minimal Residual

The global quasi-minimal residual (QMR) method is a popular iterative method for the solution of linear systems with multiple right-hand sides. In this paper, we consider the application of the global QMR method to classical ill-posed problems arising from image restoration. Since the scale of the problem is usually very large, the computations with the blurring matrix can be very expensive. In this regard, we use a Kronecker product approximation of the blurring matrix to benefit the computation. In order to reduce the disturbance of noise to the solution, the Tikhonov regularization technique is adopted to produce better approximation of the desired solution. Numerical results show that the global QMR method outperforms the classic CGLS method and the global GMRES method.

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