GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fundamentals of digital image processing
Fundamentals of digital image processing
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Iterative methods for X − AXB = C
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Global FOM and GMRES algorithms for matrix equations
Applied Numerical Mathematics
Tikhonov Regularization and Total Least Squares
SIAM Journal on Matrix Analysis and Applications
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Tikhonov regularization and the L-curve for large discrete ill-posed problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Digital Image Restoration
Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions
SIAM Journal on Matrix Analysis and Applications
Iterative Identification and Restoration of Images (The International Series in Engineering and Computer Science)
Applied Numerical Mathematics
Convex constrained optimization for large-scale generalized Sylvester equations
Computational Optimization and Applications
A generalized global Arnoldi method for ill-posed matrix equations
Journal of Computational and Applied Mathematics
Conditional gradient Tikhonov method for a convex optimization problem in image restoration
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization problem leads to the generalized Sylvester matrix equation. For large-scale problems, we use the global-GMRES method which is an orthogonal projection method onto a matrix Krylov subspace. We present some theoretical results and give numerical tests in image restoration.