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
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)
Sylvester Tikhonov-regularization methods in image restoration
Journal of Computational and Applied Mathematics
An interior-point method for large constrained discrete ill-posed problems
Journal of Computational and Applied Mathematics
A reduced Newton method for constrained linear least-squares problems
Journal of Computational and Applied Mathematics
Convex constrained optimization for large-scale generalized Sylvester equations
Computational Optimization and Applications
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In this paper, we consider the problem of image restoration with Tikhonov regularization as a convex constrained minimization problem. Using a Kronecker decomposition of the blurring matrix and the Tikhonov regularization matrix, we reduce the size of the image restoration problem. Therefore, we apply the conditional gradient method combined with the Tikhonov regularization technique and derive a new method. We demonstrate the convergence of this method and perform some numerical examples to illustrate the effectiveness of the proposed method as compared to other existing methods.