Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Global Total Variation Minimization
SIAM Journal on Numerical Analysis
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
Iterative image restoration using approximate inverse preconditioning
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
An adaptive level set method for nondifferentiable constrained image recovery
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
An iterative Lagrange method for the regularization of discrete ill-posed inverse problems
Computers & Mathematics with Applications
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In the last years, Total Variation minimization has become a popular and valuable technique for the restoration of noisy and blurred images. In this paper, we present a new technique for image restoration based on Total Variation minimization and the discrepancy principle. The new approach replaces the original image restoration problem with an equality constrained minimization problem. An inexact Newton method is applied to the first-order conditions of the constrained problem. The stopping criterium is derived from the discrepancy principle. Numerical results of image denoising and image deblurring test problems are presented to illustrate the effectiveness of the new approach.