Identification of discontinuous parameters in flow equations
SIAM Journal on Control and Optimization
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
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
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 Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Fast CG-Based Methods for Tikhonov--Phillips Regularization
SIAM Journal on Scientific Computing
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
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
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In many science and engineering applications, the discretization of linear ill-posed problems gives rise to large ill-conditioned linear systems with the right-hand side degraded by noise. The solution of such linear systems requires the solution of minimization problems with one quadratic constraint, depending on an estimate of the variance of the noise. This strategy is known as regularization. In this work, we propose a modification of the Lagrange method for the solution of the noise constrained regularization problem. We present the numerical results of test problems, image restoration and medical imaging denoising. Our results indicate that the proposed Lagrange method is effective and efficient in computing good regularized solutions of ill-conditioned linear systems and in computing the corresponding Lagrange multipliers. Moreover, our numerical experiments show that the Lagrange method is computationally convenient. Therefore, the Lagrange method is a promising approach for dealing with ill-posed problems.