Remarks on choosing a regularization parameter using the quasioptimality and ratio criterion
USSR Computational Mathematics and Mathematical Physics
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
A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal on Scientific Computing
An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
SIAM Journal on Control and Optimization
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
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
An Analysis of the Zero-Crossing Method for Choosing Regularization Parameters
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates
SIAM Journal on Numerical Analysis
SIAM Journal on Imaging Sciences
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Gradient-based estimation of Manning's friction coefficient from noisy data
Journal of Computational and Applied Mathematics
A two-stage method for inverse medium scattering
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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In this paper we develop a novel rule for choosing regularization parameters in nonsmooth Tikhonov functionals. It is solely based on the value function and applicable to a broad range of nonsmooth models, and it extends one known criterion. A posteriori error estimates of the approximations are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are discussed. Numerical results for several common nonsmooth models are presented, including deblurring natural images. The numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice, and the algorithm merits a fast and steady convergence.