On the quasi-optimality principle for ill-posed problems in Hilbert space
USSR Computational Mathematics and Mathematical Physics
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 general heuristic for choosing the regularization parameter in ill-posed problems
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints
SIAM Journal on Scientific Computing
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
SIAM Journal on Imaging Sciences
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Calcolo: a quarterly on numerical analysis and theory of computation
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
Sparsity reconstruction in electrical impedance tomography: An experimental evaluation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper, we are interested in heuristic parameter-choice rules for general convex variational regularization which are based on error estimates. Two such rules are derived and generalize those from quadratic regularization, namely, the Hanke-Raus rule and quasi-optimality criterion. A posteriori error estimates are shown for the Hanke-Raus rule, and convergence for both rules is also discussed. Numerical results for both rules are presented to illustrate their applicability.