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
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error
Applied Numerical Mathematics
Regularization of ill-posed problems: optimal parameter choice in finite dimensions
Journal of Approximation Theory
SIAM Journal on Matrix Analysis and Applications
A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization
IEEE Transactions on Pattern Analysis and Machine Intelligence
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal on Scientific Computing
A general heuristic for choosing the regularization parameter in ill-posed problems
SIAM Journal on Scientific Computing
Generalized cross validation for wavelet thresholding
Signal Processing
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)
On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems
Mathematics of Computation
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
Iteratively Regularized Gauss-Newton Method for Nonlinear Inverse Problems with Random Noise
SIAM Journal on Numerical Analysis
Parameter choice methods using minimization schemes
Journal of Complexity
Parameter choice methods using minimization schemes
Journal of Complexity
Journal of Computational and Applied Mathematics
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
Stopping rules for iterative methods in nonnegatively constrained deconvolution
Applied Numerical Mathematics
A control Liapunov function approach to generalized and regularized descent methods for zero finding
International Journal of Hybrid Intelligent Systems
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Abstract: In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluates and compares them in a large simulation study for spectral cut-off and Tikhonov regularization. The test cases cover a wide range of linear inverse problems with both white and colored stochastic noise. The results show some marked differences between the methods, in particular, in their stability with respect to the noise and its type. We conclude with a table of properties of the methods and a summary of the simulation results, from which we identify the best methods.