Level choice in truncated total least squares
Computational Statistics & Data Analysis
Determining the regularization parameters for super-resolution problems
Signal Processing
On Regularization Parameters Estimation in Edge---Preserving Image Reconstruction
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
Regularization Parameter Selection in Discrete Ill-Posed Problems-The Use of the U-Curve
International Journal of Applied Mathematics and Computer Science
Unsupervised blind separation and debluring of mixtures of sources
KES'07/WIRN'07 Proceedings of the 11th international conference, KES 2007 and XVII Italian workshop on neural networks conference on Knowledge-based intelligent information and engineering systems: Part III
An evolutionary approach to inverse gray level quantization
VISUAL'07 Proceedings of the 9th international conference on Advances in visual information systems
Original Article: Comparingparameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
A maximum product criterion as a Tikhonov parameter choice rule for Kirsch's factorization method
Journal of Computational and Applied Mathematics
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
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The Tikhonov regularization method for discrete ill-posed problems is considered. For the practical choice of the regularization parameter $\alpha$, some authors use a plot of the norm of the regularized solution versus the norm of the residual vector for all $\alpha$ considered. This paper contains an analysis of the shape of this plot and gives a theoretical justification for choosing the regularization parameter so it is related to the "L-corner" of the plot considered in the logarithmic scale. Moreover, a new criterion for choosing $\alpha$ is introduced (independent of the shape of the plot) which gives a new interpretation of the "corner criterion" mentioned above. The existence of "L-corner" is discussed.