The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal on Scientific Computing
Two stable methods with numerical experiments for solving the backward heat equation
Applied Numerical Mathematics
Adaptive multiple-frame image super-resolution based on U-curve
IEEE Transactions on Image Processing
Adaptive regularization parameter for graph cut segmentation
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
A control Liapunov function approach to generalized and regularized descent methods for zero finding
International Journal of Hybrid Intelligent Systems
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To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.