Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation

2009 ◽  
Vol 25 (9) ◽  
pp. 095005 ◽  
Author(s):  
Johnathan M Bardsley ◽  
John Goldes
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regularization Parameter ◽  
Likelihood Estimation ◽  
Parameter Selection ◽  
Selection Methods ◽  
Ill Posed ◽  
Regularization Parameter Selection

scholarly journals Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve

2007 ◽  
Vol 17 (2) ◽  
pp. 157-164 ◽  
Author(s):  
Dorota Krawczyk-Stańdo ◽  
Marek Rudnicki
Keyword(s):  
Regularization Parameter ◽  
Parameter Selection ◽  
Tikhonov Regularization Method ◽  
Smooth Solutions ◽  
Solution Versus ◽  
Regularization Parameters ◽  
Ill Posed ◽  
New Criterion ◽  
Regularization Parameter Selection ◽  
Regularized Solution

Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-CurveTo 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.

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