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Selecting the corner in the L-curve approach to Tikhonov regularization

Citation

Johnston, PR and Gulrajani, M, Selecting the corner in the L-curve approach to Tikhonov regularization, IEEE Transactions on Biomedical Engineering, 47, (9) pp. 1293-1296. ISSN 0018-9294 (2000) [Refereed Article]

DOI: doi:10.1109/10.867966

Abstract

The performance of two methods for selecting the corner in the L-curve approach to Tikhonov regularization is evaluated via computer simulation. These methods are selecting the corner as the point of maximum curvature in the L-curve, and selecting it as the point where the product of abcissa and ordinate is a minimum. It is shown that both these methods resulted in significantly better regularization parameters than that obtained with an often-used empirical Composite REsidual and Smoothing Operator approach, particularly in conditions where correlated geometry noise exceeds Gaussian measurement noise. It is also shown that the regularization parameter that results with the minimum-product method is identical to that selected with another empirical zero-crossing approach proposed earlier. | The performance of two methods for selecting the corner in the L-curve approach to Tikhonov regularization is evaluated via computer simulation. These methods are selecting the corner as the point of maximum curvature in the L-curve, and selecting it as the point where the product of abcissa and ordinate is a minimum. It is shown that both these methods resulted in significantly better regularization parameters than that obtained with an often-used empirical Composite REsidual and Smoothing Operator approach, particularly in conditions where correlated geometry noise exceeds Gaussian measurement noise. It is also shown that the regularization parameter that results with the minimum-product method is identical to that selected with another empirical zero-crossing approach proposed earlier.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Ordinary Differential Equations, Difference Equations and Dynamical Systems
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Johnston, PR (Dr Peter Johnston)
ID Code:18687
Year Published:2000
Web of Science® Times Cited:72
Deposited By:Medicine (Discipline)
Deposited On:2000-08-01
Last Modified:2001-05-03
Downloads:0

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