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

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 ord...

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Bibliographic Details
Published in:IEEE transactions on biomedical engineering 2000-09, Vol.47 (9), p.1293-1296
Main Authors: Johnston, P.R., Gulrajani, R.M.
Format: Article
Language:English
Subjects:
Australia Council
Biological and medical sciences
Biomedical Engineering
Biomedical measurements
Biometry
Computational geometry
Computer Simulation
Electrocardiography - statistics & numerical data
Electrocardiography. Vectocardiography
Electrodiagnosis. Electric activity recording
Electroencephalography
Electroencephalography - statistics & numerical data
Geometry
Heart
Humans
Inverse problems
Investigative techniques, diagnostic techniques (general aspects)
Mathematical operators
Matrix decomposition
Medical sciences
Noise measurement
Singular value decomposition
Smoothing methods
Spurious signal noise
Testing
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Summary: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.
ISSN:0018-9294
1558-2531
DOI:10.1109/10.867966