Improved parameter choice methods and temporal filtering for the generalized eigensystem method applied to the inverse problem of electrocardiography

R. D. Throne, L. G. Olson, John Robert Windle

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Of the two algorithms used to estimate the regularization parameters, the composite residual and smoothing operator (CRESO) generally outperforms the generalized cross validation (GCV) for both GES and Tikhonov. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov. In general, the epicardial estimates using the GES method are more accurate than the estimates generated using zero order Tikhonov regularization.

Original languageEnglish (US)
Pages (from-to)339-365
Number of pages27
JournalInverse Problems in Engineering
Volume9
Issue number4
DOIs
StatePublished - Jan 1 2001

Fingerprint

Electrocardiography
Inverse problems
Tikhonov Regularization
Inverse Problem
Filtering
Estimate
Generalized Cross-validation
Formulation
Moving Average
Composite materials
Regularization Parameter
Zero
Instant
Smoothing
Experiments
Composite
Alternatives
Operator
Experiment
Heart

Keywords

  • Generalized eigensystem
  • Inverse electrocardiography
  • Parameter selection
  • Temporal filtering
  • Tikhonov regularization

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics

Cite this

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title = "Improved parameter choice methods and temporal filtering for the generalized eigensystem method applied to the inverse problem of electrocardiography",
abstract = "We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Of the two algorithms used to estimate the regularization parameters, the composite residual and smoothing operator (CRESO) generally outperforms the generalized cross validation (GCV) for both GES and Tikhonov. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov. In general, the epicardial estimates using the GES method are more accurate than the estimates generated using zero order Tikhonov regularization.",
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AU - Windle, John Robert

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N2 - We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Of the two algorithms used to estimate the regularization parameters, the composite residual and smoothing operator (CRESO) generally outperforms the generalized cross validation (GCV) for both GES and Tikhonov. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov. In general, the epicardial estimates using the GES method are more accurate than the estimates generated using zero order Tikhonov regularization.

AB - We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Of the two algorithms used to estimate the regularization parameters, the composite residual and smoothing operator (CRESO) generally outperforms the generalized cross validation (GCV) for both GES and Tikhonov. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov. In general, the epicardial estimates using the GES method are more accurate than the estimates generated using zero order Tikhonov regularization.

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