A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem


Aydin U., SERİNAĞAOĞLU DOĞRUSÖZ Y.

MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, vol.49, no.9, pp.1003-1013, 2011 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 9
  • Publication Date: 2011
  • Doi Number: 10.1007/s11517-011-0757-8
  • Title of Journal : MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING
  • Page Numbers: pp.1003-1013
  • Keywords: Inverse problem of electrocardiography, Geometric errors, Kalman filter, Expectation maximization, CARDIAC ELECTROPHYSIOLOGY, TORSO INHOMOGENEITIES, EPICARDIAL POTENTIALS, HEART POSITION, ELECTROCARDIOGRAPHY, RECONSTRUCTION, REGULARIZATION, MODEL, ALGORITHM

Abstract

In this article, we aimed to reduce the effects of geometric errors and measurement noise on the inverse problem of Electrocardiography (ECG) solutions. We used the Kalman filter to solve the inverse problem in terms of epicardial potential distributions. The geometric errors were introduced into the problem via wrong determination of the size and location of the heart in simulations. An error model, which is called the enhanced error model (EEM), was modified to be used in inverse problem of ECG to compensate for the geometric errors. In this model, the geometric errors are modeled as additive Gaussian noise and their noise variance is added to the measurement noise variance. The Kalman filter method includes a process noise component, whose variance should also be estimated along with the measurement noise. To estimate these two noise variances, two different algorithms were used: (1) an algorithm based on residuals, (2) expectation maximization algorithm. The results showed that it is important to use the correct noise variances to obtain accurate results. The geometric errors, if ignored in the inverse solution procedure, yielded incorrect epicardial potential distributions. However, even with a noise model as simple as the EEM, the solutions could be significantly improved.