ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models.


Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study
Onak, Onder Nazim; Serinağaoğlu Doğrusöz, Yeşim; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2019-05-01)
In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of...
A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem
Aydin, Umit; Serinağaoğlu Doğrusöz, Yeşim (Springer Science and Business Media LLC, 2011-09-01)
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 compens...
Bayesian solutions and performance analysis in bioelectric inverse problems
Serinağaoğlu Doğrusöz, Yeşim; MacLeod, RS (Institute of Electrical and Electronics Engineers (IEEE), 2005-06-01)
In bioelectric inverse problems, one seeks to recover bioelectric sources from remote measurements using a mathematical model that relates the sources to the measurements. Due to attenuation and spatial smoothing in the medium between the sources and the measurements, bioelectric inverse problems are generally ill-posed. Bayesian methodology has received increasing attention recently to combat this ill-posedness, since it offers a general formulation of regularization constraints and additionally provides s...
The effects of geometric errors on inverse ECG solutions using Kalman filter and Bayesian MAP estimation Kalman filtre ve Bayes-MAP ile ters EKG çözümlerinde geometrik hatalarin etkisi
Aydin, Ümit; Serinağaoğlu Doğrusöz, Yeşim (2009-10-27)
Geometric errors in inverse ECG are usually the errors occur in the mathematical model used for solution due to wrong interpretation of heart's position and size, conductivities of organs in the model and electrode positions. In this study the effects of geometric errors in inverse ECG problem for Kalman filter and Bayes-AMP methods are studied Furthermore the method suggested by Kaipio et. al., which assumes that these geometric errors are additive noise and independent of the epicardial potentials, is imp...
Parallel implementation of the accelerated BEM approach for EMSI of the human brain
ATASEVEN, YOLDAŞ; Akalin-Acar, Z.; Acar, C. E.; Gençer, Nevzat Güneri (Springer Science and Business Media LLC, 2008-07-01)
Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable valu...
Citation Formats
T. Erenler and Y. Serinağaoğlu Doğrusöz, “ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging,” MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, pp. 2093–2113, 2019, Accessed: 00, 2020. [Online]. Available: