Comparison of Kalman filter and Bayesian-MAP approaches in the spatio-temporal solution of the inverse electrocardiography Ters elektrokardiyografinin zaman-uzamsal çözümünde Kalman filtre ve Bayes-MAP yöntemlerinin karşilaştirilmasi

In this study some of the spatial and spatio-temporal methods for the solution of the inverse problem of electrocardiography (ECG) are compared with each other. Comparisons are also made for the cases with geometric errors, where the location of the heart is shifted for 10mm and the size of the heart is reduced by 5%. The compared methods are the Kalman filter and Bayesian maximum a posteriori estimation (MAP). Two different Bayesian-MAP algorithms are used. While one uses only spatial information the other uses spatio-temporal information. In Kalman filter algorithms the state transition matrix (STM) that contains the spatio-temporal information is calculated with two different scenarios. In the first case the STM is calculated directly from the training set and in the second case the solution of the spatial Bayesian-MAP is employed to calculate STM.


Comparison of Bayesian MAP Estimation and Kalman Filter Methods in the Solution of Spatio-Temporal Inverse ECG Problem
Aydin, Umit; Serinağaoğlu Doğrusöz, Yeşim (2009-09-12)
In this study, spatial only, and spatio-temporal Bayesian Maximum a Posteriori (MAP) methods and an another spatio-temporal method, the Kalman filter approach, are used to solve the inverse electrocardiography (ECG) problem. Training sets are used to obtain the required a priori information for all methods. Two different approaches are employed to calculate the state transition matrix (STM), which maps the epicardial potentials in two consecutive time instants in the Kalman filter method. The first one uses...
Estimation of state transition matrix in the Kalman filter based inverse ECG solution with the help of training sets Ters EKG probleminin Kalman filtre ile çözümünde durum geçiş matrisinin eǧitici kümeler yardimi ile kestirimi
Aydin, Ümit; Serinağaoğlu Doğrusöz, Yeşim (2009-10-27)
At this study the main motivation is to solve inverse problem of ECG with Kalman filter. In order to obtain feasible solutions determination of the state transition matrix (STM) correctly is vital. In literature the STM is usually found by using the test data itself which is not a realistic scenario. The major goal of this study is to determine STM without using test data. For that purpose a two stage method is suggested. At the first step the probability density function (pdf) is calculated using training ...
Use of Activation Time Based Kalman Filtering in Inverse Problem of Electrocardiography
Aydin, Umit; Serinağaoğlu Doğrusöz, Yeşim (2008-11-27)
The goal of this study is to solve inverse problem of electrocardiography (ECG) in terms of epicardial potentials using body surface (torso) potential measurements. The problem is ill-posed and regularization must be applied. Kalman filter is one of the regularization approaches, which includes both spatial and temporal correlations of epicardial potentials. However, in order to use the Kalman filter, one needs the state transition matrix (STM) that models the time evolution of the epicardial potentials. In...
Comparison of missing value imputation methods in time series: the case of Turkish meteorological data
Yozgatlıgil, Ceylan; İyigün, Cem; Batmaz, İnci (2013-04-01)
This study aims to compare several imputation methods to complete the missing values of spatio-temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with co...
Convergence Error and Higher-Order Sensitivity Estimations
Eyi, Sinan (2012-10-01)
The aim of this study is to improve the accuracy of the finite-difference sensitivities of differential equations solved by iterative methods. New methods are proposed to estimate the convergence error and higher-order sensitivities. The convergence error estimation method is based on the eigenvalue analysis of linear systems, but it can also be used for nonlinear systems. The higher-order sensitivities are calculated by differentiating the approximately constructed differential equation with respect to the...
Citation Formats
Ü. Aydin and Y. Serinağaoğlu Doğrusöz, “Comparison of Kalman filter and Bayesian-MAP approaches in the spatio-temporal solution of the inverse electrocardiography Ters elektrokardiyografinin zaman-uzamsal çözümünde Kalman filtre ve Bayes-MAP yöntemlerinin karşilaştirilmasi,” 2010, Accessed: 00, 2020. [Online]. Available: