Use of Activation Time Based Kalman Filtering in Inverse Problem of Electrocardiography

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 inverse ECG literature, STM is either chosen as identity matrix or calculated from true epicardial potentials. The latter approach gives better results, however 1) It yields a matrix equation with a large size. 2) Not realistic. In this study we address the 1(st) shortcoming. Usually epicardial potential in one lead only depends on a limited number of leads; STM entries are close to zero for the remaining leads. In this study, we used simulated torso potentials, and constructed STM from true epicardial potentials. We used three different approaches to reduce the dimension of the problem: epicardial potential at one lead is assumed to be related to 1) Only the leads in its neighborhood, 2) The leads that are activated at around the same time (close activation times), (3) Both the leads with close activation times and its first order neighbors. The STM estimation problem is redefined to calculate only the limited number of related entries; the remaining STM entries are set to zero, hence reducing the problem size. The calculated STM is then used in the Kalman filter to estimate the epicardial potential distribution and later in the Kalman smoother to further reduce errors.


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 genetic algorithm for selection of regularization parameters in multiple constraint inverse ECG problem
Mazloumi Gavgani, Alireza; Serinağaoğlu Doğrusöz, Yeşim; Department of Electrical and Electronics Engineering (2011)
The main goal in inverse and forward problems of electrocardiography (ECG) is to better understand the electrical activity of the heart. In the forward problem of ECG, one obtains the body surface potential (BSP) distribution (i.e., the measurements) when the electrical sources in the heart are assumed to be known. The result is a mathematical model that relates the sources to the measurements. In the inverse problem of ECG, the unknown cardiac electrical sources are estimated from the BSP measurements and ...
Improved performance of Bayesian solutions for inverse Electrocardiography using multiple information sources
Serinağaoğlu Doğrusöz, Yeşim; MACLEOD, Robert (2006-10-01)
The usual goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface potentials and a mathematical model that relates the sources to the measurements. Due to attenuation and smoothing that occurs in the thorax, the inverse ECG problem is ill-posed and imposition of a priori constraints is needed to combat this ill-posedness. When the problem is posed in terms of reconstructing heart surface potentials, solutions have not yet achieved clinical utility; limitation...
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
Aydin, Ümit; Serinağaoğlu Doğrusöz, Yeşim (2010-07-15)
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...
Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem
ONAK, Onder Nazim; Serinağaoğlu Doğrusöz, Yeşim; WEBER, GERHARD WİLHELM (2018-01-01)
The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso-heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decom...
Citation Formats
U. Aydin and Y. Serinağaoğlu Doğrusöz, “Use of Activation Time Based Kalman Filtering in Inverse Problem of Electrocardiography,” 2008, vol. 22, Accessed: 00, 2020. [Online]. Available: