Comparison of ML and MAP parameter estimation techniques for the solution of inverse electrocardiography problem

Erenler, Taha
This study aims to determine the cardiac electrical activity from body surface potential measurements. This problem is called the inverse problem of electrocardiography. Reconstruction of the cardiac electrical activity from the body surface potential measurements is not an easy task, since this problem has an ill-posed nature due to attenuation and spatial smoothing inside the medium between the source and the measurement sites, meaning that even small errors in the mathematical model or noise in the measurements may yield unbounded errors or large oscillations in the solutions. One remedy for this ill-posedness is to apply regularization, where one imposes deterministic or statistical constraints on the solution based on available a priori information. In this thesis, Tikhonov regularization, Bayesian maximum a posteriori estimation (BMAP), Kalman filter and regularized Kalman filter approaches are used to solve the inverse problem of electrocardiography. In the context of Kalman filter, maximum likelihood (ML) and maximum a posteriori (MAP) estimation are used to find Kalman filter parameters. By estimating Kalman filter parameters, we aim to find an answer to an open question of how the essential parameters in the state-space representation are found without claiming strong assumptions in the literature. The results showed that the mean correlation coefficient ranges from 0.99 to 0.66 for MLIF and from 0.97 to 0.72 for MAPIF under 30 dB measurement noise. Our study showed that ML estimation works well when the training set data and test data are similar. However, due to over-fitting nature of the ML estimation, MAP estimation should be preferred in order to improve generalizability of the method.