A Learning Based Statistical Approach for Combining Multiple Measurements in Electrocardiographic Imaging

Kalman filter has been applied in literature to inverse electrocardiography problem as a spatio-temporal method. However, there is still an open question of how the essential parameters in the state-space representation are found without claiming strong assumptions. In this study, we proposed a maximum likelihood (ML) estimation based method which incorporates multiple body surface measurements to estimate the parameters that are essential to use Kalman filter. Our proposed approach, Maximum Likelihood Inference & Filtering (MLIF), was compared with zero order Tikhonov regularization and Bayesian maximum a posteriori estimation (BMAP) by using three different training sets under two different measurement noise levels. The results showed that mean correlation coefficient (CC) for Tikhonov regularization is 0.60, and mean CC ranges 0.64 to 0.82, and 0.66 to 0.99 for Bayesian MAP and MLIF under 30 dB SNR measurement noise, respectively. Under 10 dB SNR, mean CC is 0.37 for Tikhonov regularization, and mean CC ranges 0.53 to 0.78, and 0.53 to 0.98 for Bayesian MAP and MLIF, respectively.