[EM algorithm for the inverse problem of electrocardiography].

The endeavors to solve the inverse problem of electrocardiography embody the approach to calculate the epicardial potentials using the measured body-surface-potential distribution; it is important for pathology and very useful for clinical application. In this paper, we construct the 2D human torso model using the FEM method and solve the forward problem. In the constructed state-space equations, and the relationship between the body surface potentials and epicardial potentials in the FEM torso model is the measurement equation, and the relationship of the adjacent states is the state process equation. To solve the problem of uncertainty of the parameters, we design the likelihood function and introduce the Expectation Maximization (EM) algorithm. Step E (Expectation) estimates the parameters using the Kalman filter; step M (Maximization) re-estimates the parameters using the likelihood functions, step E and step M iterate. Simulations of the whole process show that EM algorithm leads to better convergence of the solutions than does the traditional Kalman filtering, and the relative errors are much smaller than before.