Implementation of the minimum relative (cross) entropy method for the solution of inverse ECG problem

Minimum relative (cross) entropy method can be used to solve linear inverse electrocardiography (ECG) problem. Inverse ECG problem has a form d=Gm where m is a vector of unknown model parameters (epicardial potentials), d is a vector of measurements (torso potentials) and G is the forward transfer matrix. MRE method treats the elements of m as random variables and obtains the potential distribution and the solution as the expected value of the posterior distribution. The prior information about lower and upper bounds of m and a prior expected value of m are needed to obtain the epicardial potential distribution. In this study, MRE method is tested with various lower and upper bounds and expected values. Test results are compared with the true potentials, with each other and with Tikhonov regularization method results. These results show that similar solutions to Tikhonov are obtained with robust prior information and better results are obtained with better prior information. In addition, prior expected value of m is more effective than the lower and upper bounds of m.