A Bayesian approach to inclusion and performance analysis of using extra information in bioelectric inverse problems

Due to attenuation and spatial smoothing that occurs in the conducting media, the bioelectric inverse problem of estimating sources from remote measurements is ill-posed and solution requires regularization. Recent studies showed that employing Bayesian methods could help increase accuracy. The basic limitations are the availability of good a priori information about the solution, and the lack of a "good" error metric. In this paper, we employ Bayesian methods, and present the mathematical framework for incorporating additional information in the form of prior statistics, and extra measurements. We also use Bayesian error metrics to evaluate the reconstructions, and select prior models. We apply the methods to inverse electrocardiography problem. The results show that we can improve the reconstructions by including extra information, and Bayesian error metrics are useful in evaluating the results.