Adaptive regularization based on noise estimation and its application to the inverse problem in electrocardiography

The inverse problem was solved to reconstruct endocardial electrograms from cavitary electrograms measured with a noncontact multielectrode probe. Noise levels were estimated at each time instant by extrapolating noise energy from high spatial frequency components of probe potentials. Based on estimated noise and energy distribution of probe potentials, a matrix of weighting factors was derived to inversely mimic the band shape of the energy spectrum. By incorporating those weighting factors into the inverse procedure, a set of regularization parameters was derived and applied in solving the inverse problem (i.e. adaptive regularization). Adaptive regularization was tested on an experimental canine model. Both traditional uniform regularization and adaptive regularization were applied to compute endocardial electrograms during normal as well as paced rhythms. Adaptive regularization demonstrated a great improvement over uniform regularization in terms of improved correlation coefficients, reduced relative error, better estimation of activation times and localization of pacing sites