Regression or Pseudo-Inverse – Which Method Should be Preferred When Developing Inverse Linear ECG-Lead Transformations?

Abstract

Linear ECG-lead transformations estimate or derive unrecorded target leads by applying a number of recorded basis leads to a so-called linear ECG-lead transformation matrix. The inverse transform of such a linear ECG-lead transformation performs a transformation in the opposite direction (from the target leads to the basis leads). The pseudo-inverse of a given transformation matrix can be used to perform such an inverse transformation. Linear regression based inverse transformation matrices are, provided that sufficient training data for their development is available, an alternative to pseudo-inverse matrices. The aim of this research was to compare the estimation performance of pseudo-inverse and linear regression based inverse transformations. This comparison was performed for two example inverse transformations. The performance of the different transformations was assessed using root-mean-squared-error (RMSE) values between the QRS-T complexes of recorded and derived leads. Typical mean RMSE values associated with the regression based approach were found to be approximately two thirds to half of the mean RMSE values achieved by the approach based upon the pseudo-inverse. Provided that sufficient data are available, linear regression should be used for the development of inverse ECG-lead transformation matrices.