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

Daniel Guldenring1, Ali Rababah2, Dewar Finlay2, Raymond Bond2, Alan Kennedy3, Khaled Rjoob2, Michael Jennings2, James McLaughlin2
1HTW Berlin, 2Ulster University, 3PulseAI Ltd


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 for two example linear ECG-lead transformations. First, 12-lead ECGs and Frank VCGs of n=726 subjects were divided into one training dataset (DTrain) and one testing dataset (DTest). Second, linear regression and the data in DTrain were used to generate two linear ECG-lead transformation matrices (one for the transformation of the 12-lead ECG to the Frank VCG and one for the opposite direction). Third, the pseudo-inverse for each of the two transformation matrices was computed. Forth, the four matrices and the data in DTest were used for the estimation of the Frank VCG and the 12-lead ECG. Fifth, root-mean-squared-error (RMSE) values between the QRS-T complexes of recorded and derived leads were determined. Mean RMSE values associated with the pseudo-inverse, were found to be approximately a factor of two higher, than those associated with the approach based upon linear regression. For example, the RMSE values (mean; (95% confidence interval)) when estimating Frank VCG lead X from the 12-lead ECG using the linear regression and the pseudo-inverse approach were found to be 30µV; (27µV;33µV) and 63µV; (56µV;70µV) respectively. Provided that sufficient training data are available, linear regression should be used for the development of inverse ECG-lead transformation matrices.