The use of the singular value decomposition in electrocardiography

Abstract

In the paper it is shown that singular value decomposition (s.v.d.) is an excellent tool for studying the limit properties of a feasible solution for the inverse problem in electrocardiography. When s.v.d. is applied to the transfer matrix, relating equivalent heart sources to the skin potentials, it provides a measure of the observability. In an example presented, a series of orthonormal potential patterns on a pericardial surface are found in an order of decreasing observability. When s.v.d. is applied to a data matrix, consisting of skin potentials as a function of time and position, one finds the normalised principal components both in time and space. An appropriate use of the singular values leads to a noise filtering algorithm, which at the same time results in useful data reduction. Comparison of spatial potential patterns derived from both the transfer matrix and the data matrix may, finally, be used to evaluate the assumptions on the transfer.