Fr\'echet means of curves for signal averaging and application to ECG data analysis

TL;DR

This paper introduces a method for signal averaging using Fréchet means of curves, which effectively accounts for geometric variability in time, demonstrated on ECG data to estimate average heart cycles.

Contribution

It presents a novel algorithm for signal averaging based on Fréchet means in non-Euclidean spaces, eliminating the need for a reference template.

Findings

Effective estimation of mean heart cycle from ECG data

Improved alignment and averaging of noisy signals

Demonstrated numerical performance of the proposed method

Abstract

Signal averaging is the process that consists in computing a mean shape from a set of noisy signals. In the presence of geometric variability in time in the data, the usual Euclidean mean of the raw data yields a mean pattern that does not reflect the typical shape of the observed signals. In this setting, it is necessary to use alignment techniques for a precise synchronization of the signals, and then to average the aligned data to obtain a consistent mean shape. In this paper, we study the numerical performances of Fr\'echet means of curves which are extensions of the usual Euclidean mean to spaces endowed with non-Euclidean metrics. This yields a new algorithm for signal averaging without a reference template. We apply this approach to the estimation of a mean heart cycle from ECG records.