Fréchet means of curves for signal averaging and application to ECG data analysis

Jérémie Bigot (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 Fréchet 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.

Mots clés: Signal averaging; Mean shape; Fréchet means; Curve registration; Geometric variability; Deformable models; ECG data

Domaines: Applications [stat.AP]

Jérémie Bigot. Fréchet means of curves for signal averaging and application to ECG data analysis. 2011. ⟨hal-00639094⟩