Damped ellipse decomposition for bivariate signals

This paper introduces SONATA: a method that decomposes a polarized bivariate signal into a sum of damped ellipses. To do this, a damped ellipse is seen as a specific quaternion-valued signal for which dynamical parameters (damping and frequency) are separated from the geometrical/polarization parameters which are here considered constant in time. To obtain the parameters of this model, SONATA relies on alternated optimization. While updating the geometrical parameters is done in the quaternion-domain, the update of dynamical parameters is performed via complex structured low-rank approximations. Finally, a gravitational wave data analysis is demonstrated: an example for which the low-rank model of SONATA is adequate.