A fundamental problem in signal processing is designing models, which are theoretically sound, practical to implement, and describe well the variability of real-world signals. Finding accurate models of signals sets the foundation to state-of-the-art signal analysis, filtering, prediction, and noise suppression.
We develop methods for building intrinsic representations of measured signals, with special focus on time-series arising from (nonlinear) dynamical systems. Measuring the same phenomena several times usually yields different measurement realizations. In addition, the same phenomena can be measured using multiple types of instruments or sensors. As a result, each set of related measurements of the same phenomenon will have different characteristics and structures, depending on the specific instrument and the specific realization.
We have shown that building models that describe the observed phenomena in terms of their physical attributes independently of the way they are measured is feasible. We refer to such models as intrinsic. We are developing mathematically sound toolboxes of analytics for building intrinsic models from observations, which are noise resilient and invariant to the observation modality.