"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. In recent years there has been a considerable effort to derive data-driven modeling schemes based on low dimensional geometric analysis, however, several aspects have not yet been thoroughly addressed. For example, measuring the same phenomena several times usually yields different signal realizations. In addition, the same phenomena can be measured using multiple types of instruments. As a result, each set of related signal measurements of the same phenomenon will have a different geometric structure; this poses a limitation to geometric analysis methods. The goal of this project is to delve into these aspects and to devise empirical intrinsic models for nonlinear signal processing, which are noise resilience and invariant to the observation modality. Intrinsic models may bring significant benefits to numerous applications without existing definitive representations by enabling the fusion of similar phenomena partially observed through different modalities. The availability of intrinsic models will allow for the design of new processing methodologies that take advantage of the intrinsic properties, e.g. noise robustness and low dimensionality. I will examine both theoretical and practical aspects as well as develop tools designed to push forward the applicability of geometric analysis. Combining my experience with the expertise in related fields provided by the host institution will allow to advance the current state of the art in geometric signal analysis and nonlinear signal processing as well as nurture collaborations within Europe and abroad."
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