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Periodic Report Summary 1 - EMP-INT-MODEL-NL-SP (Empirical Intrinsic Modeling for Nonlinear Signal Processing)

A fundamental problem in signal processing is designing models for signal representation, which are theoretically sound, practical to implement, and describe well the variability of real-world signals. Finding an accurate representation of a signal may set the stage for state of the art analysis, filtering, noise suppression, and prediction. Common practice largely relies on parametric models, in which the choice of a model mainly depends on the prior knowledge, intuition, and experience of the researcher, and then, the most suitable model parameters are rigorously estimated based on the signals at hand. In order to circumvent arbitrary and subjective model assumptions, we aim in this project to develop modeling methods driven by signal observations rather than methods based on priors.
A widely spread assumption in contemporary data analysis is that the data do not fill the ambient space uniformly but rather lie on a low-dimensional manifold. The low-dimensionality assumption can similarly be applied to temporal signals, since they are often controlled by few underlying drivers, whose evolution in time can be compactly described by dynamical processes on a low-dimensional manifold. In particular, we focus on two particular aspects of low-dimensional signal modeling. First, 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 a different geometric structure (manifold), depending on the specific instrument and the specific realization. We aspire to build models that describe the observed phenomena in terms of their physical attributes independently of the way they are measured. We will refer to such model as intrinsic. Second, the dynamics of data streams and time-series convey substantial information. While most existing manifold-based modeling methods disregard the statistical and dynamical features of the signals, we intend to utilize the dynamics information and to encode it into the inferred model. The goal of this project is therefore 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.
Thus far, in the first reporting period of this proposal, we have developed new analysis, methodologies, and algorithms to build data-driven intrinsic models for real-world signals. In addition, we investigated the question: what is a “good” geometric description of a signal. We examined this formulation and defined rigorous conditions. In addition, we developed tests for assessing the quality of the geometric description in light of the defined conditions.
We believe that the developed 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.
A class of signal processing problems, where we have identified significant gap in their existing models and arguably lag behind with respect to modern data analysis tools, arises from biomedicine applications. Harnessing the signal analysis toolbox developed in this project, we have addressed the problem of epilepsy seizure identification from intracranial (implanted) EEG electrodes. We have managed to show that our methodology enables us to build models solely from signal observations, which accurately extract brain activity trends related to epilepsy. By departing from classic linear and parametric signal processing and using nonlinear and data-driven methods, we try to push the boundaries of current research in signal processing and to prepare the ground for more advanced analysis, techniques, and applications.
The details on these projects are available at:
In the second reporting period, we will continue to examine both theoretical and practical aspects. In particular, based on the developed intrinsic modeling technique, we will devise a Bayesian framework for data-driven nonlinear filtering. This framework will allow to optimally process natural signals without a priori knowledge of models. We expect to gain significant advantages in signal processing by utilizing the low dimensionality and “intrinsic-ness” (e.g., robustness to noise and to instrumental modalities) of the new data-driven models, compared to processing in the original measurements domain.
We see our new approach widely influencing physical and biological science by enabling, through data-driven intrinsic coordinates, the fusion of similar phenomena partially observed through different instrumental modalities. In addition, we hope to achieve significant progress in the understanding of biomedical signals, which will allow for the development of new technology and instruments for detection and treatment of various diseases as well as analysis of symptoms. With the expertise in related fields provided by Technion, and by continuing to collaborate with top researchers within Europe and abroad, we hope to further advance the current state of the art in geometric signal analysis and nonlinear signal processing.

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Life Sciences
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