Nonlinear Signal Processing Based on Empirical Intrinsic Geometry
In this talk, I will present a method for nonlinear signal processing based on empirical intrinsic geometry (EIG). This method provides a convenient framework for combining geometric and statistical analysis and incorporates concepts from information geometry. Unlike classic information geometry that assumes known probabilistic models, we empirically infer an intrinsic model of distribution estimates, while maintaining similar theoretical guarantees. The key observation is that the probability distributions of signals, rather than specific realizations, uncover relevant geometric information. The proposed modeling exhibits two important properties which demonstrate its advantage compared to common geometric algorithms. We show that our model is noise resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two properties make the proposed model especially suitable for signal processing. We revisit the Bayesian approach and incorporate statistical dynamics and empirical intrinsic geometric models into a unified nonlinear filtering framework. We then apply the proposed method to nonlinear and non-Gaussian filtering problems. In addition, we show applications to biomedical signal analysis and acoustic signal processing.