CIF: Small: Resonance-Based Signal Analysis: Algorithms and Applications

New York University, New York NY

Investigators

Abstract

Resonance-Based Signal Analysis: Algorithms and Applications Ivan Selesnick Many signals arising from physiological and physical processes are not only non-stationary but also posses a mixture of sustained oscillations and non-oscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geophysical signals. For example, EEG signals contain rhythmic oscillations (alpha waves, etc) but they also contain transients due to measurement artifacts and non-rhythmic brain activity. This research program involves the development and application of new algorithms designed to decompose such signals into 'resonance' components - a high-resonance component being a signal consisting of multiple simultaneous sustained oscillations; a low-resonance component being a signal consisting of non-oscillatory transients of unspecified shape and duration. While frequency components are straightforwardly defined and can be obtained by linear filtering, resonance components are more difficult to define and procedures to obtain resonance components are necessarily nonlinear. It is envisioned that the decomposition of a non-stationary multi-resonance signal into resonance components will enable the more effective utilization of existing processing methods specialized to each component. For example, sinusoidal modeling of speech is most efficient and effective for signals consisting primarily of sustained oscillations (high-resonance signals). On the other hand, time-domain and wavelet-domain methods are most effective for piecewise smooth signals that are defined primarily by their transients or singularities (low-resonance signals). This research utilizes recent developments in signal processing, including sparse signal representations, morphological component analysis, constant-Q (wavelet) transforms with varying Q-factors, fast algorithms for L1-norm regularized linear inverse problems, and related algorithms. The research consists of developing algorithms for resonance-based signal decomposition and generalizations, and assessing their effectiveness for the processing of signals arising from several physical and physiological processes.