Stable time-frequency contours for sparse signal representation

Many signals cannot be resolved in time and frequency with a single time-scale of analysis and multi-band representations are needed that can adapt to the local signal content. Using a newly developed contour-based representation of signals, we show that efficient multi-band representations arise when long-range, structurally stable shapes are enhanced relative to background. For the examples provided here, resolution in time and frequency is distributed adaptively so that each component of a signal is represented in its most parsimonious form. The resulting representation is characterized by simple shapes in the time-frequency plane.