Multi-Resolution Analysis of Dynamical Systems using Dynamic Mode Decomposition
نویسندگان
چکیده
We introduce the method of dynamic mode decomposition (DMD) for robustly separating complex systems into a hierarchy of multi-resolution time-scaled components. The method includes a methodology for background (low-rank) and foreground (sparse) separation of dynamical data. The method involves a technique used for characterizing nonlinear dynamical systems in an equation-free manner by decomposing the state of the system into low-rank terms whose Fourier components in time are known. DMD terms with Fourier frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given dynamics, and the terms with Fourier frequencies bounded away from the origin are their sparse counterparts. The DMD method is demonstrated on video content where a time-frequency analysis can be made of multiple time-scales in video.
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