Phase-Aligned Spectral Filtering for Decomposing Spatiotemporal Dynamics

Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about such dynamics via data assimilation and modeling. It is assumed that the observed spatiotemporal data represent superimposed lower-rank smooth oscillations and movements from a generative dynamic system, mixed with higher-rank random noises. Separating the signals from noises is essential for us to visualize, model and understand these lower-rank dynamic systems. It is also often the case that such a lower-rank dynamic system have multiple independent components, corresponding to different trends or functionalities of the system under study. In this paper, we present a novel filtering framework for identifying lower-rank dynamics and its components embedded in a high dimensional spatiotemporal system. It is based on an approach of structural decomposition and phase-aligned construction in the frequency domain. In both our simulated examples and real data applications, we illustrate that the proposed method is able to separate and identify meaningful lower-rank movements, while existing methods fail.