Wave Equation Extraction from A Video Using Sparse Modeling

The identification of partial differential equations (PDEs) governing physical systems based solely on data recently has attracted significant research attention. Previous work in this area has concerned applications to notional or synthetic models or direct measurements of signals. For real signals, noise and missing data present significant obstacles to identification of PDEs. Further, indirect observations of dynamic systems, e.g. video data, present additional challenges which include the identification of the salient physical phenomena in the video frames. In this work, we use robust principal component analysis to extract the dynamic part of each frame in a water tank wave video and demonstrate a sparse-modeling method to extract the PDE governing the wave propagation in the video. From the video we correctly identify the wave equation and can extract the phase speed.

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