期刊
JOURNAL OF COMPUTATIONAL DYNAMICS
卷 7, 期 2, 页码 469-487出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/jcd.2020019
关键词
Data driven; dynamic mode decomposition; model order reduction; Kalman Filter; denoising
In this research, we investigate the application of Dynamic Mode Decomposition combined with Kalman Filtering, Smoothing, and Wavelet Denoising (DMD-KF-W) for denoising time-resolved data. We also compare the performance of this technique with state-of-the-art denoising methods such as Total Variation Diminishing (TV) and Divergence-Free Wavelets (DFW), when applicable. Dynamic Mode Decomposition (DMD) is a data-driven method for finding the spatio-temporal structures in time series data. In this research, we use an autoregressive linear model resulting from applying DMD to the time-resolved data as a predictor in a Kalman Filtering-Smoothing framework for the purpose of denoising. The DMD-KF-W method is parameter-free and runs autonomously. Tests on numerical phantoms show lower error metrics when compared to TV and DFW, when applicable. In addition, DMD-KF-W runs an order of magnitude faster than DFW and TV. In the case of synthetic datasets, where the noise-free datasets were available, our method was shown to perform better than TV and DFW methods (when applicable) in terms of the defined error metric.
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