A data set over space and time is assumed to have a low-rank representation in separated spatial and temporal modes. The problem of evaluating these modes from a temporal series of partial measurements is considered. Each elementary instantaneous measurement captures only a “window” (in space) of the observed data set, but the position of this window varies in time so as to cover the entire region of interest and would allow for a complete measurement would the scene be static. A novel procedure, alternative to the Gappy Proper Orthogonal Decomposition (GPOD) methodology, is introduced. It is a fixed-point iterative procedure where modes are evaluated sequentially. Tested upon very sparse acquisition (1% of measurements being available) and very noisy synthetic data sets (10% noise), the proposed algorithm is shown to outperform two variants of the GPOD algorithm, with much faster convergence, and better reconstruction of the entire data set.
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@article{CRMECA_2019__347_11_863_0,
author = {Cl\'ement Jailin and St\'ephane Roux},
title = {Modal decomposition from partial measurements},
journal = {Comptes Rendus. M\'ecanique},
pages = {863--872},
publisher = {Elsevier},
volume = {347},
number = {11},
year = {2019},
doi = {10.1016/j.crme.2019.11.011},
language = {en},
}
Clément Jailin; Stéphane Roux. Modal decomposition from partial measurements. Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 863-872. doi : 10.1016/j.crme.2019.11.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.011/
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