Comptes Rendus
Modal decomposition from partial measurements
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 863-872.

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.

Published online:
DOI: 10.1016/j.crme.2019.11.011
Keywords: Modal analysis, Proper generalized decomposition, Dynamic stereo-vision, Dynamic tomography, Field recovery, Gappy proper orthogonal decomposition

Clément Jailin 1, 2; Stéphane Roux 1

1 LMT (ENS Paris-Saclay/CNRS/Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan, France
2 Safran Tech, rue des Jeunes-Bois, 78772 Magny-les-Hameaux, France
     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},
AU  - Clément Jailin
AU  - Stéphane Roux
TI  - Modal decomposition from partial measurements
JO  - Comptes Rendus. Mécanique
PY  - 2019
SP  - 863
EP  - 872
VL  - 347
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2019.11.011
LA  - en
ID  - CRMECA_2019__347_11_863_0
ER  - 
%0 Journal Article
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%A Stéphane Roux
%T Modal decomposition from partial measurements
%J Comptes Rendus. Mécanique
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%P 863-872
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%I Elsevier
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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.

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