Singular value decomposition of noisy data: noise filtering

In fluid mechanics, singular value decomposition (SVD) and proper orthogonal decomposition (POD) Footnote 1 are used for particle image velocimetry (PIV) data regression (Sherry et al. 2013 ; Raiola et al. 2015 ; Mendez et al. 2017 ; Brindise and Vlachos 2017 ); identification of coherent structures (Kriegseis et al. 2009 ; Druault et al. 2012 ; Kourentis and Konstantinidis 2012 ; Marié et al. 2013 ; Xu et al. 2013 ; Gandhi et al. 2015 ); low-order modeling, possibly for flow control (Ma et al. 2003 ; Feng et al. 2011 ; Feng and Wang 2014 ); optimal sensor placement (Cohen et al. 2004 ); dynamic mode decomposition (Schmid 2010 ; Dawson et al. 2016 ); and more. In (Epps and Krivitzky 2019 ), we considered mode corruption due to noise present in the data, building on the works of Kato ( 1976 ), Breuer and Sirovich ( 1991 ), Venturi ( 2006 ) and Epps and Techet ( 2010 ). Herein, we consider use of the SVD/POD for data de-noising.