An application of Gappy POD

An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt Soc Am A 12(8):1657–1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38, and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge by examining the subspace spanned by the POD eigenfunctions.

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