  Experimental spatio-temporal flow data often contain gaps or other types of
undesired artifacts. To reconstruct flow data in the compromised or missing
regions, a data completion method based on spectral proper orthogonal
decomposition (SPOD) is developed. The algorithm leverages the temporal
correlation of the SPOD modes with preceding and succeeding snapshots, and
their spatial correlation with the surrounding data at the same time instant.
For each gap, the algorithm first computes the SPOD of the remaining,
unaffected data. In the next step, the compromised data are projected onto the
basis of the SPOD modes. This corresponds to a local inversion of the SPOD
problem and yields expansion coefficients that permit the reconstruction in the
affected regions. This local reconstruction is successively applied to each
gap. After all gaps are filled in, the procedure is repeated in an iterative
manner until convergence. This method is demonstrated on two examples: direct
numerical simulation of laminar flow around a cylinder, and time-resolved PIV
data of turbulent cavity flow obtained by Zhang et al. (2019). Randomly added
gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption,
and in the presence of measurement noise in the experimental data, the
algorithm recovers 97% and 80% of the original data in the corrupted regions of
the simulation and PIV data, respectively. These values are higher than those
achieved by established methods like gappy POD and Kriging.
