Robust Principal Component Analysis of Corrupted Flow Fields

When particle image velocimetry (PIV) is used to quantitatively measure fluid flows, noise and spurious velocity vectors can reduce measurement quality and degrade subsequent analysis. Standard post-processing methods involve subjective outlier identification and interpolation, which can discard useful data and produce non-physical flow fields. Here, we present a new method to clean and de-noise PIV measurements using robust principal component analysis (RPCA). RPCA can uncover and isolate the low-rank coherent structure of data, objectively identifying and removing noise and sparse outliers. We demonstrate the RPCA algorithm on simulations and experiments where the flow physics are well-known. We analyze the turbulence spectra of flow measurements from high-fidelity numerical simulations before and after RPCA to show that dominant coherent structures are not degraded. Additionally, the dimension of the low-rank subspace and percentage of non-zero elements in the sparse subspace are analyzed to determine how aggressively to filter.