Library-learning-assisted robust principal component analysis for denoising severely corrupted flow fields
Abstract
Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.
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BibTeX
@misc{koop2026librarylearningassisted,
title = {{Library-learning-assisted robust principal component analysis for denoising severely corrupted flow fields}},
author = {Pablo Koop and Isabel Scherl and Kai Fukami},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18015},
eprint = {2609.18015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18015},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Library-learning-assisted robust principal component analysis for denoising severely corrupted flow fields
AU - Pablo Koop
AU - Isabel Scherl
AU - Kai Fukami
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18015
UR - https://arxiv.org/abs/2609.18015
AB - Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.
ER -