Adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction

This work presents a novel method for replacing erroneous measurements in digital particle image velocimetry (DPIV) data using an adaptive reconstruction with gappy proper orthogonal decomposition (POD). Previous studies have shown that gappy POD can be used to replace erroneous data with high accuracy. Conventional gappy POD methods employ a spatially constant number of modes for reconstructing the missing information across the entire field. In contrast, the method presented herein proposes a locally adaptive criterion that allows for determination of the optimum number of POD modes required for the reconstruction of each replaced measurement. This reconstruction produces higher accuracy results using more POD modes than with previous POD methods. The new method was compared against commonly utilized techniques for DPIV vector replacement, namely Kriging, bootstrapping and basic interpolation, as well as previously presented POD reconstruction techniques. The results showed that the adaptive gappy POD reconstruction provides higher accuracy and robustness. (paper)