Spurious PIV vector detection and correction using a penalized least-squares method with adaptive order differentials

Spurious vectors (also called “outliers”) in particle image velocimetry (PIV) experiments can be classified into two categories according to their space distribution characteristics: scattered and clustered outliers. Most of the currently used validation and correction methods treat these two kinds of outliers together without discrimination. In this paper, we propose a new technique based on a penalized least-squares (PLS) method, which allows automatic classification of flows with different types of outliers. PIV vector fields containing scattered outliers are detected and corrected using higher-order differentials, while lower-order differentials are used for the flows with clustered outliers. The order of differentials is determined adaptively by generalized cross-validation and outlier classification. A simple calculation method of eigenvalues of different orders is also developed to expedite computation speed. The performance of the proposed method is demonstrated with four different velocity fields, and the results show that it works better than conventional methods, especially when the number of outliers is large.