Effects of Disparate Bases and Norms on Minimizing a Least-Squares Reconstruction Error

摘要

As with facial image reconstructions with eigenfaces [1], partially obstructed or immeasurable flow data can be estimated using the proper orthogonal decomposition (POD) procedure for gappy data, also referred to as gappy POD [2]. As its name suggests, gappy POD hinges on a "gappy" norm, an alteration of the L2 norm neglecting unknown missing data, and a "POD" basis to rectify obscure measurements in a least-squares sense. Interestingly, the same gappy data restoration problem can be addressed by probabilistic principal component analysis (PPCA), which is a probabilistic generalization of principal component analysis (PCA) [3].