Determination of data dimensionality in hyperspectral imagery -- PNAPCA (Q1307708)

The main purpose of the paper is to propose and perform a Partitioned version of the Noise-Adjusted Principal Component Analysis (PNAPCA) to resolve the inaccurate estimation of noise in the NAPCA method. PNAPCA provides also more effective means to obtain a better solution to the intrinsic dimensionality problem in an unknown noise environment. In contrast to the PCA-based approaches which consider inter-relationships within a set of variables, PNAPCA focuses on the relationship between two distinct subspaces which are partitioned from the original data space by a simultaneous transform. According to an error analysis of NAPCA, the diagonal elements of the covariance matrix in PNAPCA can be partitioned into two distinct groups of eigenvalues: one associated with large covariance for signal plus noise, and its complementary with less or equal unity covariance for noise only. The number of endmembers can then be determined by performing a designed union-intersection margin test and by counting the number of covariance values larger than unity. The performance of PNAPCA is evaluated by two experiments using simulated and real imaging spectrometer data sets collected by the airborne visible infrared imaging spectrometer. The experimental results demonstrate the effectiveness of the PNAPCA method to determine the intrinsic dimensionality of remote sensing images.