Determination of Data Dimensionality in Hyperspectral Imagery—PNAPCA

Abstract

Minimum noise fraction (MNF) transformation or noise-adjusted principal component analysis (NAPCA) is frequently used to determine the inherent dimensionality for remote sensing images. However, these approaches are limited primarily in that the noise must be accurately estimated from the data or a priori. Inaccurately estimating the noise seriously degrades the validity of the calculated dimensionality. In this work, we apply NAPCA to a partitioned data space to resolve the inaccuracy of the noise estimation and properly estimate the data dimensionality. This approach is referred to herein as PNAPCA. In contrast to the PCA-based approaches which consider interrelationships within a set of variables, PNAPCA focuses on the relationship between two distinct subspaces which are partitioned from the data space of the original image by a simultaneous transformation. This partitioning causes the gap between the group of eigenvalues for signal plus noise and noise only to become larger than all other PCA-based approaches. The number of endmembers can then be determined by a designed union-intersection margin testing (UIMT). In addition, the performance of PNAPCA is assessed by two experiments using simulated and real imaging spectrometer data sets collected by the Airborne Visible Infrared Imaging Spectrometer (AVIRIS). Experimental results demonstrate that the proposed method can effectively determine the intrinsic dimensionality of remote sensing images.