Noise subspace projection approaches to determination of intrinsic dimensionality of hyperspectral imagery

Determination of Intrinsic Dimensionality (ID) for remotely sensed imagery has been a challenging problem. For multispectral imagery it may be solvable by Principal Components Analysis (PCA) due to a small number of spectral bands which implies that ID is also small. However, PCA method may not be effective if it is applied to hyperspectral images. This may arise in the fact that a high spectral-resolution hyperspectral sensor may also extract many unknown interfering signatures in addition to endmember signatures. So, determining the ID of hyperspectral imagery is more problematic than that of multispectral imagery. This paper presents a Neyman-Pearson detection theory-based eigen analysis for determination of ID for hyperspectral imagery, particularly, a new approach referred to as Noise Subspace Projection (NSP)-based eigen-thresholding method. It is derived from a noise whitening process coupled with a Neyman-Pearson detector. The former estimates the noise covariance matrix which will be used to whiten the data sample correlation matrix, whereas the latter converts the problem of determining ID to a Nevman-Pearosn decision with the Receiver Operating Characteristics (ROC) analysis used as a thresholding technique to estimate ID. In order to demonstrate the effectiveness of the proposed method AVIRIS are used for experiments.