Using random matrix theory to determine the intrinsic dimension of a hyperspectral image

Abstract

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process, since under- or over- estimation of this number may lead to incorrect unmixing for unsupervised methods. In this thesis we introduce a new method for determining the intrinsic dimension, using recent advances in Random Matrix Theory (RMT). This method is not sensitive to non-i.i.d. and correlated noise, and it is entirely unsupervised and free from any user-determined parameters. The new RMT method is mathematically derived, and robustness tests are run on synthetic data to determine how the results are a ected by: image size; noise levels; noise variability; noise approximation; spectral characteristics of the endmembers, etc. Success rates are determined for many di erent synthetic images, and the method is compared to two principal state of the art methods, Noise Subspace Projection (NSP) and HySime. All three methods are then tested on twelve real hyperspectral images, including images acquired by satellite, airborne and land-based sensors. When images that were acquired by di erent sensors over the same spatial area are evaluated, RMT gives consistent results, showing the robustness of this method to sensor characterisics.