On the use of ritz values for calculating the number of endmembers in hyperspectral images

Abstract

Signal subspace identification is a crucial step in many hyperspectral processing algorithms such as target detection, change detection, classification, and unmixing. This is due to the fact that a correct dimensionality reduction improves algorithm performances and reduces their complexity and data requirements. This paper introduces a new method for this task which is based on the Ritz values obtained in methods such as the restarted Arnoldi method or the Lanczos method for calculating the eigenvalues and eigenvectors of a given matrix. In particular, it first calculates a high number of eigenvalues and eigenvectors, and a Ritz value per eigenvalue calculated and then, it estimates the dimension of the signal subspace according to the Ritz values obtained. The results obtained with the proposed method for synthetic and real hyperspectral images verify the performance of the introduced methodology to estimate the number of endmembers in different types of hyperspectral images. Moreover, these results are better than the ones obtained, for the same images, with the most popular algorithm for this task in the state of the art, i.e. the HySIME and the Virtual Dimensionality algorithms.