Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach

Linear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms.