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

Abderrahim Halimi 1 Paul Honeine 2, 1 Malika Kharouf 1 Cédric Richard 3, 4 Jean-Yves Tourneret 5, 6
2 DocApp - LITIS - Equipe Apprentissage
LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
4 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : 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.
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Abderrahim Halimi, Paul Honeine, Malika Kharouf, Cédric Richard, Jean-Yves Tourneret. Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach. IEEE Transactions on Geoscience and Remote Sensing, Institute of Electrical and Electronics Engineers, 2016, vol. 54 (n° 7), pp.3811-3821. ⟨10.1109/TGRS.2016.2528298⟩. ⟨hal-01325467⟩

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