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) , Jean-Yves Tourneret (4, 5, 6)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
2 DocApp - LITIS - Equipe Apprentissage
3 LAGRANGE - Joseph Louis LAGRANGE
4 IRIT-MINDS - CoMputational imagINg anD viSion
5 TéSA - Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics
6 Toulouse INP - Institut National Polytechnique (Toulouse)

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.

Mots clés: Eigengap approach; Hyperspectral imaging; Linear spectral mixture; Endmember number; Random matrix theory(RMT); Sample covariance matrix

Domaines: Traitement du signal et de l'image [eess.SP]

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, 2016, vol. 54 (n° 7), pp.3811-3821. ⟨10.1109/TGRS.2016.2528298⟩. ⟨hal-01325467⟩