Minimum Dispersion Constrained Nonnegative Matrix Factorization to Unmix Hyperspectral Data

Abstract : This paper considers the problem of spectral unmixing. In the fields of spectral data analysis or hyperspectral image analysis, the acquired data can be considered as a collection of observed spectra. Each observed spectrum is assumed to be a noised linear mixture of pure material spectra, namely endmembers. For each observed spectral pixel, the mixing coefficients, usually called abundances, are positive and summed to unity. A Nonnegative Matrix Factorization (NMF) based approach seems very suitablet to recover the endmember spectra and the abundance coefficients (i.e. unmix data), as they consider both the endmember spectra positivity and the abundance positivity. However, they basically do not include the sum-to-unity constraint which leads to degenerate solutions. Moreover, usual NMF algorithms are known to be trapped in stationnary points, which genarally lead to unusable results for spectral unmixing purposes. In this paper, we propose a suitable regularization function to ensure a ”minimum dispertion” of the endmember spectra, and we consider the sum-to-unitity constraint. The regularized function is minimized with a Projected Gradient (PG) sheme and we propose a new technique to evaluate the PG step-size, leading to time savings comparatively to existing PG algorithms. The resluting algorithm is called MiniDisCo, for Minimum Dispertion Constrained NMF. MiniDisco is compared to reference unmixing algorithms through a variety of simulations on synthetic data and we present unmixing results obtained on a real data set.
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Submitted on : Thursday, April 8, 2010 - 3:31:40 PM
Last modification on : Monday, March 4, 2019 - 2:04:12 PM

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Alexis Huck, Mireille Guillaume. Minimum Dispersion Constrained Nonnegative Matrix Factorization to Unmix Hyperspectral Data. IEEE Transactions on Geoscience and Remote Sensing, Institute of Electrical and Electronics Engineers, 2010, PP (99), pp.1-13. ⟨10.1109/TGRS.2009.2038483⟩. ⟨hal-00471583⟩

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