A Gradient Based Method for Fully Constrained Least-Squares Unmixing of Hyperspectral Images

Jie Chen (1, 2) , Cédric Richard (2) , Henri Lantéri (3, 4) , Céline Theys (3) , Paul Honeine (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
2 FIZEAU - Laboratoire Hippolyte Fizeau
3 LAGRANGE - Joseph Louis LAGRANGE
4 UNS UFR Sciences - Université Nice Sophia Antipolis - Faculté des Sciences

Linear unmixing of hyperspectral images is a popular approach to determine and quantify materials in sensed images. The linear unmixing problem is challenging because the abundances of materials to estimate have to satisfy non-negativity and full-additivity constraints. In this paper, we investigate an iterative algorithm that integrates these two requirements into the coefficient update process. The constraints are satisfied at each iteration without using any extra operations such as projections. Moreover, the mean transient behavior of the weights is analyzed analytically, which has never been seen for other algorithms in hyperspectral image unmixing. Simulation results illustrate the effectiveness of the proposed algorithm and the accuracy of the model.

Mots clés: non-negativity; sparsity; hyperspectral; gradient methods; geophysical image processing; least squares approximations; remote sensing; gradient based method; constrained least-squares unmixing; hyperspectral images; Mathematical model; Materials; Hyperspectral imaging; hyperspectral image unmixing; mean transient behavior; coefficient update process; Hyperspectral imagery; linear unmixing; Pixel; Equations; Signal processing algorithms; sensed images; linear unmixing problem; non-negativity constraints; full-additivity constraints; iterative algorithm; estimation under constraints

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Jie Chen, Cédric Richard, Henri Lantéri, Céline Theys, Paul Honeine. A Gradient Based Method for Fully Constrained Least-Squares Unmixing of Hyperspectral Images. Proc. IEEE workshop on Statistical Signal Processing (SSP), 2011, Nice, France. pp.301-304, ⟨10.1109/SSP.2011.5967687⟩. ⟨hal-01966030⟩