Blind Nonlinear Hyperspectral Unmixing Using an $\ell_{q}$ Regularizer

Hyperspectral unmixing consists of estimating pure material spectra (endmembers) and their corresponding abundances in hyperspectral images. In this paper, a blind nonlinear hyperspectral unmixing algorithm is presented. The algorithm promotes sparse abundance maps using an $\ell_{q}$ regularizer and assumes that the spectra are mixed according to an extension to generalized bilinear model, called the Fan model. The algorithm is evaluated using both simulated and real hyperspectral data.

[1]  José M. Bioucas-Dias,et al.  Vertex component analysis: a fast algorithm to unmix hyperspectral data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[2]  Jean-Yves Tourneret,et al.  Nonlinear unmixing of hyperspectral images using a generalized bilinear model , 2011 .

[3]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[4]  Yannick Deville,et al.  Linear-Quadratic Blind Source Separation Using NMF to Unmix Urban Hyperspectral Images , 2014, IEEE Transactions on Signal Processing.

[5]  Biao Hou,et al.  Sparsity-constrained generalized bilinear model for hyperspectral unmixing , 2015, 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).

[6]  Andrzej Cichocki,et al.  Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization , 2007, ICA.

[7]  Paul D. Gader,et al.  A Review of Nonlinear Hyperspectral Unmixing Methods , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[8]  Paul D. Gader,et al.  A sparsity promoting bilinear unmixing model , 2012, 2012 4th Workshop on Hyperspectral Image and Signal Processing (WHISPERS).

[9]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[10]  Jun Zhou,et al.  Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Jiahua Chen,et al.  Extended Bayesian information criteria for model selection with large model spaces , 2008 .

[12]  Alfred O. Hero,et al.  Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms , 2013, IEEE Signal Processing Magazine.

[13]  Olivier Eches,et al.  A Bilinear–Bilinear Nonnegative Matrix Factorization Method for Hyperspectral Unmixing , 2014, IEEE Geoscience and Remote Sensing Letters.

[14]  J. Freud.  Theory Of Reflectance And Emittance Spectroscopy , 2016 .

[15]  John R. Miller,et al.  Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated‐forest hyperspectral data , 2009 .