Multilinear spectral unmixing of hyperspectral multiangle images

Spectral unmixing is one of the most important and studied topics in hyperspectral image analysis. By means of spectral unmixing it is possible to decompose a hyperspectral image in its spectral components, the so-called endmembers, and their respective fractional spatial distributions, so-called abundance maps. New hyperspectral missions will allow to acquire hyperspectral images in new ways, for instance, in temporal series or in multi-angular acquisitions. Working with these incoming huge databases of multi-way hyperspec-tral images will raise new challenges to the hyperspectral community. Here, we propose the use of compression-based non-negative tensor canonical polyadic (CP) decompositions to analyze this kind of datasets. Furthermore, we show that the non-negative CP decomposition could be understood as a multi-linear spectral unmixing technique. We evaluate the proposed approach by means of Mars synthetic datasets built upon multi-angular in-lab hyperspectral acquisitions.

[1]  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.

[2]  Alfonso Fernández-Manso,et al.  Spectral unmixing , 2012 .

[3]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[4]  F. L. Hitchcock The Expression of a Tensor or a Polyadic as a Sum of Products , 1927 .

[5]  Jon Atli Benediktsson,et al.  Recent Advances in Techniques for Hyperspectral Image Processing , 2009 .

[6]  Ieee Staff 2017 25th European Signal Processing Conference (EUSIPCO) , 2017 .

[7]  A F Goetz,et al.  Imaging Spectrometry for Earth Remote Sensing , 1985, Science.

[8]  P. Paatero A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .

[9]  Pierre Comon,et al.  Tensors : A brief introduction , 2014, IEEE Signal Processing Magazine.

[10]  H. Kiers Towards a standardized notation and terminology in multiway analysis , 2000 .

[11]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[12]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[13]  Pierre Comon,et al.  Nonnegative approximations of nonnegative tensors , 2009, ArXiv.

[14]  Pierre Comon,et al.  Fast Decomposition of Large Nonnegative Tensors , 2015, IEEE Signal Processing Letters.