Canonical polyadic decomposition of hyperspectral patch tensors. Veganzones, M. A., Cohen, J. E., Farias, R. C., Usevich, K., Drumetz, L., Chanussot, J., & Comon, P. In *2016 24th European Signal Processing Conference (EUSIPCO)*, pages 2176-2180, Aug, 2016.

Paper doi abstract bibtex

Paper doi abstract bibtex

Spectral unmixing (SU) 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. The Canonical Polyadic (CP) tensor decomposition has proved to be a powerful tool to decompose a tensor data onto a few rank-one terms in a multilinear fashion. Here, we establish the connection between the CP decomposition and the SU problem when the tensor data is built by stacking small patches of the hyperspectral image. It turns out that the CP decomposition of this hyperspectral patch-tensor is equivalent to solving a blind regularized Extended Linear Mixing Model (ELMM).

@InProceedings{7760634, author = {M. A. Veganzones and J. E. Cohen and R. C. Farias and K. Usevich and L. Drumetz and J. Chanussot and P. Comon}, booktitle = {2016 24th European Signal Processing Conference (EUSIPCO)}, title = {Canonical polyadic decomposition of hyperspectral patch tensors}, year = {2016}, pages = {2176-2180}, abstract = {Spectral unmixing (SU) 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. The Canonical Polyadic (CP) tensor decomposition has proved to be a powerful tool to decompose a tensor data onto a few rank-one terms in a multilinear fashion. Here, we establish the connection between the CP decomposition and the SU problem when the tensor data is built by stacking small patches of the hyperspectral image. It turns out that the CP decomposition of this hyperspectral patch-tensor is equivalent to solving a blind regularized Extended Linear Mixing Model (ELMM).}, keywords = {hyperspectral imaging;image representation;matrix algebra;ELMM;blind regularized extended linear mixing model;canonical polyadic tensor decomposition;fractional spatial distributions;hyperspectral image analysis;spectral unmixing;hyperspectral patch tensors;Tensile stress;Hyperspectral imaging;Matrix decomposition;Europe;Signal processing algorithms;Signal processing;Stacking;Spectral unmixing;extended linear mixing model;Canonical Polyadic;nonnegative tensor decomposition;patch tensor}, doi = {10.1109/EUSIPCO.2016.7760634}, issn = {2076-1465}, month = {Aug}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2016/papers/1570255787.pdf}, }

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