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Impact of sparse representation on the admissible solutions of spectral unmixing by non-negative matrix factorization

Abstract : Spectral unmixing in the linear mixing model case can be addressed using non-negative matrix factorization (NMF) algorithms. However, NMF algorithms do not yield a unique solution when the data at hand does not satisfy some uniqueness conditions. Therefore, a set of admissible solutions will be found. The main purpose of this paper is to discuss how much a sparse representation of the data matrix can reduce this set of admissible solutions in the case of spectral unmixing. We propose an algorithm allowing to perform efficiently the sparse representation of data matrix under non-negativity constraints and to assess the admissible solutions when the NMF is performed on the sparse data matrix in the case of reflectance hyperspectral imaging data.
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https://hal.archives-ouvertes.fr/hal-02563696
Contributor : Jérôme Idier Connect in order to contact the contributor
Submitted on : Tuesday, May 5, 2020 - 3:11:27 PM
Last modification on : Wednesday, April 27, 2022 - 4:41:44 AM

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Neeraj Kumar, Saïd Moussaoui, Jérôme Idier, David Brie. Impact of sparse representation on the admissible solutions of spectral unmixing by non-negative matrix factorization. 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, WHISPERS 2015, Jun 2015, Tokyo, Japan. ⟨10.1109/WHISPERS.2015.8075372⟩. ⟨hal-02563696⟩

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