Cardinality-constrained sparse spectral unmixing can be solved using Branch-and-Bound algorithms, provided that the number of reference endmembers and the cardinality constraint are reasonably small. However, focusing solely on the best solution may not always be the most relevant approach, especially in the presence of high correlation between endmembers, solutions close to the optimal one-in terms of objective function-but with different supports (activated endmembers) may offer better interpretability.
We focus on the exact resolution of sparse spectral unmixing problems, that is, the search for cardinality-limited linear least squares solutions under non-negativity and sum-to-one constraints.
We propose an algorithm that exactly solves the cardinality-constrained sparse spectral unmixing problem.
Implementation of the branch-and-bound algorithm for sparse spectral unmixing. The version submitted to the [EUSIPCO 2025](https://www.eusipco2025.org/) conference is based on the [UNMIX](https://gitlab.com/mlatif/bbhs_ext_cpp) C++ prototype. Supplementary material can be found [here](https://gitlab.univ-nantes.fr/ls2n-sims/l0-sparse-unmix-eusipco-supplementary-materials).
September 2021 – LS2N SiMS team seminar.