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Nonlinear hyperspectral unmixing with robust NMF

We introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. The new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects, that are treated as sparsely distributed additive outliers.With the standard nonnegativity and sum-to-one constraints inherent to spectral unmixing, our model leads to a new form of robust nonnegative matrix factorization (rNMF) with a group-sparse outlier term. The factorization is posed as an optimization problem which is addressed with a block-coordinate descent algorithm involving majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods.

The model as well as the robust NMF algorithm are described in the paper published in IEEE Trans. Image Processing in 2015:

The rNMF algorithm is available as a MATLAB code:

PyTorch-library (GPU) and NumPy (CPU) implementations have been released by Neel Dey, New York University, and are available through his GitHub:

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