Nonnegative block-term decomposition with the β-divergence: joint data fusion and blind spectral unmixing

We present a new method for solving simultaneously hyperspectral super-resolution and spectral unmixing of the unknown super-resolution image. Our method relies on three key elements: (1) the nonnegative decomposition in rank-($L_r$,$L_r$,1) block-terms, (2) joint tensor factorization with multiplicative updates, and (3) the formulation of a family of optimization problems with $\beta$-divergences objective functions. We come up with a family of simple, robust and efficient algorithms, adaptable to various noise statistics. Experiments show that our approach competes favorably with state-of-the-art methods for solving both problems at hand for various noise statistics.