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Traditional hyperspectral unmixing methods neglect the underlying variabilityof spectral signatures often observed in typical hyperspectral images (HI),propagating these missmodeling errors throughout the whole unmixing process.Attempts to model material spectra as members of sets or as random variablestend to lead to severely ill-posed unmixing problems. Although parametricmodels have been proposed to overcome this drawback by handling endmembervariability through generalizations of the mixing model, the success of thesetechniques depend on employing appropriate regularization strategies. Moreover,the existing approaches fail to adequately explore the natural multidimensinalrepresentation of HIs. Recently, tensor-based strategies considered low-rankdecompositions of hyperspectral images as an alternative to imposelow-dimensional structures on the solutions of standard and multitemporalunmixing problems. These strategies, however, present two main drawbacks: 1)they confine the solutions to low-rank tensors, which often cannot representthe complexity of real-world scenarios; and 2) they lack guarantees thatendmembers and abundances will be correctly factorized in their respectivetensors. In this work, we propose a more flexible approach, called ULTRA-V,that imposes low-rank structures through regularizations whose strictness iscontrolled by scalar parameters. Simulations attest the superior accuracy ofthe method when compared with state-of-the-art unmixing algorithms that accountfor spectral variability.

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability