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

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these mismodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember (EM) variability through generalizations of the mixing model, the success of these techniques depends on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of HIs as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems. These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios and 2) they lack guarantees that EMs and abundances will be correctly factorized in their respective tensors. In this article, we propose a more flexible approach, called unmixing with low-rank tensor regularization algorithm accounting for EM variability (ULTRA-V), that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.