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

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often obeserved in typical hyperspectral images, propagating these missmodeling 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. To overcome this drawback, endmember variability has been handled through generalizations of the mixing model, combined with spatial regularization over the abundance and endmember estimations. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images 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 endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called 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.