Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures. We propose a more flexible approach called ULTRA-V that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters.
Traditional hyperspectral unmixing methods neglect the underlying variability
of 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 variables
tend to lead to severely ill-posed unmixing problems. Although parametric
models have been proposed to overcome this drawback by handling endmember
variability through generalizations of the mixing model, the success of these
techniques depend 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 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.