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

Abstract

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.

A Blind Multiscale Spatial Regularization Framework for Kernel-Based Spectral Unmixing

“…The reconstructed abundance maps of the nonlinear SU algorithms are presented in Figure 4, where four endmembers whose distribution could be clearly distinguished in the scene were selected [55]. The results for all depicted algorithms are generally compatible and agree with previous studies of this scene [55], [28], [34]. Nevertheless, a careful analysis reveal that the BMUA-N results, displayed in the bottom row of Figure 4, show smoother abundance reconstructions without compromising image details and discontinuities.…”

“…Water absorption and low SNR bands were removed before processing, resulting in 188 bands. Previous works indicate that 14 endmembers are present at the Cuprite mining field [55], [28], [34]. We used the same endmember signatures as in [28], [34].…”

“…Previous works indicate that 14 endmembers are present at the Cuprite mining field [55], [28], [34]. We used the same endmember signatures as in [28], [34]. The reconstructed abundance maps of the nonlinear SU algorithms are presented in Figure 4, where four endmembers whose distribution could be clearly distinguished in the scene were selected [55].…”

“…This property can be leveraged to improve the conditioning of the unmixing problem. Spatial regularization has already been shown to improve the performance of linear [23], [24] and sparse [25], [26] SU, as well as spectral-variability-aware SU [27], [28], [5], [29]. However, spatial information has seldom been enforced in nonlinear unmixing algorithms, partly due to the challenges associated with more complex observation models.…”

Deep Generative Endmember Modeling: An Application to Unsupervised Spectral Unmixing

“…Parametric models are raising considerable interest since they lead to good unmixing results and avoid the main drawbacks of the other groups of SU methods that address EM variability, namely the dependence on a priori knowledge of libraries of material spectra or the need for strong assumptions on the statistical distribution of the EMs for mathematical tractability [13], [14]. Recently proposed parametric models attempt to capture spectral variability by extending the LMM using either additive [10] or multiplicative [11], [12], [15], [16] scaling factors, or by considering tensor-based formulations [17], [18].…”