Blind Hyperspectral Unmixing Using an Extended Linear Mixing Model to Address Spectral Variability

Abstract

Spectral unmixing is one of the main research topics in hyperspectral imaging. It can be formulated as a source separation problem, whose goal is to recover the spectral signatures of the materials present in the observed scene (called endmembers) as well as their relative proportions (called fractional abundances), and this for every pixel in the image. A linear mixture model (LMM) is often used for its simplicity and ease of use, but it implicitly assumes that a single spectrum can be completely representative of a material. However, in many scenarios, this assumption does not hold, since many factors, such as illumination conditions and intrinsic variability of the endmembers, induce modifications on the spectral signatures of the materials. In this paper, we propose an algorithm to unmix hyperspectral data using a recently proposed extended LMM. The proposed approach allows a pixelwise spatially coherent local variation of the endmembers, leading to scaled versions of reference endmembers. We also show that the classic nonnegative least squares, as well as other approaches to tackle spectral variability can be interpreted in the framework of this model. The results of the proposed algorithm on two different synthetic datasets, including one simulating the effect of topography on the measured reflectance through physical modelling, and on two real data sets, show that the proposed technique outperforms other methods aimed at addressing spectral variability, and can provide an accurate estimation of endmember variability along the scene because of the scaling factors estimation.

Advances in Hyperspectral Image and Signal Processing: A Comprehensive Overview of the State of the Art

“…If the linear assumption does not hold, nonlinear unmixing techniques should be used. In addition, as mentioned in previous section, if the spectral variability or endmember variability is being considered, the mixture model must be modified accordingly, which is traditionally accomplished by generating modified/extended linear mixture models [158][159][160].…”

A Comparative Review of Manifold Learning Techniques for Hyperspectral and Polarimetric SAR Image Fusion

“…With the rapid development of Earth observation missions, such as the Sentinel-1 [15], Sentinel-2 [16], and the upcoming EnMAP [17], the availability of both data sources create a huge potential for Earth-oriented information retrieval. Among all optical data [18][19][20], hyperspectral data are well known for their distinguishing power that originates from their rich spectral information [21][22][23][24]. Similarly, polarimetric SAR (PolSAR) data are a popular choice for classification task in the field of SAR because it can reflect the geometric and the dielectric property of the scatterers [25][26][27][28][29].…”

Joint Local Block Grouping with Noise-Adjusted Principal Component Analysis for Hyperspectral Remote-Sensing Imagery Sparse Unmixing

“…Similarly as to modelling the differences, perturbed linear mixing model (PLMM) was introduced with a perturbation term accounting for the endmember variability [23]. Considering the scale differences between endmembers, extended liner mixing model (ELMM) was presented [24]. Later, an augmented linear mixing model (ALMM) to address spectral variability for hyperspectral unmixing [25] was proposed combining the advantages of PLMM and ELMM, together with the novel idea about the spectral variability dictionary, which has led to the state-of-the-art performance.…”