Hyperspectral Unmixing with a Modified Augmented Linear Mixing Model Addressing Spectral Variability

Hyperspectral data, collected from air/spaceborne sensors, are generally subject to the spectral variability phenomenon, which makes the problem of spectral unmixing more complex in terms of precise estimation of endmember spectra and their corresponding abundance maps. The standard Linear Mixing Model (LMM) ignores this issue, which recently led to the development of other sophisticated LMMs for addressing this phenomenon. Some of them consider this intra-class variability on the spectral part of variables by means of huge matrices, thus requiring a significant computational capacity and limiting their applicability to large images. Other models consider this phenomenon on the spatial part of variables by using matrices that do not respect the nonnegativity constraint, thus leading to the use of more complex algorithms requiring also a significant computation time. In this paper, a modified Augmented LMM (ALMM) is proposed to address the spectral variability, considered on the spatial part of variables, by means of matrices of smaller sizes and obeying the nonnegativity constraint, thus allowing the use of a less complicated algorithm based on Nonnegative Matrix Factorization (NMF). The proposed modified ALMM models, as the original ALMM, the most important scaling factor spectral variabilities, and other ones by introducing additive nonnegative, unlike the ALMM, matrices. The deduced NMF-based algorithm proves to be very attractive as evidently reported by achieved tests.