A GRADIENT-BASED METHOD FOR THE MODIFIED AUGMENTED LINEAR MIXING MODEL ADDRESSING SPECTRAL VARIABILITY FOR HYPERSPECTRAL UNMIXING

Remote sensing hyperspectral images are usually subject to the intra-class variability phenomenon that complicates the precise estimation of endmember spectra and their abundance fractions when using the spectral unmixing process with the typical Linear Mixing Model (LMM), which ignores this concern. Thus, other refined LMMs, which deal with this issue, were developed. Some of them consider this spectral variability on the spectral part of variables, while other ones consider the same phenomenon on the spatial part of variables. In this work, a recent modified Augmented LMM (ALMM) is used to deal with the intra-class variability, considered on the spatial part of variables, by using smaller matrices that also obey the nonnegativity constraint. Furthermore, a projected gradient-based algorithm, based on Nonnegative Matrix Factorization (NMF), is proposed for the used modified ALMM. This Gradient-NMF-based technique proves to be useful as clearly reported by conducted experiments.