A Penalization-Based NMF Approach for Hyperspectral Unmixing Addressing Spectral Variability with an Additively-Tuned Mixing Model

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Abstract
Remote sensing hyperspectral sensors are often limited in their spatial resolutions, which leads to mixed pixels. The linear spectral unmixing process is frequently used to extract endmember spectra and their abundance fractions. The standard linear mixing model considers that each endmember is represented by the same spectral signature in the entire image. However, such a basic hypothesis is not relevant in most practical situations since the spectral signature of an endmember can spatially vary. This intra-class variability phenomenon can be considered by introducing the concept of classes of endmembers. Recently, a structured additively-tuned linear mixing model, with its constraints, was proposed, with an associated unmixing method, to address this phenomenon. That method, based on Nonnegative Matrix Factorization (NMF), optimizes a cost function with iterative and multiplicative update rules supplemented by additional constraints that control the spectral variability. In the present work, two penalization terms that more efficiently manage the spectral variability are added to the considered cost function, for the same structured mixing model, and new NMF-based iterative and multiplicative update rules are deduced for achieving the unmixing process taking the considered phenomenon into account. The proposed algorithm proves to be very attractive as clearly reported by conducted experiments based on synthetic data.

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