Hyperspectral unmixing addressing spectral variability remains an important challenge. In this field, unmixing methods do not exploit the possible availability of some spectral information that corresponds to known spectra of some pure materials present in an acquired scene. In this work, a hyperspectral unmixing method, which considers not only the spectral variability phenomenon but also exploits one or more available known pure material spectra, is proposed. Such a combination, initially proposed here, constitutes the originality of the conducted work that distinguishes it from other investigations in the hyperspectral unmixing topic. The proposed method, based on an informed nonnegative matrix factorization technique, employs a partial structured additively-tuned linear mixing model that deals with spectral variability. Experimental results, based on real data, show that the designed informed algorithm, which addresses spectral variability, yields very satisfactory results and outperforms tested literature approaches. Thus, such an unmixing algorithm may be used for automatically detecting and mapping, using hyperspectral data, materials of interest whose spectra are known while dealing with their spectral variability.
Remote sensing hyperspectral sensors, with high spectral resolution, allow precise classification of endmembers present in imaged areas. These sensors have a limited spatial resolution, which results in mixed pixels. The mixture is usually assumed to be linear and blind linear spectral unmixing (LSU) methods are used to unmix all observed pixel spectra. Most blind LSU approaches assume that each endmember is represented by a unique spectrum in all image pixels. But, in many practical applications, this assumption is not valid and more complex models are needed to describe other phenomena, e.g. when each endmember needs to be represented by slightly different spectra in all image pixels. This spectral variability must be handled by replacing the concept of endmembers by classes of endmembers, to avoid errors when processing the considered data. In this paper, a new linear mixing model is firstly introduced in order to handle the spectral variability. In the proposed model, the endmember spectra are additively tuned. Then, an algorithm, based on pixel-by-pixel nonnegative matrix factorization, is proposed for unmixing the considered data. That algorithm, which derives, for each class of endmembers, slightly different estimated spectra in all pixels, optimizes a cost function and uses additional constraints that are related to the introduced linear mixing model. Experiments, based on realistic synthetic data, are conducted to evaluate the performance of the proposed algorithm. The obtained results are compared to those of three approaches from the literature. These test results show that the proposed approach outperforms all other tested methods.
This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.
In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.
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