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.

The aim of fusing hyperspectral and multispectral images is to overcome the limitation of remote sensing hyperspectral sensors by improving their spatial resolutions. This process, also known as hypersharpening, generates an unobserved high-spatial-resolution hyperspectral image. To this end, several hypersharpening methods have been developed, however most of them do not consider the spectral variability phenomenon; therefore, neglecting this phenomenon may cause errors, which leads to reducing the spatial and spectral quality of the sharpened products. Recently, new approaches have been proposed to tackle this problem, particularly those based on spectral unmixing and using parametric models. Nevertheless, the reported methods need a large number of parameters to address spectral variability, which inevitably yields a higher computation time compared to the standard hypersharpening methods. In this paper, a new hypersharpening method addressing spectral variability by considering the spectra bundles-based method, namely the Automated Extraction of Endmember Bundles (AEEB), and the sparsity-based method called Sparse Unmixing by Variable Splitting and Augmented Lagrangian (SUnSAL), is introduced. This new method called Hyperspectral Super-resolution with Spectra Bundles dealing with Spectral Variability (HSB-SV) was tested on both synthetic and real data. Experimental results showed that HSB-SV provides sharpened products with higher spectral and spatial reconstruction fidelities with a very low computational complexity compared to other methods dealing with spectral variability, which are the main contributions of the designed method.

Hypersharpening consists in generating an unobservable high-spatial-resolution hyperspectral image by fusing an observed low-spatial-resolution hyperspectral image with an observed high-spatial-resolution panchromatic or multispectral one. The obtained image preserves the high spectral resolution of the first image and the high spatial resolution of the second one. Unlike standard hypersharpening methods that do not consider the spectral variability phenomenon, in this letter, a new approach, which addresses this phenomenon, is proposed for fusing hyperspectral and multispectral remote sensing images. This approach, linked to linear spectral unmixing methods, is based on an extension of nonnegative matrix factorization (NMF), namely the inertia-constrained pixel-by-pixel NMF (IP-NMF) algorithm. The developed fusion algorithm, called hyperspectral and multispectral data fusion based on IP-NMF (HMF-IPNMF), is applied to synthetic and real data sets. Experimental results clearly show that the developed fusion method yields sharpened hyperspectral images with higher spectral and spatial fidelities when compared to those provided by tested state-of-the-art methods that do not take spectral variability into account.

In a previous paper, we introduced (i) a specific hyperspectral mixing model for the sea bottom, based on a detailed physical analysis that includes the adjacency effect, and (ii) an associated unmixing method that is supervised (i.e., not blind) in the sense that it requires a prior estimation of various parameters of the mixing model, which is constraining. We here proceed much further, by first analytically showing that the above model can be seen as a specific member of the general class of mixing models involving spectral variability. Therefore, we then process such data with the IP-NMF unsupervised (i.e., blind) unmixing method that we proposed in previous works to handle spectral variability. Such variability especially occurs when the sea depth significantly varies over the considered scene. We show that IP-NMF then yields significantly better pure spectra estimates than a classical method from the literature that was not designed to handle such variability. We present test results obtained with realistic synthetic data. These tests address several reference water depths, up to 7.5 m, and clear or standard water. For instance, they show that when the reference depth is set to 7.5 m and the water is clear, the proposed approach is able to distinguish various classes of pure materials when the water depth varies up to $\pm 0.2$ m around this reference depth, over all pixels of the analyzed scene or over a “subscene”: the overall scene may first be segmented, to obtain smaller depths variations over each subscene. The proposed approach is therefore effective and can be used as a building block in performing the subpixel classification of the sea bottom for shallow water.

Remote sensing hyperspectral sensors are often limited in their spatial resolutions, which results in mixed pixels. The mixture is, usually, assumed to be linear and linear spectral unmixing techniques are employed to unmix observed pixel spectra. Most of these techniques consider that each endmember is represented by the same spectrum in the whole image. Nevertheless, in various situations, each endmember needs to be represented by slightly different spectra in all observed pixels. This spectral variability phenomenon must be tackled by introducing the concept of classes of endmembers. In this paper, a structured additively-tuned linear mixing model, without physical considerations, is first introduced to address this phenomenon. Then, an algorithm, based on nonnegative matrix factorization, is proposed for unmixing the considered data. This algorithm, which minimizes a cost function by using multiplicative update rules supplemented by additional constraints, derives, for each class of endmembers, slightly different estimated spectra in all pixels. The designed update rules are obtained by considering the structured variables introduced in the used mixing model. To assess the performance of the designed algorithm, experiments, based on realistic synthetic data, are conducted and obtained results are compared to those of approaches from the literature. This comparison shows that the proposed approach outperforms all other tested methods.

In this work, a hypersharpening approach, creating fused hyperspectral remote sensing images with high spatial and spectral resolutions, is introduced. This approach, linked to linear spectral unmixing (LSU) methods and based on a multiplicative nonnegative matrix factorization (NMF) technique, extends the Joint-Criterion NMF (JCNMF) algorithm, by addressing the spectral variability phenomenon. This method is designed for combining low spatial resolution hyperspectral and high spatial resolution multispectral data. It optimizes the considered criterion that deals with the spectral variability phenomenon by using a specific structure of involved matrices. The introduced algorithm, which uses multiplicative and iterative update rules, is applied to realistic synthetic data, and its effectiveness, in the spatial and spectral domains, is evaluated by considering commonly used assessment protocol and performance criteria. The obtained results prove that the introduced algorithm yields fused hyperspectral data with good spectral and spatial fidelities. These results also illustrate that the proposed algorithm significantly outperforms two tested literature ones that do not take the spectral variability phenomenon into account.