Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

From representation learning to thematic classification - Application to hierarchical analysis of hyperspectral images

Numerous frameworks have been developed in order to analyze the increasing amount of available image data. Among those methods, supervised classification has received considerable attention leading to the development of state-of-the-art classification methods. These methods aim at inferring the class of each observation given a specific class nomenclature by exploiting a set of labeled observations. Thanks to extensive research efforts of the community, classification methods have become very efficient. Nevertheless, the results of a classification remains a highlevel interpretation of the scene since it only gives a single class to summarize all information in a given pixel. Contrary to classification methods, representation learning methods are model-based approaches designed especially to handle high-dimensional data and extract meaningful latent variables. By using physic-based models, these methods allow the user to extract very meaningful variables and get a very detailed interpretation of the considered image. The main objective of this thesis is to develop a unified framework for classification and representation learning. These two methods provide complementary approaches allowing to address the problem using a hierarchical modeling approach. The representation learning approach is used to build a low-level model of the data whereas classification is used to incorporate supervised information and may be seen as a high-level interpretation of the data. Two different paradigms, namely Bayesian models and optimization approaches, are explored to set up this hierarchical model. The proposed models are then tested in the specific context of hyperspectral imaging where the representation learning task is specified as a spectral unmixing proble