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 using a semiparametric model and spatial regularization

Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an $\ell_1$ local variation norm as the spatial regularizer, is derived. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.Comment: 5 pages, 1 figure, submitted to ICASSP 201

Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

Estimating the number of endmembers in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm.

This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images

Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm