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

Implementation strategies for hyperspectral unmixing using Bayesian source separation

Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has been so far limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy which allows one to apply these algorithms on a full hyperspectral image, as typical in Earth and Planetary Science, is introduced. Effects of pixel selection, the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different dataset have been used: a synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and Remote Sensing in the special issue on Hyperspectral Image and Signal Processing (WHISPERS

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

Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery

This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images

Hyperspectral unmixing accounting for spatial correlations and endmember variability

International audienceThis paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing accounting for endmember variability. This variability is obtained by assuming that each pixel is a linear combination of random endmembers weighted by their corresponding abundances. An additive noise is also considered in the proposed model generalizing the normal compositional model. The proposed model is unsupervised since it estimates the abundances and both the mean and the covariance matrix of each endmember. A classification map indicating the class of each pixel is also obtained based on the estimated abundances. Simulations conducted on a real dataset show the potential of the proposed model in terms of unmixing performance for the analysis of hyperspectral images

Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organised rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e, there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature