Robust Linear Spectral Unmixing using Anomaly Detection

This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers, corrupted by an additional nonlinear term modelling anomalies and additive Gaussian noise. A Markov random field is used for anomaly detection based on the spatial and spectral structures of the anomalies. This allows outliers to be identified in particular regions and wavelengths of the data cube. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint linear unmixing and anomaly detection algorithm. Simulations conducted with synthetic and real hyperspectral images demonstrate the accuracy of the proposed unmixing and outlier detection strategy for the analysis of hyperspectral images

Hyperspectral Unmixing with Endmember Variability using Partial Membership Latent Dirichlet Allocation

The application of Partial Membership Latent Dirichlet Allocation(PM-LDA) for hyperspectral endmember estimation and spectral unmixing is presented. PM-LDA provides a model for a hyperspectral image analysis that accounts for spectral variability and incorporates spatial information through the use of superpixel-based 'documents.' In our application of PM-LDA, we employ the Normal Compositional Model in which endmembers are represented as Normal distributions to account for spectral variability and proportion vectors are modeled as random variables governed by a Dirichlet distribution. The use of the Dirichlet distribution enforces positivity and sum-to-one constraints on the proportion values. Algorithm results on real hyperspectral data indicate that PM-LDA produces endmember distributions that represent the ground truth classes and their associated variability

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

Uncertainty Assessment of Spectral Mixture Analysis in Remote Sensing Imagery

Spectral mixture analysis (SMA), a scheme of sub-pixel-based classifications, is one of the widely used models to map fractional land use and land cover information in remote sensing imagery. It assumes that: 1) a mixed pixel is composed by several pure land cover classes (endmembers) linearly or nonlinearly, and 2) the spectral signature of each endmember is a constant within the entire spatial extent of analysis. SMA has been commonly applied to impervious surface area extraction, vegetation fraction estimation, and land use and land cover change (LULC) mapping. Limitations of SMA, however, still exist. First, the existence of between- and within-class variability prevents the selection of accurate endmembers, which results in poor accuracy of fractional land cover estimates. Weighted spectral mixture analysis (WSMA) and transformed spectral mixture analysis (TSMA) are alternate means to address the within- and between- class variability. These methods, however, have not been analyzed systematically and comprehensively. The effectiveness of each WSMA and TSMA scheme is still unknown, in particular within different urban areas. Second, multiple endmember SMA (MESMA) is a better alternative to address spectral mixture model uncertainties. It, nonetheless, is time consuming and inefficient. Further, incorrect endmember selections may still limit model performance as the best-fit endmember model might not be the optimal model due to the existence of spectral variability. Therefore, this study aims 1) to explore endmember uncertainties by examining WSMA and TSMA modeling comprehensively, and 2) to develop an improved MESMA model in order to address the uncertainties of spectral mixture models. Results of the WSMA examination illustrated that some weighting schemes did reduce endmember uncertainties since they could improve the fractional estimates significantly. The results also indicated that spectral class variance played a key role in addressing the endmember uncertainties, as the better performing weighting schemes were constructed with spectral class variance. In addition, the results of TSMA examination demonstrated that some TSMAs, such as normalized spectral mixture analysis (NSMA), could effectively solve the endmember uncertainties because of their stable performance in different study areas. Results of Class-based MEMSA (C-MESMA) indicated that it could address spectral mixture model uncertainties by reducing a lot of the calculation burden and effectively improving accuracy. Assessment demonstrated that C-MEMSA significantly improving accuracy. Major contributions of this study can be summarized as follow. First, the effectiveness of addressing endmember uncertainties have been fully discussed by examining: 1) the effectiveness of ten weighted spectral mixture models in urban environments; and 2) the effectiveness of 26 transformed spectral mixture models in three locations. Constructive guidance regarding handling endmember uncertainties using WSMA and TSMA have been provided. Second, the uncertainties of spectral mixture model were reduced by developing an improved MESMA model, named C-MESMA. C-MESMA could restrict the distribution of endmembers and reduce the calculation burden of traditional MESMA, increasing SMA accuracy significantly