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

Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

Automated lithological mapping using airborne hyperspectral thermal infrared data: A case study from Anchorage Island, Antarctica

The thermal infrared portion of the electromagnetic spectrum has considerable potential for mineral and lithological mapping of the most abundant rock-forming silicates that do not display diagnostic features at visible and shortwave infrared wavelengths. Lithological mapping using visible and shortwave infrared hyperspectral data is well developed and established processing chains are available, however there is a paucity of such methodologies for hyperspectral thermal infrared data. Here we present a new fully automated processing chain for deriving lithological maps from hyperspectral thermal infrared data and test its applicability using the first ever airborne hyperspectral thermal data collected in the Antarctic. A combined airborne hyperspectral survey, targeted geological field mapping campaign and detailed mineralogical and geochemical datasets are applied to small test site in West Antarctica where the geological relationships are representative of continental margin arcs. The challenging environmental conditions and cold temperatures in the Antarctic meant that the data have a significantly lower signal to noise ratio than is usually attained from airborne hyperspectral sensors. We applied preprocessing techniques to improve the signal to noise ratio and convert the radiance images to ground leaving emissivity. Following preprocessing we developed and applied a fully automated processing chain to the hyperspectral imagery, which consists of the following six steps: (1) superpixel segmentation, (2) determine the number of endmembers, (3) extract endmembers from superpixels, (4) apply fully constrained linear unmixing, (5) generate a predictive classification map, and (6) automatically label the predictive classes to generate a lithological map. The results show that the image processing chain was successful, despite the low signal to noise ratio of the imagery; reconstruction of the hyperspectral image from the endmembers and their fractional abundances yielded a root mean square error of 0.58%. The results are encouraging with the thermal imagery allowing clear distinction between granitoid types. However, the distinction of fine grained, intermediate composition dykes is not possible due to the close geochemical similarity with the country rock

Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms, and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.Comment: 30 pages, 2 figures, 7 tables. Main change: Improvement of the bound of the main theorem (Th. 3), replacing r with sqrt(r

Imaging White Blood Cells using a Snapshot Hyper-Spectral Imaging System

Automated white blood cell (WBC) counting systems process an extracted whole blood sample and provide a cell count. A step that would not be ideal for onsite screening of individuals in triage or at a security gate. Snapshot Hyper-Spectral imaging systems are capable of capturing several spectral bands simultaneously, offering co-registered images of a target. With appropriate optics, these systems are potentially able to image blood cells in vivo as they flow through a vessel, eliminating the need for a blood draw and sample staining. Our group has evaluated the capability of a commercial Snapshot Hyper-Spectral imaging system, specifically the Arrow system from Rebellion Photonics, in differentiating between white and red blood cells on unstained and sealed blood smear slides. We evaluated the imaging capabilities of this hyperspectral camera as a platform to build an automated blood cell counting system. Hyperspectral data consisting of 25, 443x313 hyperspectral bands with ~3nm spacing were captured over the range of 419 to 494nm. Open-source hyperspectral datacube analysis tools, used primarily in Geographic Information Systems (GIS) applications, indicate that white blood cells\u27 features are most prominent in the 428-442nm band for blood samples viewed under 20x and 50x magnification over a varying range of illumination intensities. The system has shown to successfully segment blood cells based on their spectral-spatial information. These images could potentially be used in subsequent automated white blood cell segmentation and counting algorithms for performing in vivo white blood cell counting

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