Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

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Vertex component analysis: a fast algorithm to unmix hyperspectral data

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 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.

/pdf/hyperspectral-unmixing-overview-geometrical-statistical-and-2lb11fr9l4.pdf

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.

Imaging Spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)

[1] The HiRISE camera features a 0.5 m diameter primary mirror, 12 m effective focal length, and a focal plane system that can acquire images containing up to 28 Gb (gigabits) of data in as little as 6 seconds. HiRISE will provide detailed images (0.25 to 1.3 m/pixel) covering ∼1% of the Martian surface during the 2-year Primary Science Phase (PSP) beginning November 2006. Most images will include color data covering 20% of the potential field of view. A top priority is to acquire ∼1000 stereo pairs and apply precision geometric corrections to enable topographic measurements to better than 25 cm vertical precision. We expect to return more than 12 Tb of HiRISE data during the 2-year PSP, and use pixel binning, conversion from 14 to 8 bit values, and a lossless compression system to increase coverage. HiRISE images are acquired via 14 CCD detectors, each with 2 output channels, and with multiple choices for pixel binning and number of Time Delay and Integration lines. HiRISE will support Mars exploration by locating and characterizing past, present, and future landing sites, unsuccessful landing sites, and past and potentially future rover traverses. We will investigate cratering, volcanism, tectonism, hydrology, sedimentary processes, stratigraphy, aeolian processes, mass wasting, landscape evolution, seasonal processes, climate change, spectrophotometry, glacial and periglacial processes, polar geology, and regolith properties. An Internet Web site (HiWeb) will enable anyone in the world to suggest HiRISE targets on Mars and to easily locate, view, and download HiRISE data products.

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Mars Reconnaissance Orbiter's High Resolution Imaging Science Experiment (HiRISE)

[1] Imaging spectroscopy is a tool that can be used to spectrally identify and spatially map materials based on their specific chemical bonds. Spectroscopic analysis requires significantly more sophistication than has been employed in conventional broadband remote sensing analysis. We describe a new system that is effective at material identification and mapping: a set of algorithms within an expert system decision-making framework that we call Tetracorder. The expertise in the system has been derived from scientific knowledge of spectral identification. The expert system rules are implemented in a decision tree where multiple algorithms are applied to spectral analysis, additional expert rules and algorithms can be applied based on initial results, and more decisions are made until spectral analysis is complete. Because certain spectral features are indicative of specific chemical bonds in materials, the system can accurately identify and map those materials. In this paper we describe the framework of the decision making process used for spectral identification, describe specific spectral feature analysis algorithms, and give examples of what analyses and types of maps are possible with imaging spectroscopy data. We also present the expert system rules that describe which diagnostic spectral features are used in the decision making process for a set of spectra of minerals and other common materials. We demonstrate the applications of Tetracorder to identify and map surface minerals, to detect sources of acid rock drainage, and to map vegetation species, ice, melting snow, water, and water pollution, all with one set of expert system rules. Mineral mapping can aid in geologic mapping and fault detection and can provide a better understanding of weathering, mineralization, hydrothermal alteration, and other geologic processes. Environmental site assessment, such as mapping source areas of acid mine drainage, has resulted in the acceleration of site cleanup, saving millions of dollars and years in cleanup time. Imaging spectroscopy data and Tetracorder analysis can be used to study both terrestrial and planetary science problems. Imaging spectroscopy can be used to probe planetary systems, including their atmospheres, oceans, and land surfaces.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2002JE001847

Imaging spectroscopy: Earth and planetary remote sensing with the USGS Tetracorder and expert systems

Thirty samples of amphibole-rich rock from the largest mined vermiculite deposit in the world in the Rainy Creek alkaline-ultramafic complex near Libby, Montana, were collected and analyzed. The amphibole-rich rock is the suspected cause of an abnormally high number of asbestos-related diseases reported in the residents of Libby, and in former mine and mill workers. The amphibole-rich samples were analyzed to determine composition and morphology of both fibrous and non-fibrous amphiboles. Sampling was carried out across the accessible portions of the deposit to obtain as complete a representation of the distribution of amphibole types as possible. The range of amphibole compositions, determined from electron probe microanalysis and X-ray diffraction analysis, indicates the presence of winchite, richterite, tremolite, and magnesioriebeckite. The amphiboles from Vermiculite Mountain show nearly complete solid solution between these end-member compositions. Magnesio-arfvedsonite and edenite may also be present in low abundance. An evaluation of the textural characteristics of the amphiboles shows the material to include a complete range of morphologies from prismatic crystals to asbestiform fibers. The morphology of the majority of the material is intermediate between these two varieties. All of the amphiboles, with the possible exception of magnesioriebeckite, can occur in fibrous or asbestiform habit. The Vermiculite Mountain amphiboles, even when originally present as massive material, can produce abundant, extremely fine fibers by gentle abrasion or crushing.

/pdf/the-composition-and-morphology-of-amphiboles-from-the-rainy-2uflkyltty.pdf

The Composition and Morphology of Amphiboles from the Rainy Creek Complex, Near Libby, Montana

Mineral abundance maps of 18 minerals were made of the Cuprite Mining District using 1990 AVIRIS data and the Multiple Spectral Feature Mapping Algorithm (MSFMA) as discussed in Clark et al. This technique uses least-squares fitting between a scaled laboratory reference spectrum and ground calibrated AVIRIS data for each pixel. Multiple spectral features can be fitted for each mineral and an unlimited number of minerals can be mapped simultaneously. Quality of fit and depth from continuum numbers for each mineral are calculated for each pixel and the results displayed as a multicolor image.

Steve J. Sutley

Papers

Imaging spectroscopy: Earth and planetary remote sensing with the USGS Tetracorder and expert systems

The Composition and Morphology of Amphiboles from the Rainy Creek Complex, Near Libby, Montana

Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada

USGS Digital Spectral Library splib05a

Environmental studies of the World Trade Center area after the September 11, 2001 attack