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.

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Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

The Nature of Remote Sensing: Introduction. Remote Sensing. Information Extraction from Remote-Sensing Images. Spectral Factors in Remote Sensing. Spectral Signatures. Remote-Sensing Systems. Optical Sensors. Temporal Characteristics. Image Display Systems. Data Systems. Summary. Exercises. References. Optical Radiation Models: Introduction. Visible to Short Wave Infrared Region. Solar Radiation. Radiation Components. Surface-Reflected. Unscattered Component. Surface-Reflected. Atmosphere-Scattered Component. Path-Scattered Component. Total At-Sensor. Solar Radiance. Image Examples in the Solar Region. Terrain Shading. Shadowing. Atmospheric Correction. Midwave to Thermal Infrared Region. Thermal Radiation. Radiation Components. Surface-Emitted Component. Surface-Reflected. Atmosphere-Emitted Component. Path-Emitted Component. Total At-Sensor. Emitted Radiance. Total Solar and Thermal Upwelling Radiance. Image Examples in the Thermal Region. Summary. Exercises. References. Sensor Models: Introduction. Overall Sensor Model. Resolution. The Instrument Response. Spatial Resolution. Spectral Resolution. Spectral Response. Spatial Response. Optical PSFopt. Image Motion PSFIM. Detector PSFdet. Electronics PSFel. Net PSFnet. Comparison of Sensor PSFs. PSF Summary for TM. Imaging System Simulation. Amplification. Sampling and Quantization. Simplified Sensor Model. Geometric Distortion. Orbit Models. Platform Attitude Models. Scanner Models. Earth Model. Line and Whiskbroom ScanGeometry. Pushbroom Scan Geometry. Topographic Distortion. Summary. Exercises. References. Data Models: Introduction. A Word on Notation. Univariate Image Statistics. Histogram. Normal Distribution. Cumulative Histogram. Statistical Parameters. Multivariate Image Statistics. Reduction to Univariate Statistics. Noise Models. Statistical Measures of Image Quality. Contrast. Modulation. Signal-to-Noise Ratio (SNR). Noise Equivalent Signal. Spatial Statistics. Visualization of Spatial Covariance. Covariance with Semivariogram. Separability and Anisotropy. Power Spectral Density. Co-occurrence Matrix. Fractal Geometry. Topographic and Sensor Effects. Topography and Spectral Statistics. Sensor Characteristics and Spectral Stastistics. Sensor Characteristics and Spectral Scattergrams. Summary. Exercises. References. Spectral Transforms: Introduction. Feature Space. Multispectral Ratios. Vegetation Indexes. Image Examples. Principal Components. Standardized Principal Components (SPC) Transform. Maximum Noise Fraction (MNF) Transform. Tasseled Cap Tranformation. Contrast Enhancement. Transformations Based on Global Statistics. Linear Transformations. Nonlinear Transformations. Normalization Stretch. Reference Stretch. Thresholding. Adaptive Transformation. Color Image Contrast Enhancement. Min-max Stretch. Normalization Stretch. Decorrelation Stretch. Color Spacer Transformations. Summary. Exercises. References. Spatial Transforms: Introduction. An Image Model for Spatial Filtering. Convolution Filters. Low Pass and High Pass Filters. High Boost Filters. Directional Filters. The Border Region. Characterization of Filtered Images. The Box Filter Algorithm. Cascaded Linear Filters. Statistical Filters. Gradient Filters. Fourier Synthesis. Discrete Fourier Transforms in 2-D. The Fourier Components. Filtering with the Fourier Transform. Transfer Functions. The Power Spectrum. Scale Space Transforms. Image Resolution Pyramids. Zero-Crossing Filters. Laplacian-of-Gaussian (LoG) Filters. Difference-of-Gaussians (DoG) Filters.Wavelet Transforms. Summary. Exercises. References. Correction and Calibration: Introduction. Noise Correction. Global Noise. Sigma Filter. Nagao-Matsuyama Filter. Local Noise. Periodic Noise. Distriping 359. Global,Linear Detector Matching. Nonlinear Detector Matching. Statistical Modification to Linear and Nonlinear Detector. Matching. Spatial Filtering Approaches. Radiometric Calibration. Sensor Calibration. Atmospheric Correction. Solar and Topographic Correction. Image Examples. Calibration and Normalization of Hyperspectral Imagery. AVIRIS Examples. Distortion Correction. Polynomial Distortion Models. Ground Control Points (GCPs). Coordinate Transformation. Map Projections. Resampling. Summary. Exercises References. Registration and Image Fusion: Introduction. What is Registration? Automated GCP Location. Area Correlation. Other Spatial Features. Orthrectification. Low-Resolution DEM. High-Resolution DEM. Hierarchical Warp Stereo. Multi-Image Fusion. Spatial Domain Fusion. High Frequency Modulation. Spectral Domain Fusion. Fusion Image Examples. Summary. Exercises. References. Thematic Classification: Introduction. The Importance of Image Scale. The Notion of Similarity. Hard Versus Soft Classification. Training the Classifier. Supervised Training. Unsupervised Training. K-Means Clustering Algorithm. Clustering Examples. Hybrid Supervised/Unsupervised Training. Non-Parametric Classification Algorithms. Level-Slice. Nearest-Mean. Artificial Neural Networks (ANNs). Back-Propagation Algorithm. Nonparametric Classification Examples. Parametric Classification Algorithms. Estimation of Model-Parameters. Discriminant Functions. The Normal Distribution Model. Relation to the Nearest-Mean Classifier. Supervised Classification Examples and Comparison to Nonparametric Classifiers. Segmentation. Region Growing. Region Labeling. Sub-Pixel Classification. The Linear Mixing Model. Unmixing Model. Hyperspectral Image Analysis. Visualization of the Image Cube. Feature Extraction. Image Residuals. Pre-Classification Processing and Feature Extraction. Classification Algorithms. Exercises. Error Analysis. Multitemporal Images. Summary. References. Index.

Remote sensing, models, and methods for image processing

Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

Spectral unmixing using hyperspectral data represents a significant step in the evolution of remote decompositional analysis that began with multispectral sensing. It is a consequence of collecting data in greater and greater quantities and the desire to extract more detailed information about the material composition of surfaces. Linear mixing is the key assumption that has permitted well-known algorithms to be adapted to the unmixing problem. In fact, the resemblance of the linear mixing model to system models in other areas has permitted a significant legacy of algorithms from a wide range of applications to be adapted to unmixing. However, it is still unclear whether the assumption of linearity is sufficient to model the mixing process in every application of interest. It is clear, however, that the applicability of models and techniques is highly dependent on the variety of circumstances and factors that give rise to mixed pixels. The outputs of spectral unmixing, endmember, and abundance estimates are important for identifying the material composition of mixtures.

Spectral unmixing

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.

The nature of the interactions of visible and NIR radiation with the surfaces of rock and mineral samples was investigated by measuring the reflectance and the polarization properties of scattered and reflected light for slab samples of obsidian and fine-grained basalt, prepared to controlled surface roughness It is shown that the degree to which radiation can penetrate a surface and then scatter back out, an essential criterion for mineralogic determinations based on reflectance spectra, depends not only upon the composition of the material, but also on its physical condition such as sample grain size and surface roughness Comparison of the experimentally measured reflectance and polarization from smooth and rough slab materials with the predicted models indicates that single Fresnel reflections are responsible for the largest part of the reflected intensity resulting from interactions with the surfaces of dielectric materials; multiple Fresnel reflections are much less important for such surfaces

Interactions of light with rough dielectric surfaces - Spectral reflectance and polarimetric properties

The Moon Mineralogy Mapper (M3) was selected as a NASA Discovery Mission of Opportunity in early February 2005 and entered phase B in May 2005. The primary science goal is to characterize and map the lunar surface composition m the context ol its geologic evolution.The primary exploration goal is to assess and map the Moon mineral resources at high spatial resolution to support planning lor future, targeted missions. The M3 science instrument is a high uniformity and high precision imaging spectrometer of the pushbroom type operating m the solar reflected energy portion of the electromagnetic spectrum. M3 is planned to be launched as a guest instrument on the Chandrayaan-1 mission of the Indian Space Research Organization (ISRO) in early 2008. As a guest instrument, M3 was required to be low mass, low volume and low power. Yet, the imaging spectroscopy science required a broad spectral range, excellent radiometric precision and unmatched uniformity. The complete M3 instrument measures the spectral range from 430 to 3000 nm at 10 nm sampling, with a 24-degree cross-track field-of-view and 0.7 milliradian sampling as well as greater than 90%spectral cross-track uniformity and 90% spectral IFOV uniformity. The mass and power of the M3 instrument are 8.3 kilograms and 16 Watts average. The volume of the optical and detector assembly is 25 X 18 X 12 centimeters.The M3 instrument preship review was successfully completed on the 3rd of May 2007. In this paper, the M3 of dust and mineral mixtures as well as to measure spectra characteristics and initial laboratory calibration results are presented.

Moon Mineralogy Mapper Imaging Spectrometer Science Measurements

Introduction: In the visible and near-infrared wavelength region, reflectance spectrum of olivine and orthopyroxene (opx), which are two of the most common rock-forming minerals, exhibit some characteristic absorption features especially fit for remote sensing. Opx has two absorption bands around 0.9 μm and 2 μm, whereas olivine shows a complex absorption band around 1 μm and no band around 2 μm. Each of the absorption bands of opx consists of a single absorption, and the 1 μm band of olivine is a composite of three [e.g., 1]. The 1 μm band is generally referred to as the “Band I” and the 2 μm band as the “Band II”. One of the methods for estimating the olivine/opx modal abundances from their reflectance spectra is a plot of the Band I center versus Band II/Band I (BII/BI) area ratio [2, 3]. Cloutis et al. [2] estimated the modal abundance from the reflectance spectra of laboratory olivine-opx mixtures using various methods. Gaffey et al. [3] used the Band I center vs. BII/BI area ratio plot and explained the relationship between the S-type asteroids and ordinary chondrites (OCs). Presented here is the possibility that the space weathering and grain size effects have significant influence on the Band I center vs. the BII/BI area ratio plot.

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Changes of Band I Center and Band II/Band I Area Ratio in Reflectance Spectra of Olivine-Pyroxene Mixtures Due to the Space Weathering and Grain Size Effects

Using proton radiation from the moon to search for diurnal variation of regolith hydrogenation

Expanding the Modified Gaussian Model to Include the Space Weathering Effects: Estimation of the Weathering Degrees of Pulse-Laser Treated Olivine Samples

Carle M. Pieters

Papers

Interactions of light with rough dielectric surfaces - Spectral reflectance and polarimetric properties

Moon Mineralogy Mapper Imaging Spectrometer Science Measurements

Changes of Band I Center and Band II/Band I Area Ratio in Reflectance Spectra of Olivine-Pyroxene Mixtures Due to the Space Weathering and Grain Size Effects

Using proton radiation from the moon to search for diurnal variation of regolith hydrogenation

Expanding the Modified Gaussian Model to Include the Space Weathering Effects: Estimation of the Weathering Degrees of Pulse-Laser Treated Olivine Samples