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.

“Mafic Mound” is a distinctive and enigmatic feature 75 km across and 1 km high near the center of the vast South Pole-Aitken Basin (SPA). Using several modern data sets, we characterize the composition, morphology, and gravity signature of the structure in order to assess its origin. Mafic Mound is found to exhibit a perched circular depression and a homogeneous high-Ca pyroxene-bearing composition. Several formation hypotheses based on known lunar processes are evaluated, including the possibilities that Mafic Mound represents (1) uplifted mantle, (2) SPA-derived impact melt, (3) a basalt-filled impact crater, or (4) a volcanic construct. Individually, these common processes cannot fully reproduce the properties of Mafic Mound. Instead, we propose a hybrid origin in which Mafic Mound is an edifice formed by magmatic processes induced by the formation and evolution of SPA. This form of nonmare volcanism has not previously been documented on the Moon.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015GL065718

The nature and origin of Mafic Mound in the South Pole-Aitken Basin

Remote sensing observations have identified aluminate spinel, in the absence of measureable olivine and pyroxene, as a globally distributed component of the lunar crust. Earlier remote sensing observations and returned samples did not indicate the presence of this component, leaving its geologic significance unclear. Here, we report visible to mid-infrared (V-IR) reflectance (300–25 000 nm) and Mossbauer spectra of aluminate spinels, synthesized at lunar-like oxygen fugacity (ƒO2), that vary systematically in Fe abundance. Reflectance spectra of particulate ( 6 Fe#. Although the 2000 and 2800 nm bands are assigned to Fe 2+ IV electronic transitions, spectra of aluminate spinels with excess Al2O3 demonstrate that the strengths of the 1000 nm bands are related to the abundance of Fe 2+ VI. The abundance of Fe 2+ VI depends on bulk Fe content as well as factors that control the degree of structural order-disorder, such as cooling rate. Consequently the strength of the 1000 nm bands are useful for constraining the Fe content and cooling rate of remotely sensed spinel. Controlling for cooling rate, particle size, and ƒO2, we conclude that spinels with >12 Fe# (<88 Mg#) have observable 1000 nm bands under ambient lunar conditions and that only very Mg-rich spinels lack 1000 nm bands in their spectra. This links remote observations of spinel anorthosite to Mg-Suite magmatism. The combined effects of Fe oxidation state, abundance of coexisting plagioclase, and space weathering have not been explored here, and may add additional constraints. The relative strengths of the distinctive 1000 and 2000 nm bands of the spinels associated with pyroclastic deposits at Sinus Aestuum suggest fast cooling rates, possibly in the absence of an extensive vapor cloud.

Visible-infrared spectral properties of iron-bearing aluminate spinel under lunar-like redox conditions†

Extraction of Compositional Information from Olivine Reflectance Spectra: A New Capability for Lunar Exploration

Room-temperature 57 Fe Mossbauer spectra of synthetic orthopyroxenes equilibrated between 900-1000 °C and spanning the compositional range from ferrosilite to nearly enstatite were acquired. Peak areas corresponding to Fe 2+ in the M1 and M2 sites of the structure were corrected for effects of thickness and differential recoil-free fractions (f) on the two sites using a constant value of C = 1.1, the correction parameter. The distribution coefÞ cient, KD, for Fe and Mg in M1 and M2 was calculated for all samples, and results were compared to KD values from previous studies where C was assumed to be unity. Our results demonstrate that choice of C dramatically ins uences calculated KD values. Thus, the failure of previous studies to consider C corrections may well be responsible for differences between Mossbauer and XRD studies of site occupancies noted by previous workers. Further characterizations of f for pyroxenes of variable compositions are needed.

http://www.planetary.brown.edu/pdfs/3449.pdf

Effects of differential recoil-free fraction on ordering and site occupancies in Mössbauer spectroscopy of orthopyroxenes

The Clementine UVVIS images and the spectral and chemical (mineral) characteristics of lunar soil samples previously measured by the Lunar Samples Characterization Consortium were used to map the plagioclase and clinopyroxene abundance in the lunar surface material. An excess of plagioclase was found in young highland craters (e.g., in the crater Tycho) and in their ray systems. For clinopyroxenes, analogous behavior was observed in mare craters (e.g., in the crater Aristarchus). The maps for the FeO and Al2O3 bulk contents and the contents of these oxides in plagioclase and clinopyroxene were estimated by the same technique. These maps were compared to each other and to the predicted distribution of the lunar regolith maturity. The regolith of highland ray systems (e.g., the Tycho crater system) is characterized not only by low maturity but also by peculiar iron and aluminum contents: the lower the soil maturity degree, the smaller the iron content and the greater the aluminum content. This is confirmed by the data for the lunar soil samples from the Apollo 16 landing site. A cluster analysis of the “clinopyroxene content-maturity” and “plagioclase content-maturity” correlation diagrams allowed the mineral mapping of the lunar surface to be performed.

http://www.planetary.brown.edu/pdfs/3280.pdf

Carle M. Pieters

Papers

The nature and origin of Mafic Mound in the South Pole-Aitken Basin

Visible-infrared spectral properties of iron-bearing aluminate spinel under lunar-like redox conditions†

Extraction of Compositional Information from Olivine Reflectance Spectra: A New Capability for Lunar Exploration

Effects of differential recoil-free fraction on ordering and site occupancies in Mössbauer spectroscopy of orthopyroxenes

Lunar Clinopyroxene and Plagioclase: Surface Distribution and Composition