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.

/pdf/vertex-component-analysis-a-fast-algorithm-to-unmix-1egulrpm76.pdf

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.

The Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission is the fifth NASA Medium-class Explorer (MIDEX), launched on February 17, 2007 to determine the trigger and large-scale evolution of substorms. The mission employs five identical micro-satellites (hereafter termed “probes”) which line up along the Earth’s magnetotail to track the motion of particles, plasma and waves from one point to another and for the first time resolve space–time ambiguities in key regions of the magnetosphere on a global scale. The probes are equipped with comprehensive in-situ particles and fields instruments that measure the thermal and super-thermal ions and electrons, and electromagnetic fields from DC to beyond the electron cyclotron frequency in the regions of interest. The primary goal of THEMIS, which drove the mission design, is to elucidate which magnetotail process is responsible for substorm onset at the region where substorm auroras map (∼10 RE): (i) a local disruption of the plasma sheet current (current disruption) or (ii) the interaction of the current sheet with the rapid influx of plasma emanating from reconnection at ∼25 RE. However, the probes also traverse the radiation belts and the dayside magnetosphere, allowing THEMIS to address additional baseline objectives, namely: how the radiation belts are energized on time scales of 2–4 hours during the recovery phase of storms, and how the pristine solar wind’s interaction with upstream beams, waves and the bow shock affects Sun–Earth coupling. THEMIS’s open data policy, platform-independent dataset, open-source analysis software, automated plotting and dissemination of data within hours of receipt, dedicated ground-based observatory network and strong links to ancillary space-based and ground-based programs. promote a grass-roots integration of relevant NASA, NSF and international assets in the context of an international Heliophysics Observatory over the next decade. The mission has demonstrated spacecraft and mission design strategies ideal for Constellation-class missions and its science is complementary to Cluster and MMS. THEMIS, the first NASA micro-satellite constellation, is a technological pathfinder for future Sun-Earth Connections missions and a stepping stone towards understanding Space Weather.

The THEMIS Mission

Signal subspace identification is a crucial first step in many hyperspectral processing algorithms such as target detection, change detection, classification, and unmixing. The identification of this subspace enables a correct dimensionality reduction, yielding gains in algorithm performance and complexity and in data storage. This paper introduces a new minimum mean square error-based approach to infer the signal subspace in hyperspectral imagery. The method, which is termed hyperspectral signal identification by minimum error, is eigen decomposition based, unsupervised, and fully automatic (i.e., it does not depend on any tuning parameters). It first estimates the signal and noise correlation matrices and then selects the subset of eigenvalues that best represents the signal subspace in the least squared error sense. State-of-the-art performance of the proposed method is illustrated by using simulated and real hyperspectral images.

/pdf/hyperspectral-subspace-identification-4cvaygfbm7.pdf

Hyperspectral Subspace Identification

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Chaos and nonlinear dynamics of single‐particle orbits in a magnetotaillike magnetic field

A kinetic theory in the form of an integral equation is provided to study the electrostatic oscillations in a collisionless plasma immersed in a uniform magnetic field and a nonuniform transverse electric field. In the low temperature limit the dispersion differential equation is recovered for the transverse Kelvin-Helmholtz modes for arbitrary values of K parallel, where K parallel is the component of the wave vector in the direction of the external magnetic field assumed in the z direction. For higher temperatures the ion-cyclotron-like modes described earlier in the literature by Ganguli, Lee and Plamadesso are recovered. In this article, the integral equation is reduced to a second-order differential equation and a study is made of the kinetic Kelvin-Helmholtz and ion-cyclotron-like modes that constitute the two branches of oscillation in a magnetized plasma including a transverse inhomogeneous dc electric field.

https://apps.dtic.mil/sti/pdfs/ADA193404.pdf

Kinetic theory for electrostatic waves due to transverse velocity shears

We report recent progress using a filter vector technique to analyze the data from a hyperspectral image. The filter vector technique finds the optimal filter vectors for demixing the complex patterns found in the hyperspectral image. The method has the potential to be implemented in real time since it is fully parallel. Computation of the filter vectors for a given family of known species vectors is fast and direct and improved algorithms for developing of the algorithm which may be updated as conditions change is possible. Advantages of using the filter vector techniques over the technique of pattern matching will be discussed. The portable hyperspectral images for low light spectroscopy (PHILLS) instrument has been used on a number of depolyments in the last year. Typically, the instrument files on the Naval Research Laboratory's P-3 Orion aircraft. Currently, the PHILLS instrument records over 1000 wavelength bands between UV and near IR. Results from a number of deployment and test situations is shown.

Use of filter vectors in hyperspectral data analysis

We have performed a model calculation of the ion heating rate due to electrostatic ion cyclotron turbulence in the topside ionosphere, with the assumption that the formation of a plateau on the electron velocity distribution is inhibited. Ion temperature profiles are obtained and the implications of the heating effect on anomalous resistivity calculations are discussed.

Topside ionosphere ion heating due to electrostatic ion cyclotron turbulence

A new mechanism that can destabilize kinetic ion‐cyclotron waves in the presence of a nonuniform electric field perpendicular to the uniform ambient magnetic field is given. In the absence of the electric field, the mode energy is positive, while in the presence of a uniform electric field the mode energy could be negative. However, when the electric field is nonuniform, it is possible for a finite region to be a negative wave energy surrounded by regions of positive wave energy. A nonlocal wave packet couples the two regions so that a flow of energy from the region of negative wave energy to the region of positive wave energy will cause the mode to brow. This gives rise to the instability.

Peter J. Palmadesso

Papers

Chaos and nonlinear dynamics of single‐particle orbits in a magnetotaillike magnetic field

Kinetic theory for electrostatic waves due to transverse velocity shears

Use of filter vectors in hyperspectral data analysis

Topside ionosphere ion heating due to electrostatic ion cyclotron turbulence

Electrostatic ion-cyclotron instability caused by a nonuniform electric field perpendicular to the external magnetic field