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

Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions

Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three arbitrary functions in the corresponding Lagrangian/Hamiltonian) and not just those allowed by spherically symmetric general relativity. This freedom can be interpreted as the freedom to accommodate certain quantum gravity corrections in these models even in the absence of higher curvature terms (at a semi-classical level, at least). For a particular choice of the arbitrary functions it is shown that the new theories map to spherically symmetric general relativity in arbitrary number of (integer) dimensions thus explicitly demonstrating that when working with midisuperspace models, one loses the information about the dimensionality of the full spacetime. In addition, it is shown that these new theories can accommodate scenarios of fractional spacetime dimensions as well as those of emergent spacetime dimensions -- a possibility suggested by various approaches to quantum gravity.Comment: 10 page

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps

H2_2 dissociation over Au-nanowires and the fractional conductance quantum

The dissociation of H$_2$ molecules on stretched Au nanowires and its effect on the nanowire conductance are analyzed using a combination of Density Functional (DFT) total energy calculations and non-equilibrium Keldish-Green function methods. Our DFT simulations reproduce the characteristic formation of Au monoatomic chains with a conductance close to % the conductance quantum $G_0 = 2e^2/h$. These stretched Au nanowires are shown to be better catalysts for H$_2$ dissociation than Au surfaces. This is confirmed by the nanowire conductance evidence: while not affected practically by molecular hydrogen, atomic hydrogen induces the appearance of fractional conductances ($G \sim 0.5 G_0$) as observed experimentally.Comment: 4 pages, 3 figure

Output from Bose condensates in tunnel arrays: the role of mean-field interactions and of transverse confinement

We present numerical studies of atomic transport in 3D and 1D models for a mode-locked, pulsed atom laser as realized by Anderson and Kasevich [Science 281 (1998) 1686] using an elongated Bose condensate of ${}^{87}$Rb atoms poured into a vertical optical lattice. From our 3D results we ascertain in a quantitative manner the role of mean-field interactions in determining the shape and the size of the pulses in the case of Gaussian transverse confinement. By comparison with 1D simulations we single out a best-performing 1D reduction of the mean-field interactions, which yields quantitatively useful predictions for all main features of the matter output.Comment: 12 pages, 2 figure