John H. Gruninger

The sequential maximum angle convex cone (SMACC) endmember model

A new endmember extraction method has been developed that is based on a convex cone model for representing vector data. The endmembers are selected directly from the data set. The algorithm for finding the endmembers is sequential: the convex cone model starts with a single endmember and increases incrementally in dimension. Abundance maps are simultaneously generated and updated at each step. A new endmember is identified based on the angle it makes with the existing cone. The data vector making the maximum angle with the existing cone is chosen as the next endmember to add to enlarge the endmember set. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The algorithm terminates when all of the data vectors are within the convex cone, to some tolerance. The method offers advantages for hyperspectral data sets where high correlation among channels and pixels can impair un-mixing by standard techniques. The method can also be applied as a band-selection tool, finding end-images that are unique and forming a convex cone for modeling the remaining hyperspectral channels. The method is described and applied to hyperspectral data sets.

Shadow-insensitive material detection/classification with atmospherically corrected hyperspectral imagery

Shadow-insensitive detection or classification of surface materials in atmospherically corrected hyperspectral imagery can be achieved by expressing the reflectance spectrum as a linear combination of spectra that correspond to illumination by the direct sum and by the sky. Some specific algorithms and applications are illustrated using HYperspectral Digital Imagery Collection Experiment (HYDICE) data.

Automated optimal channel selection for spectral imaging sensors

A method of optimizing the selection of spectral channels in a spectral-spatial remote sensor has been developed that is applicable to the design of multispectral, hyperspectral and ultra spectral resolution sensors. The approach is based on an end member analysis technique that has been refined to select the most information dense channels. The algorithm operates sequentially and at any step in the sequence, the channel selected is the most independent form all previously selected channels. After the channel selection process, highly correlated channels, which are contiguous to those selected, can be merged to form bands. This process increases the signal to noise for the new broader spectral bands. The resulting bands, potentially of unequal width and spacing, collect the most uncorrelated spectral information present in the data. The band selection provides a physical interpretation of the data and has applications in spectral feature selection and data compression.

The extension of endmember extraction to multispectral scenes

A multiple simplex endmember extraction method has been developed. Unlike convex methods that rely on a single simplex, the number of endmembers is not restricted by the number of linearly independent spectral channels. The endmembers are identified as the extreme points in the data set. The algorithm for finding the endmembers can simultaneously find endmember abundance maps. Multispectral and hyperspectral scenes can be complex and contain many materials under a variety of illumination and environmental conditions, but individual pixels typically contain only a few materials in a small subset of the illumination and environmental conditions which exist in the scene. This forms the physical basis for the approach that restricts the number of endmembers that combine to model a single pixel. No restriction is placed on the total number of endmembers, however. The algorithm for finding the endmembers and their abundances maps is sequential. Extreme points are identified based on the angle they make with the existing set. The point making the maximum angle with the existing set is chosen as the next endmember to add to enlarge the endmember set. The maximum number of endmembers that are allowed to be in a subset model for individual pixels is controlled by an input parameter. The subset selection algorithm is sequential and takes place simultaneously with the overall endmember extraction. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The method offers advantages in multispectral data sets where the limited number of channels impairs material un-mixing by standard techniques. A description of the method is presented herein and applied to real and synthetic hyperspectral and multispectral data sets.

Extraction of spatial and spectral scene statistics for hyperspectral scene simulation

A method for extracting statistics from hyperspectral data and generating synthetic scenes suitable for scene generation models is presented. Regions composed of a general surface type with a small intrinsic variation, such as a forest or crop field, are selected. The spectra are decomposed using a basis set derived from spectra present in the scene and the abundances of the basis members in each pixel spectrum found. Statistics such as the abundance means, covariances and channel variances are extracted. The scenes are synthesized using a coloring transform with the abundance covariance matrix. The pixel-to-pixel spatial correlations are modeled by an autoregressive moving average texture generation technique. Synthetic reflectance cubes are constructed using the generated abundance maps, the basis set and the channel variances. Enhancements include removing any pattern from the scene and reducing the skewness. This technique is designed to work on atmospherically-compensated data in any spectral region, including the visible-shortwave infrared HYDICE and AVIRIS data presented here. Methods to evaluate the performance of this approach for generating scene textures include comparing the statistics of the synthetic surfaces and the original data, using a signal-to-clutter ratio metric, and inserting sub-pixel spectral signatures into scenes for detection using spectral matched filters.

Innovative Minimally Intrusive Sensor Technology Development for Versatile Affordable Advanced Turbine Engine Combustors

The feasibility of an innovative minimally intrusive sensor for monitoring the hot gas stream at the turbine inlet in high performance aircraft gas turbine engines was demonstrated. The sensor uses passive fiber-optical probes and a remote readout device to collect and analyze the spatially resolved spectral signature of the hot gas in the combustor/turbine flowpaths. Advanced information processing techniques are used to extract the average temperature, temperature pattern factor, and chemical composition on a sub-second time scale. Temperatures and flame composition were measured in a variety of combustion systems including a high pressure, high temperature combustion cell. Algorithms for real-time temperature measurements were developed and demonstrated. This approach should provide a real-time temperature profile, temperature pattern factor, and chemical species sensing capability for multi-point monitoring of high temperature and high pressure flow at the combustor exit with application as an engine development diagnostic tool, and ultimately, as a real-time active control component for high performance gas turbines.Copyright

Hyperspectral Detection and Identification with Constrained Target Subspaces

Subspace methods for hyperspectral imagery enable detection and identification of targets under unknown environmental conditions by specifying a subspace of possible target spectral signatures (and, optionally, a background subspace) and identifying closely fitting spectra in the image. In this study, detection performance in the thermal infrared (IR) was compared using various constrained and unconstrained basis set expansions of low-dimensional target subspaces. An initial investigation of detection using retrieved atmospheric parameters to reduce subspace size and/or dimensionality has also been performed.

Application of convex cone analysis to hyperspectral and multispectral scenes

A new end-member analysis method based on convex cones has been developed. The method finds extreme points in a convex set. Unlike convex methods that rely on a simplex, the number of end-members is not restricted by the number of spectral channels. The algorithm simultaneously finds fractional abundance maps. The fractional abundances are the fractions of the total spectrally integrated radiance of a pixel that are contributed by the end-members. A physical model of the hyper-spectral or multi-spectral scene is obtained by combining subsets of the end-members into bundles of spectra for each scene material. The bundle spectra represent the spectral variability of the material in the scene induced by illumination, shadowing, weathering and other environmental effects. The method offers advantages in multi-spectral data sets where the limited number of channels impairs material un-mixing by standard techniques. The method can also be applied to compress hyper-spectral data. The fractional abundance matrices are sparse and offer an additional compression capability over standard matrix factorization techniques. A description of the method and applications to real and synthetic hyper-spectral and multi-spectral data sets will be presented.

Radiation transport effects and the interpretation of infrared images of gravity waves and turbulence

Radiation transport modulates the spatial frequencies of atmospheric structures, acting as a low pass filter, which causes the power spectra of the accumulated radiance to have different power spectral slopes than the underlying atmospheric structure. Additional effects arise because of the non-stationarity of the atmosphere. The SHARC atmospheric radiance code is used to model both non- stationarity of the atmosphere. The SHARC atmospheric radiance code is used to model both equilibrium and non- equilibrium radiance and radiance fluctuation statistics. It predicts two dimensions. Radiance spatial covariance functions and power spectral densities, PSDs. Radiance power spectral slopes for paths through isotropic Kolmogorov turbulence are predicted to vary from -5/3 to -8/3 depending on the length of the path through the turbulence. The input gravity wave 3D covariances and PSDs of atmospheric temperature are consistent with current gravity wave theory, having vertical and horizontal power spectral indices of -3 and -5/3, respectively. Altitude profiles of variances and correlation lengths account of the non-stationary of the gravity wave structure in the atmosphere. The radiance covariance and PSD power spectral slopes differ from the atmospheric gravity wave temperature model values of -3 and -5/3. These modulations depend on LOS orientations, and scale lengths of the sampled altitudes along the LOS.

Boundary constraints for singular value decomposition of spectral data

Singular value decomposition (SVD) and principal component analysis enjoy a broad range of applications, including, rank estimation, noise reduction, classification and compression. The resulting singular vectors form orthogonal basis sets for subspace projection techniques. The procedures are applicable to general data matrices. Spectral matrices belong to a special class known as non-negative matrices. A key property of non-negative matrices is that their columns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to the cone. This special property has been implicitly used in popular rank estimation techniques know as virtual dimension (VD) and hyperspectral signal identification by minimum error (HySime). Data sets of spectra reside in non-negative orthants. The subspace spanned by a SVD of a set of spectra includes all orthants. However SVD projections can be constrained to the non-negative orthants. In this paper two types of singular vector projection constraints are identified, one that confines the projection to lie within the cone formed by the spectral data set, and a second that only restricts projections to the non-negative orthant. The former is referred to here as the inner constraint set, the latter the outer constraint set. The outer constraint set forms a broader cone since it includes projections outside the cone formed by the data array. The two cones form boundaries for the cones formed by non-negative matrix factorizations (NNF). Ambiguities in the NNF lead to a variety of possible sets of left and right non-negative vectors and their cones. The paper presents the constraint set approach and illustrates it with applications to spectral classification.