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23 September 2003 Applications of eigenvalue distribution theory to hyperspectral processing
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The theory of asymptotic eigenvalue distributions of sample covariance matrices has been applied to array processing and model identification problems that require characterization of signal and noise modes in vector-valued observations. It naturally applies in cases where the dimensionality of the observation space is large compared with the signal model order. A similar situation holds for most hyperspectral image observations. Hyperspectral data is frequently described in terms of a "signal" component composed of linear combinations of endmember basis spectra, plus random additive "noise" from the sensor and environment. The number of resolvable signal modes is typically much smaller than the number of spectral bands, and most of the orthogonal spectral dimensions generated by a principal components analysis are dominated by noise. Analytical characterization of the "noise eigenmodes" of a hyperspectral data cube supports the development of objective methods for estimating image noise statistics, signal-to-noise ratio, and the complexity and content of the underlying spectral scene. This paper reviews some fundamental results in eigenvalue distribution theory for high-dimensional data, and explores potential applications of the theory to hyperspectral data analysis. Specific applications developed and illustrated in the paper include scene-based estimation of noise-equivalent spectral radiance (NESR), and automated selection of signal-bearing and noise-limited subspaces for spectral analysis.
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Alan D. Stocker, Eskandar Ensafi, and Clark Oliphint "Applications of eigenvalue distribution theory to hyperspectral processing", Proc. SPIE 5093, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, (23 September 2003);


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