Analysis of Imaging Spectrometer Data Using $N$ -Dimensional Geometry and a Mixture-Tuned Matched Filtering Approach

Imaging spectrometers collect unique data sets that are simultaneously a stack of spectral images and a spectrum for each image pixel. While these data can be analyzed using approaches designed for multispectral images, or alternatively by looking at individual spectra, neither of these takes full advantage of the dimensionality of the data. Imaging spectrometer spectral radiance data or derived apparent surface reflectance data can be cast as a scattering of points in an n-dimensional Euclidean space, where n is the number of spectral channels and all axes of the n-space are mutually orthogonal. Every pixel in the data set then has a point associated with it in the n- d space, with its Cartesian coordinates defined by the values in each spectral channel. Given n-dimensional data, convex and affine geometry concepts can be used to identify the purest pixels in a given scene (the “endmembers”). N-dimensional visualization techniques permit human interpretation of all spectral information of all image pixels simultaneously and projection of the endmembers back to their locations in the imagery and to their spectral signatures. Once specific spectral endmembers are defined, partial linear unmixing (mixture-tuned matched filtering or “MTMF”) can be used to spectrally unmix the data and to accurately map the apparent abundance of a known target material in the presence of a composite background. MTMF incorporates the best attributes of matched filtering but extends that technique using the linear mixed-pixel model, thus leading to high selectivity between similar materials and minimizing classification and mapping errors for analysis of imaging spectrometer data.