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

Abstract

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.

Global spectroscopic survey of cloud thermodynamic phase at high spatial resolution, 2005–2015

“…To account for this, we estimated the noise level independently for each integration timestep and each spectral channel. We used the common method of pairwise differences between spectra at neighboring locations (Boardman and Kruse, 2011). Since the spatial field was mostly uniform over small distances, these differences conservatively estimated the measurement noise σ in each channel.…”

DMBLC: An Indirect Urban Impervious Surface Area Extraction Approach by Detecting and Masking Background Land Cover on Google Earth Image

“…On the one hand, MF calculates the spectral similarity between the undetermined pixel and known target spectrum [38], and produces a result called the MF score to describe their similarity qualitatively. On the other hand, MT reduces the false positive problem in MF processing [39], and produces a result called the infeasibility value to describe the false positivity qualitatively. Thus, undetermined pixels or segments with a high MF score and a low infeasibility value can be identified as targets.…”

A theoretical‐experimental methodology for assessing the sensitivity of biomedical spectral imaging platforms, assays, and analysis methods

“…Similar to CEM, this technique is useful in quantifying the abundance of a known spectral signature where other spectral signatures may crowd the desired signal [93]. However, unlike CEM, MTMF magnifies the signal-to-noise ratio of the desired signature instead of only minimizing undesired signals.…”