Sparse Demixing of Hyperspectral Images

In the LMM for hyperspectral images, all the image spectra lie on a high-dimensional simplex with corners called endmembers. Given a set of endmembers, the standard calculation of fractional abundances with constrained least squares typically identifies the spectra as combinations of most, if not al...

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Bibliographic Details
Published in:IEEE transactions on image processing 2012-01, Vol.21 (1), p.219-228
Main Author: Greer, J. B.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation methods
Colorimetry - methods
Detection, estimation, filtering, equalization, prediction
Dictionary learning
Exact sciences and technology
Hyperspectral imaging
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Information Storage and Retrieval - methods
Information, signal and communications theory
linear mixture model (LMM)
Matching pursuit algorithms
Materials
Pattern Recognition, Automated - methods
Pixel
Reproducibility of Results
Sensitivity and Specificity
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
Sparse matrices
sparse reconstruction
Spectrum Analysis - methods
Telecommunications and information theory
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Summary:In the LMM for hyperspectral images, all the image spectra lie on a high-dimensional simplex with corners called endmembers. Given a set of endmembers, the standard calculation of fractional abundances with constrained least squares typically identifies the spectra as combinations of most, if not all, endmembers. We assume instead that pixels are combinations of only a few endmembers, yielding abundance vectors that are sparse. We introduce sparse demixing (SD), which is a method that is similar to orthogonal matching pursuit, for calculating these sparse abundances. We demonstrate that SD outperforms an existing L 1 demixing algorithm, which we prove to depend adversely on the angles between endmembers. We combine SD with dictionary learning methods to calculate automatically endmembers for a provided set of spectra. Applying it to an airborne visible/infrared imaging spectrometer image of Cuprite, NV, yields endmembers that compare favorably with signatures from the USGS spectral library.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2011.2160189