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Hyperspectral Demixing: Sparse Recovery of Highly Correlated Endmembers

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Excursions in Harmonic Analysis, Volume 1

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

We apply three different sparse reconstruction techniques to spectral demixing. Endmembers for these signatures are typically highly correlated, with angles near zero between the high-dimensional vectors. As a result, theoretical guarantees on the performance of standard pursuit algorithms like orthogonal matching pursuit (OMP) and basis pursuit (BP) do not apply. We evaluate the performance of OMP, BP, and a third algorithm, sparse demixing (SD), by demixing random sparse mixtures of materials selected from the USGS spectral library (Clark et al., USGS digital spectral library splib06a. U.S. Geological Survey, Digital Data Series 231, 2007). Examining reconstruction sparsity versus accuracy shows clear success of SD and clear failure of BP. We also show that the relative geometry between endmembers creates a bias in BP reconstructions.

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Authors and Affiliations

  1. National Geospatial-Intelligence Agency, 7500 Geoint Drive, Springfield, VA, USA

    John B. Greer

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  1. John B. Greer
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Correspondence to John B. Greer .

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Editors and Affiliations

  1. , Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, 20742-0001, Maryland, USA

    Travis D. Andrews

  2. Norbert Wiener Center, Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Radu Balan

  3. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    Wojciech Czaja

  5. , Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Kasso A. Okoudjou

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Greer, J.B. (2013). Hyperspectral Demixing: Sparse Recovery of Highly Correlated Endmembers. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 1. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8376-4_10

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