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Endmember orthonormal mapping in hyperspectral mixture analysis to address endmember variability

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Abstract

Spectral unmixing estimates the abundance of each endmember at every pixel of a hyperspectral image. Each material in traditional unmixing algorithms is represented through a constant spectral signature. However, endmember variability always exists due to environmental, atmospheric, and temporal conditions, which leads to poor accuracy of the estimated abundances. This paper proposes a new unmixing algorithm based on a new linear transformation called endmember orthonormal mapping (EOM) to overcome the aforementioned problem. The EOM transformation maps original spectral space to a new EOM space to reduce endmember variability. In the original spectral space, each material is represented by a set of spectra (endmember set) which is extracted using the automated endmember bundles (AEB) method. The EOM transforms each endmember set to a vector in the EOM space so that these vectors are orthonormal. On account of orthonormalized endmembers, the condition number of the mixing matrix in the EOM space reduces. Furthermore, we consider the noise term as an additional virtual endmember set mapped to a vector that is orthogonal to other endmembers. As a result, a promising unmixing accuracy is obtained through applying the least squares abundance estimation in the subspace orthogonal to noise. Experimental results of both synthetic and real hyperspectral images demonstrate that the proposed algorithms provide much enhanced performance compared with the state-of-the-art algorithms.

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Acknowledgments

The authors acknowledge Dr. Ben Somers for generously providing the in situ measured data. They also acknowledge the anonymous reviewers for their outstanding comments and suggestions, which greatly helped to improve the technical content and presentation of the manuscript.

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Authors and Affiliations

  1. Computer & Information Technology Engineering Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran, 1591634311, Iran

    Ali Jafari, Reza Safabakhsh & Mohammad Mehdi Ebadzadeh

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  1. Ali Jafari
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  2. Reza Safabakhsh
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  3. Mohammad Mehdi Ebadzadeh
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Correspondence to Mohammad Mehdi Ebadzadeh.

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Communicated by: H. A. Babaie

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Jafari, A., Safabakhsh, R. & Ebadzadeh, M.M. Endmember orthonormal mapping in hyperspectral mixture analysis to address endmember variability. Earth Sci Inform 9, 291–307 (2016). https://doi.org/10.1007/s12145-016-0256-4

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  • DOI: https://doi.org/10.1007/s12145-016-0256-4

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