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Abstract
A Probabilistic Weighted Archetypal Analysis method with Earth Mover’s Distance (PWAA-EMD) is proposed to extract endmembers from hyperspectral imagery (HSI). The PWAA-EMD first utilizes the EMD dissimilarity matrix to weight the coefficient matrix in the regular Archetypal Analysis (AA). The EMD metric considers manifold structures of spectral signatures in the HSI data and could better quantify the dissimilarity features among pairwise pixels. Second, the PWAA-EMD adopts the Bayesian framework and formulates the improved AA into a probabilistic inference problem by maximizing a joint posterior density. Third, the optimization problem is solved by the iterative multiplicative update scheme, with a careful initialization from the two-stage algorithm and the proper endmembers are finally obtained. The synthetic and real Cuprite Hyperspectral datasets are utilized to verify the performance of PWAA-EMD and five popular methods are implemented to make comparisons. The results show that PWAA-EMD surpasses all the five methods in the average results of spectral angle distance (SAD) and root-mean-square-error (RMSE). Especially, the PWAA-EMD obtains more accurate estimation than AA in almost all the classes of endmembers including two similar ones. Therefore, the PWAA-EMD could be an alternative choice for endmember extraction on the hyperspectral data.
Highlights
Hyperspectral imagery (HSI) processing is a hot topic in the field of remote sensing because the collected data has great potentials in differentiating distinct materials on the earth surface, using its hundreds of narrow spectral bands [1,2]
Spectral signatures of endmembers can be estimated from two divergent schemes [13,14]: (1) the reference-endmembers are manually measured on the ground or in the library using the field spectrometer, and (2) the image-endmembers are estimated from the hyperspectral imagery (HSI) data using endmember extraction methods
We focus our topic in non-pure pixel scheme because the HSI scenarios of non-pure pixels are more realistic and the estimated “virtual” endmembers are more closely associated with physically meaningful spectral signatures of true materials in the spectral library
Summary
Hyperspectral imagery (HSI) processing is a hot topic in the field of remote sensing because the collected data has great potentials in differentiating distinct materials on the earth surface, using its hundreds of narrow spectral bands [1,2]. Proper endmembers bring accurate abundance estimation at each pixel and greatly benefit the spectral unmixing in realistic applications mentioned above and vice versa. Spectral signatures of endmembers can be estimated from two divergent schemes [13,14]: (1) the reference-endmembers are manually measured on the ground or in the library using the field spectrometer, and (2) the image-endmembers are estimated from the HSI data using endmember extraction methods. Because of different collecting conditions (e.g., image sensors, atmospheric effects and scattering conditions) between hyperspectral imaging and the field spectrometer, the spectrum of reference-endmembers usually disagrees with those of image pixels [15]
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