23 September 2003 Iterative algorithms for unmixing of hyperspectral imagery
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This paper addresses the use of multiplicative iterative algorithms to compute the abundances in unmixing of hyperspectral pixels. The advantage of iterative over direct methods is that they allow incorporation of positivity and sum-to-one constraints of the abundances in an easy fashion while also allowing better regularization of the solution for the ill-conditioned case. The derivation of two iterative algorithms based on minimization of least squares and Kulback-Leibler distances are presented. The resulting algorithms are the same as the ISRA and EMML algorithms presented in the emission tomography literature respectively. We show that the ISRA algorithm and not the EMML algorithm computes the maximum likelihood estimate of the abundances under Gaussian assumptions while the EMML algorithm computes a minimum distance solution based on the Kulback-Leibler generalized distance. In emission tomography, the EMML computes the maximum likelihood estimate of the reconstructed image. We also show that, since the unmixing problem is in general overconstrained and has no solutions, acceleration techniques for the EMML algorithm such as the RBI-EMML will not converge.
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Miguel Velez-Reyes, Miguel Velez-Reyes, Angela Puetz, Angela Puetz, Michael P. Hoke, Michael P. Hoke, Ronald B. Lockwood, Ronald B. Lockwood, Samuel Rosario, Samuel Rosario, } "Iterative algorithms for unmixing of hyperspectral imagery", Proc. SPIE 5093, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, (23 September 2003); doi: 10.1117/12.497802; https://doi.org/10.1117/12.497802

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