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J. Imaging 2016, 2(1), 7; doi:10.3390/jimaging2010007

Hyperspectral Unmixing from Incomplete and Noisy Data

1
Department of Mathematics, University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
2
Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Gonzalo Pajares Martinsanz
Received: 2 October 2015 / Revised: 15 January 2016 / Accepted: 18 January 2016 / Published: 15 February 2016
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Abstract

In hyperspectral images, once the pure spectra of the materials are known, hyperspectral unmixing seeks to find their relative abundances throughout the scene. We present a novel variational model for hyperspectral unmixing from incomplete noisy data, which combines a spatial regularity prior with the knowledge of the pure spectra. The material abundances are found by minimizing the resulting convex functional with a primal dual algorithm. This extends least squares unmixing to the case of incomplete data, by using total variation regularization and masking of unknown data. Numerical tests with artificial and real-world data demonstrate that our method successfully recovers the true mixture coefficients from heavily-corrupted data. View Full-Text
Keywords: hyperspectral images; spectral unmixing; restoration; inpainting; total variation (TV) regularization; convex optimization; dual approaches hyperspectral images; spectral unmixing; restoration; inpainting; total variation (TV) regularization; convex optimization; dual approaches
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Montag, M.J.; Stephani, H. Hyperspectral Unmixing from Incomplete and Noisy Data. J. Imaging 2016, 2, 7.

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