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Proceedings Paper

M-estimation for robust sparse unmixing of hyperspectral images
Author(s): Maria Toomik; Shijian Lu; James D. B. Nelson
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Paper Abstract

Hyperspectral unmixing methods often use a conventional least squares based lasso which assumes that the data follows the Gaussian distribution. The normality assumption is an approximation which is generally invalid for real imagery data. We consider a robust (non-Gaussian) approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers and relaxes the linearity assumption. The method consists of several appropriate penalties. We propose to use an p norm with 0 < p < 1 in the sparse regression problem, which induces more sparsity in the results, but makes the problem non-convex. On the other hand, the problem, though non-convex, can be solved quite straightforwardly with an extensible algorithm based on iteratively reweighted least squares. To deal with the huge size of modern spectral libraries we introduce a library reduction step, similar to the multiple signal classification (MUSIC) array processing algorithm, which not only speeds up unmixing but also yields superior results. In the hyperspectral setting we extend the traditional least squares method to the robust heavy-tailed case and propose a generalised M-lasso solution. M-estimation replaces the Gaussian likelihood with a fixed function ρ(e) that restrains outliers. The M-estimate function reduces the effect of errors with large amplitudes or even assigns the outliers zero weights. Our experimental results on real hyperspectral data show that noise with large amplitudes (outliers) often exists in the data. This ability to mitigate the influence of such outliers can therefore offer greater robustness. Qualitative hyperspectral unmixing results on real hyperspectral image data corroborate the efficacy of the proposed method.

Paper Details

Date Published: 18 October 2016
PDF: 14 pages
Proc. SPIE 10004, Image and Signal Processing for Remote Sensing XXII, 100040V (18 October 2016); doi: 10.1117/12.2241237
Show Author Affiliations
Maria Toomik, Univ. College London (United Kingdom)
Agency for Science, Technology and Research (A*STAR) (Singapore)
Shijian Lu, Agency for Science, Technology and Research (A*STAR) (Singapore)
James D. B. Nelson, Univ. College London (United Kingdom)

Published in SPIE Proceedings Vol. 10004:
Image and Signal Processing for Remote Sensing XXII
Lorenzo Bruzzone; Francesca Bovolo, Editor(s)

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