26 March 2001 Unified Lagrangian neural network method for subpixel classification in hyperspectral imagery
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Abstract
Because of the foot print of a pixel is relative large, one pixel usually contains more than one material. The spectrum of each pixel vector can be considered as spectral mixture of all materials present in that pixel. How to unmix the spectra while dealing with constraint at the same time is a challenging problem in spectral mixture analysis. One approach is supervised constrained least squares approach, which has full knowledge about the spectrum signatures of endmembers resident in the image scene. The other is unsupervised unmixing method using Lagrangian Artificial Neural Network (LANN) with no knowledge about the image scene. The concept of unit-sum constraint is identical in both cases, the difference is whether one uses the known spectral characteristics for the supervised training or not. In practice, we need both methodologies for efficiency reasons, since there is 'curse of dimensionality' (too large degree of freedom in hyperspectral). The supervised one can reduce the search and ID size and the unsupervised one can discover the unknown interferences and thus in constrained least squares algorithms help ID. The constrained least squares method has been discussed in digital signal processing and applied to hyperspectral imagery while LANN to multispectral imagery. In this paper, we expend LANN to hyperspectral image classification and also discuss the relationship between the constrained least squares method and LANN. These two methods alleviate this problem by adopting the Lagrange multiplier in neural network to relax the sum-to-one constraint. To evaluate this designed algorithm a series of experiments using Airborne Visible/Infrared Imaging Spectrometer (AVIRIS images are conducted to show its potential usefulness in hyperspectral image classification.
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Harold H. Szu, Harold H. Szu, Hsuan Ren, Hsuan Ren, } "Unified Lagrangian neural network method for subpixel classification in hyperspectral imagery", Proc. SPIE 4391, Wavelet Applications VIII, (26 March 2001); doi: 10.1117/12.421228; https://doi.org/10.1117/12.421228
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