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A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization

A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization


Titill: A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization
Höfundur: Kizel, Fadi
Shoshany, Maxim
Netanyahu, Nathan S.
Even-Tzur, Gilad
Benediktsson, Jon Atli   orcid.org/0000-0003-0621-9647
Útgáfa: 2017
Tungumál: Enska
Umfang: 1-19
Háskóli/Stofnun: Háskóli Íslands
University of Iceland
Svið: Verkfræði- og náttúruvísindasvið (HÍ)
School of Engineering and Natural Sciences (HÍ)
Deild: Rafmagns- og tölvuverkfræðideild (HÍ)
Faculty of Electrical and Computer Engineering (UI)
Birtist í: IEEE Transactions on Geoscience and Remote Sensing;
ISSN: 0196-2892
1558-0644 (eISSN)
DOI: 10.1109/TGRS.2017.2692999
Efnisorð: Hyperspectral imaging; Spectral unmixing; Gradient methods; Optimization; Myndvinnsla; Tölvunotkun
URI: https://hdl.handle.net/20.500.11815/287

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Tilvitnun:

F. Kizel; M. Shoshany; N. S. Netanyahu; G. Even-Tzur; J. A. Benediktsson, "A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization," in IEEE Transactions on Geoscience and Remote Sensing , vol.PP, no.99, pp.1-19 doi: 10.1109/TGRS.2017.2692999

Útdráttur:

We present, in this paper, a new methodology for spectral unmixing, where a vector of fractions, corresponding to a set of endmembers (EMs), is estimated for each pixel in the image. The process first provides an initial estimate of the fraction vector, followed by an iterative procedure that converges to an optimal solution. Specifically, projected gradient descent (PGD) optimization is applied to (a variant of) the spectral angle mapper objective function, so as to significantly reduce the estimation error due to amplitude (i.e., magnitude) variations in EM spectra, caused by the illumination change effect. To improve the computational efficiency of our method over a commonly used gradient descent technique, we have analytically derived the objective function's gradient and the optimal step size (used in each iteration). To gain further improvement, we have implemented our unmixing module via code vectorization, where the entire process is ''folded'' into a single loop, and the fractions for all of the pixels are solved simultaneously. We call this new parallel scheme vectorized code PGD unmixing (VPGDU). VPGDU has the advantage of solving (simultaneously) an independent optimization problem per image pixel, exactly as other pixelwise algorithms, but significantly faster. Its performance was compared with the commonly used fully constrained least squares unmixing (FCLSU), the generalized bilinear model (GBM) method for hyperspectral unmixng, and the fast state-of-the-art methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and collaborative SUnSAL (CLSUnSAL) based on the alternating direction method of multipliers. Considering all of the prospective EMs of a scene at each pixel (i.e., without a priori knowledge which/how many EMs are actually present in a given pixel), we demonstrate that the accuracy due to VPGDU is considerably higher than that obtained by FCLSU, GBM, SUnSAL, and CLSUnSAL under varying illumination, and is, otherwise, comparable with respect to these methods. However, while our method is significantly faster than FCLSU and GBM, it is slower than SUnSAL and CLSUnSAL by roughly an order of magnitude.

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