Full Text:   <782>

Summary:  <356>

CLC number: TP75

On-line Access: 2016-03-07

Received: 2015-07-31

Revision Accepted: 2015-10-16

Crosschecked: 2016-02-23

Cited: 0

Clicked: 1611

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jing Li

http://orcid.org/0000-0001-8436-1193

Xiao-run Li

http://orcid.org/0000-0001-7611-845X

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2016 Vol.17 No.3 P.250-257

http://doi.org/10.1631/FITEE.1500244


Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction


Author(s):  Jing Li, Xiao-run Li, Li-jiao Wang, Liao-ying Zhao

Affiliation(s):  College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   lxr@zju.edu.cn

Key Words:  Endmember extraction, Modified Cholesky factorization, Spatial pixel purity index (SPPI), New simplex growing algorithm (NSGA), Kernel new simplex growing algorithm (KNSGA)


Jing Li, Xiao-run Li, Li-jiao Wang, Liao-ying Zhao. Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(3): 250-257.

@article{title="Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction",
author="Jing Li, Xiao-run Li, Li-jiao Wang, Liao-ying Zhao",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="17",
number="3",
pages="250-257",
year="2016",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1500244"
}

%0 Journal Article
%T Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction
%A Jing Li
%A Xiao-run Li
%A Li-jiao Wang
%A Liao-ying Zhao
%J Frontiers of Information Technology & Electronic Engineering
%V 17
%N 3
%P 250-257
%@ 2095-9184
%D 2016
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500244

TY - JOUR
T1 - Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction
A1 - Jing Li
A1 - Xiao-run Li
A1 - Li-jiao Wang
A1 - Liao-ying Zhao
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 17
IS - 3
SP - 250
EP - 257
%@ 2095-9184
Y1 - 2016
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1500244


Abstract: 
endmember extraction is a key step in the hyperspectral image analysis process. The kernel new simplex growing algorithm (KNSGA), recently developed as a nonlinear alternative to the simplex growing algorithm (SGA), has proven a promising endmember extraction technique. However, KNSGA still suffers from two issues limiting its application. First, its random initialization leads to inconsistency in final results; second, excessive computation is caused by the iterations of a simplex volume calculation. To solve the first issue, the spatial pixel purity index (SPPI) method is used in this study to extract the first endmember, eliminating the initialization dependence. A novel approach tackles the second issue by initially using a modified Cholesky factorization to decompose the volume matrix into triangular matrices, in order to avoid directly computing the determinant tautologically in the simplex volume formula. Theoretical analysis and experiments on both simulated and real spectral data demonstrate that the proposed algorithm significantly reduces computational complexity, and runs faster than the original algorithm.

In this paper, the authors improve KNSGA in two aspects: (1) use SPPI to solve the inconsistency in result, and (2) using Cholesky factorization to reduce the computing time. The paper is well organized.

基于改进Cholesky分解的快速核单形体体积分析端元提取算法

目的:端元提取是高光谱图像处理中的关键步骤。研究表明,核单形体增长算法(KNSGA)是一种较好的非线性端元提取算法。然而,该算法存在两个主要问题,限制了其性能。第一,随机初始化导致算法结果不稳定;第二,算法中反复计算单形体体积导致算法时间复杂度较高。本文针对这两个问题,提出改进算法,以提高算法稳定性并降低算法时间复杂度。
创新点:本文提出采用空间像元纯度指数(SPPI)来确定KNSGA算法中的初值,提高了算法的稳定性。此外,对于KNSGA中耗时的单形体体积计算,利用改进的Cholesky分解的思想,将求单形体体积最大值转化为寻找矩阵对角元素最大值,进而降低了算法的时间复杂度。
方法:SPPI越小,则像素的纯度越高,因此将具有最小SPPI的像素作为KNSGA的初始值。原始的KNSGA提取端元的过程是循环计算单形体体积值,即每增加一个端元则计算一次端元构成的单形体体积值,直至找到所有端元为止;利用改进的Choelsky分解的快速实现算法,只需在所有端元都找到之后进行一次单形体体积计算。改进后的算法简化了算法的运算复杂度,加快了算法的实现过程。
结论:本文研究针对KNSGA的改进加速算法,利用SPPI解决初值问题,利用Cholesky分解降低计算时间复杂度。实验结果表明,提出的改进算法在算法稳定性和效率上相比原算法都有一定程度提高。

关键词:端元提取;改进的Cholesky分解;空间像元纯度指数;单形体增长算法;核单形体增长算法

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Boardman, J.W., Kruse, F.A., Green, R.O., 1995. Mapping target signatures via partial unmixing of AVIRIS data. JPL Airborne Earth Science Workshop, p.23-26.

[2]Chang, C.I., Du, Q., 2004. Estimation of number of spectrally distinct signal sources in hyperspectral imagery. IEEE Trans. Geosci. Remote Sens., 42(3):608-619.

[3]Chang, C.I., Wu, C., Liu, W., et al., 2006. A new growing method for simplex-based endmember extraction algorithms. IEEE Trans. Geosci. Remote Sens., 44(10):2804-2819.

[4]Cui, J.T., Wang, J., Li, X.R., et al., 2013. Endmember extraction algorithm based on spatial pixel purity index. J. Zhejiang Univ. (Eng. Sci.), 47(9):1517-1523 (in Chinese).

[5]Dowler, S.W., Takashima, R., Andrews, M., 2013. Reducing the complexity of the N-FINDR algorithm for hyperspectral image analysis. IEEE Trans. Image Process., 22(7):2835-2848.

[6]Geng, X.R., Zhao, Y.C., Wang, F.X., et al., 2010. A new volume formula for a simplex and its application to endmember extraction for hyperspectral image analysis. Int. J. Remote Sens., 31(4):1027-1035.

[7]Geng, X.R., Xiao, Z.Q., Ji, L.Y., et al., 2013. A Gaussian elimination based fast endmember extraction algorithm for hyperspectral imagery. ISPRS J. Photogr. Remote Sens., 79(5):211-218.

[8]Gill, P.E., Murray, W., 1974. Newton-type method for unconstrained and linearly constrained optimization. Math. Programm., 7(1):311-350.

[9]Gill, P.E., Murray, W., Wright, M.H., 1981. Practical Optimization. Academic Press, London.

[10]Golub, G.H., van Loan, C.F., 1996. Matrix Computations. The John Hopkins University Press, Baltimore, Mariland.

[11]Liu, J.M., Zhang, J.S., 2012. A new maximum simplex volume method based on householder transformation for endmember extraction. IEEE Trans. Geosci. Remote Sens., 50(1):104-118.

[12]Miao, L., Qi, H., 2007. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens., 45(3):765-777.

[13]NASA, 1997. NASA AVIRIS Data. Available from http://aviris.jpl.nasa.gov.

[14]Nascimento, J.M.P., Bioucas-Dias, J.M., 2005. Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 43(4):898-910.

[15]Nascimento, J.M.P., Bioucas-Dias, J.M., 2008. New developments on VCA unmixing algorithm. SPIE, 7109: 71090F.

[16]Ren, H., Chang, C.I., 2003. Automatic spectral target recognition in hyperspectral imagery. IEEE Trans. Aerosp. Electron. Syst., 39(4):1232-1249.

[17]Schowengerdt, R.A., 1997. Remote Sensing: Models and Methods for Image Processing. Academic Press, New York.

[18]Sun, K., Geng, X., Wang, P., 2014. A fast endmember extraction algorithm based on gram determinant. IEEE Geosci. Remote Sens. Lett., 11(6):1124-1128.

[19]Tao, X., Wang, B., Zhang, L., 2009. Orthogonal bases approach for decomposition of mixed pixels for hyperspectral imagery. IEEE Geosci. Remote Sens. Lett., 6(2): 219-223.

[20]Wang, L., Wei, F., Liu, D., 2013. Fast implementation of maximum simplex volume-based endmember extraction in original hyperspectral data space. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 6(2):516-521.

[21]Wang, L.J., Li, X.R., Zhao, L.Y., 2014. Fast implement of the simplex growing algorithm for endmember extraction. Acta Opt. Sin., 34(11):1128001 (in Chinese).

[22]Xia, W., Pu, H.Y., Wang, B., et al., 2012. Triangular factorization-based simplex algorithms for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 50(11): 4420-4440.

[23]Xiong, W., Chang, C.I., Wu, C.C., 2011. Fast algorithms to implement N-FINDR for hyperspectral endmember extraction. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 4(3):545-564.

[24]Zhao, C.H., Qi, B., Wang, Y.L., 2012. An improved N-FINDR hyperspectral endmember extraction algorithm. J. Electron. Inform. Technol., 34(2):499-503 (in Chinese).

[25]Zhao, L.Y., Zheng, J.P., Li, X.R., et al., 2014. Kernel simplex growing algorithm based on a new simplex volume formula for hyperspectral endmember extraction. J. Appl. Remote Sens., 8(1):083594.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE