Analysis and acceleration strategy of endmember extraction algorithms based on convex geometry

References

• Bajorski , P. 2010 . Second moment linear dimensionality as an alternative to virtual dimensionality . IEEE Transactions on Geoscience and Remote Sensing , 48 : 1 – 7 .
   Google Scholar
• Barber , C.B. , Dobkin , D.P. and Huhdanpaa , H. 1996 . The Quickhull algorithm for convex hulls . ACM Transactions on Mathematical Software , 22 : 469 – 483 .
   Web of Science ®Google Scholar
• Bi, D.M., Zhao, L.J. and Gong, Y.J., 2009, The mathematical model of the endmembers in hyperspectral data. In International Conference on Environmental Science and Information Application Technology, 2009, pp. 609–613. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5199966 (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5199966)
   Google Scholar
• Bioucas-Dias , J.M. 2009 . “ A variable splitting augmented lagrangian approach to linear spectral unmixing ” . In the First IEEE WHISPERS, 2009
   Google Scholar
• Bioucas-Dias , J.M. and Nascimento , J.M.P. 2008 . Hyperspectral subspace identification . IEEE Transactions on Geoscience and Remote Sensing , 46 : 2435 – 2445 .
   Web of Science ®Google Scholar
• Boardman , J.W. Geometric mixture analysis of imaging spectrometry data . International Geoscience and Remote Sensing Symposium, IGARSS’94 . 8–12 August 1994 , Pasadena , CA . pp. 2369 – 2371 . New York , NY : IEEE . IEEE Catalog No. 94CH3378 Vol. IV
   Google Scholar
• Boardman , J.W. , Kruse , F.A. and Green , R.O. Mapping target signatures via partial unmixing of AVIRIS data . Proceedings of the Fifth JPL Ariborne Earth Science Workshop . 9–14 December 1995 , Pasadena , CA . pp. 23 – 26 . Pasadena : NASA JPL, JPL Publication 95-1 .
   Google Scholar
• Chan , T.H. , Chi , C.Y. , Huang , Y.M. and Ma , W.K. 2009 . A convex analysis based minimum-volume enclosing simplex algorithm for hyperspectral unmixing . IEEE Transactions on Signal Processing , 57 : 4418 – 4432 .
   Web of Science ®Google Scholar
• Chang , C.I. , Chiang , S.S. , Smith , J.A. and Ginsberg , I.W. 2002 . Linear spectral random mixture analysis for hyperspectral imagery . IEEE Transactions on Geoscience and Remote Sensing , 40 : 375 – 391 .
   Web of Science ®Google Scholar
• Chang , C.I. and Du , Q. 2004 . Estimation of number of spectrally distinct signal sources in hyperspectral imagery . IEEE Transactions on Geoscience and Remote Sensing , 42 : 608 – 619 .
   Web of Science ®Google Scholar
• Chang , C.I. and Heinz , D.C. 2000 . Constrained subpixel target detection for remotely sensed imagery . IEEE Transactions on Geoscience and Remote Sensing , 38 : 1144 – 1159 .
   Web of Science ®Google Scholar
• Chang , C.I. , Wu , C.C. , Liu , W. and Ouyang , Y.C. 2006 . A new growing method for simplex-based endmember extraction algorithms . IEEE Transactions on Geoscience and Remote Sensing , 44 : 2804 – 2819 .
   Web of Science ®Google Scholar
• Chang , C.I. , Wu , C.C. , Lo , C.S. and Chang , M.L. 2010 . Real-time simplex growing algorithms for hyperspectral endmember extraction . IEEE Transactions on Geoscience and Remote Sensing , 48 : 1834 – 1850 .
   Web of Science ®Google Scholar
• Clark , R.N. , Swayze , G.A. , Gallagher , A. , King , T.V. and Clavin , W.M. 1993 . The U.S. Geological Survey digital spectral library: Version 1: 0.2 to 3.0 μm . U.S. Geological Survey, USGS Open File Report, pp. , : 93 – 592 .
   Google Scholar
• Craig , M.D. 1994 . Minimum-volume transforms for remotely sensed data . IEEE Transactions on Geoscience and Remote Sensing , 32 : 542 – 552 .
   Web of Science ®Google Scholar
• Dobigeon , N. , Moussaoui , S. , Coulon , M. , Tourneret , J.Y. and Hero , A.O. 2009 . Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery . IEEE Transactions on Signal Processing , 57 : 4355 – 4368 .
   Web of Science ®Google Scholar
• Eches , O. , Dobigeon , N. and Tourneret , J.Y. 2010 . Estimating the number of endmember in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm . IEEE Journal of Selected Topics in Signal Processing , 4 : 582 – 591 .
   Web of Science ®Google Scholar
• Green , A.A. , Berman , M. , Swithzer , P. and Criag , M.D. 1988 . A transformation for ordering multispectral data in terms of image quality with implications for noise removal . IEEE Transactions on Geoscience and Remote Sensing , 26 : 65 – 74 .
   Web of Science ®Google Scholar
• Hapke , B. 1981 . Bidirectional reflectance spectroscopy 1. theory . Journal of Geophysical Research , 86 : 3039 – 3054 .
   Web of Science ®Google Scholar
• Heinz , D. and Chang , C.I. 2001 . Fully constrained least squares linear mixture analysis for material quantification in hyperspectral imagery . IEEE Transactions on Geoscience and Remote Sensing , 39 : 529 – 545 .
   Web of Science ®Google Scholar
• Huck , A. , Guillaume , M. and Blanc-Talon , J. 2010 . Minimum dispersion constrained nonnegative matrix factorization to unmix hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 48 : 2590 – 2602 .
   Web of Science ®Google Scholar
• Ichoku , C. and Karnieli , A. 1996 . A review of mixture modeling techniques for sub-pixel land cover estimation . Remote Sensing Reviews , 13 : 161 – 186 .
   Google Scholar
• Johnson , P. , Smith , M. , George , S.T. and Adams , J. 1983 . A semiempirical method for analysis of the reflectance spectra of binary mineral mixtures . Journal of Geophysical Research , 88 : 3557 – 3561 .
   Web of Science ®Google Scholar
• Keshava , N. 2003 . A survey of spectral unmixing algorithms . Lincoln Laboratory Journal , 14 : 55 – 78 .
   Google Scholar
• Klee , V. 1980 . On the complexity of d-dimensional voronoi diagrams . Archiv der Mathematik , 34 : 75 – 80 .
   Web of Science ®Google Scholar
• Kuybeda , O. , Malah , D. and Barzohar , M. 2007 . Rank estimation and redundancy reduction of high-dimensional noisy signals with preservation of rare vectors . IEEE Transactions on Signal Processing , 55 : 5579 – 5592 .
   Web of Science ®Google Scholar
• Li, J. and Bioucas-Dias, J., Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data. In IEEE Internatinal Geoscience and Remote Sensing Symposium-IGARSS2008, 8–12 August 2008, Boston, MA, pp. 2369–2371. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4779330 (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4779330)
   Google Scholar
• Liu , X. , Xia , W. , Wang , B. and Zhang , L. 2011 . An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 49 : 757 – 772 .
   Web of Science ®Google Scholar
• Meer , F.D. 1999 . Iterative spectral unmixing (ISU) . International Journal of Remote Sensing , 20 : 3431 – 3436 .
   Web of Science ®Google Scholar
• Miao , L. and Qi , H. 2007 . Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization . IEEE Transactions on Geoscience and Remote Sensing , 45 : 765 – 777 .
   Web of Science ®Google Scholar
• Nascimento , J. and Bioucas-Dias , J. 2005a . Does independpent component analysis play a role in unmixing hyperspectral data? . IEEE Transactions on Geoscience and Remote Sensing , 43 : 175 – 187 .
   Web of Science ®Google Scholar
• Nascimento , J. and Bioucas-Dias , J. 2005b . Vertex component analysis: a fast algorithm to unmix hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 43 : 898 – 910 .
   Web of Science ®Google Scholar
• Nascimento , J. and Bioucas-Dias , J. Learning dependent sources using mixtures of dirichlet: applications on hyperspectral unmixing . First IEEE GRSS Workshop on Hyperspectral Image and Signal Processing-WHISPERS 2009 . 26–28 August 2009 . pp. 1 – 5 . Grenoble doi: 10.1109/WHISPERS.2009.5288975
   Google Scholar
• Parra , L.C. , Sajda , P. and Du , S. November 2003 2003 . “ Recovery of constituent spectra using non-negative matrix factorization ” . In Proceedings of the SPIE November 2003 , 321 – 331 . San Diego , CA
   Google Scholar
• Plaza , A. , Martnez , P. , Pérez , R. and Plaza , J. 2002 . Spatial/spectral endmember extraction by multidimensional morphological operations . IEEE Transactions on Geoscience and Remote Sensing , 40 : 2025 – 2041 .
   Web of Science ®Google Scholar
• Plaza , A. , Martnez , P. , Pérez , R. and Plaza , J. 2004 . A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 42 : 650 – 663 .
   Web of Science ®Google Scholar
• Plaza , J. , Hendrix , E.M.T. , Garca , I. , Martn , G. and Plaza , A. 2012 . On endmember identification in hyperspectral images without pure pixels: a comparison of algorithms . Journal of Mathmatical Imaging and Vision , 42 : 163 – 175 .
   Web of Science ®Google Scholar
• Praveen , B. , Wenger , R. and Crwafis , R. 2004 . Isosurface construction in any dimension using convex hulls . IEEE Transactions on Visualization and Computer Graphics , 10 : 130 – 141 .
   PubMed Web of Science ®Google Scholar
• Preparata , F.P. and Hong , S.J. 1977 . Convex hulls of finite point sets in two and three dimensions . Communications of the ACM , 2 : 87 – 93 .
   Web of Science ®Google Scholar
• Ramli , A.A. , Watada , J. and Pedrycz , W. 2011 . Real-time fuzzy regression analysis: a convex hull approach . European Journal of Operation Research , 210 : 606 – 617 .
   Web of Science ®Google Scholar
• Singer , R.B. and McCord , T.B. 1979 . “ Mars: large scale mixing of bright and dark surface materials and implications for analysis of spectral reflectance ” . In Proceedings of 10th Lunar Planetary Science Conference, American Geophysical Union, Washington, DC 1835 – 1848 .
   Google Scholar
• Settle , J.J. and Drake , N.A. 1993 . Linear mixing and the estimation of ground cover proportions . International Journal of Remote Sensing , 14 : 1159 – 1177 .
   Web of Science ®Google Scholar
• Singh , A. and Harrison , A. 1985 . Standardized principal components . International Journal of Remote Sensing , 6 : 883 – 896 .
   Web of Science ®Google Scholar
• Somers , B. , Asner , G.P. , Tits , L. and Coppin , P. 2011 . Endmember variability in spectral mixture analysis: a review . Remote Sensing of Environment , 115 : 1603 – 1616 .
   Web of Science ®Google Scholar
• Somers , B. , Delalieux , S. , Stuckens , J. , Verstraeten , W.W. and Coppin , P. 2009 . A weighted linear spectral mixture analysis approach to address endmember variability in agricultural production systems . International Journal of Remote Sensing , 30 : 139 – 147 .
   Web of Science ®Google Scholar
• Thurau, C., Kersting, K. and Bauckhage, C., 2009, Convex nonnegative matrix factorization in the wild. In Proceedings of the 2009 Ninth IEEE International Conference on Data Mining (ICDM 2009), 6–9 December 2009, Miami, FL, pp. 523–532. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5360278 (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5360278)
   Google Scholar
• Wang , J. and Chang , C.C. 2006 . Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis . IEEE Transactions on Geoscience and Remote Sensing , 44 : 1586 – 1600 .
   Web of Science ®Google Scholar
• Winter , M.E. N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data . Proceedings of the SPIE Conference on Imaging Spectrometry V . July 1999 , Denver , CO . pp. 266 – 277 . Bellingham : International Society for Optical Engineering (SPIE) . Vol. 3753
   Google Scholar
• Wu , C.C. , Lo , C.S. and Chang , C.I. 2009 . Improved process for use of a simplex growing algorithm for endmember extraction . IEEE Geoscience and Remote Sensing Letters , 6 : 523 – 527 .
   Web of Science ®Google Scholar
• Xia , W. , Liu , X.S. , Wang , B. and Zhang , L.M. 2011 . Independent component analysis for blind unmixing of hyperspectral imagery with additional constraints . IEEE Transactions on Geoscience and Remote Sensing , 49 : 2165 – 2179 .
   Web of Science ®Google Scholar
• Xu , Z.B. , Zhang , J.S. and Leung , Y.W. 1998 . An approximate algorithm for computing multidimensional convex hulls . Applied Mathematics and Computation , 94 : 193 – 226 .
   Web of Science ®Google Scholar
• Yao , C.A. 1981 . A lower bound to finding convex hulls . Journal of the Association for computing Machinery , 28 : 780 – 787 .
   Web of Science ®Google Scholar
• Zare , A. and Gader , P. 2010 . PCE: piecewise convex endmember detection . IEEE Transactions on Geoscience and Remote Sensing , 48 : 2620 – 2632 .
   Web of Science ®Google Scholar
• Zhang , X.Q. , Tang , Z.J. , Yu , J.H. , Guo , M.M. and Jiang , L.Y. 2010 . Convex hull properites and algorithms . Applied Mathematics and Computation , 216 : 3209 – 3218 .
   Web of Science ®Google Scholar
• Zhou , X.F. , Jiang , W.H. , Tian , Y.J. and Shi , Y. 2010 . Kernel subclass convex hull sample selcetion method for SVM on face recognition . Neurocomputing , 73 : 2234 – 2246 .
   Web of Science ®Google Scholar
• Zymnis, A., Kim, S.J., Skaf, J., Parente, M. and Boyd, S., 2007, Hyperspectral image unmixing via alternating projected subgradients. In 41st Asilomar Conferece on Signals, Systems, and Computer, 4–7 November, Pacific Grove, CA, pp. 1164–1168. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4487406 (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4487406)
   Google Scholar