Spectral Mixture Analysis: Linear and Semiparametric Full and Iterated Partial Unmixing in Multi and Hyperspectral Image Data
 Allan Aasbjerg Nielsen
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As a supplement or an alternative to classification of hyperspectral image data linear and semiparametric mixture models are considered in order to obtain estimates of abundance of each class or endmember in pixels with mixed membership. Full unmixing based on both ordinary least squares (OLS) and nonnegative least squares (NNLS), and the partial unmixing methods orthogonal subspace projection (OSP), constrained energy minimization (CEM) and an eigenvalue formulation alternative are dealt with. The solution to the eigenvalue formulation alternative proves to be identical to the CEM solution. The matrix inversion involved in CEM can be avoided by working on (a subset of) orthogonally transformed data such as signal maximum autocorrelation factors, MAFs, or signal minimum noise fractions, MNFs. This will also cause the partial unmixing result to be independent of the noise isolated in the MAF/MNFs not included in the analysis. CEM and the eigenvalue formulation alternative enable us to perform partial unmixing when we know one desired endmember spectrum only and not the full set of endmember spectra. This is an advantage over full unmixing and OSP. The eigenvalue formulation of CEM inspires us to suggest an iterated CEM scheme. Also the target constrained interference minimized filter (TCIMF) is described. Spectral angle mapping (SAM) is briefly described. Finally, semiparametric unmixing (SPU) based on a combined linear and additive model with a nonlinear, smooth function to represent endmember spectra unaccounted for is introduced. An example with two generated bands shows that both full unmixing, the CEM, the iterated CEM and TCIMF methods perform well. A case study with a 30 bands subset of AVIRIS data shows the utility of full unmixing, SAM, CEM and iterated CEM to more realistic data. Iterated CEM seems to suppress noise better than CEM. A study with AVIRIS spectra generated from real spectra shows (1) that ordinary least squares in this case with one unknown spectrum performs better than nonnegative least squares, and (2) that although not fully satisfactory the semiparametric model gives better estimates of endmember abundances than the linear model.
 Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Croz, J.D., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., and Sorenson, D. 1995. LAPACK Users' Guide 2nd ed. Society for Industrial and Applied Mathematics Philadelphia.
 Anderson, T.W. 1984. An Introduction to Multivariate Statistical Analysis, 2nd ed. John Wiley: New York.
 AVIRIS, http://makalu.jpl.nasa.gov/aviris.html. Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, CA.
 Bernard, A., Kanellopoulos, I., and Wilkinson, G.G. 1997. Training strategies for neural network soft classification of remotely sensed imagery. International Journal of Remote Sensing, 18(8):1851–1856.
 Chambers, J.M. and Hastie T.J. (Eds.) 1992. Statistical Models in S. Wadsworth and Brooks/Cole: Pacific Grove, CA.
 Conradsen, K., Ersbøll, B.K.,* and Nielsen, A.A. 1991. Noise removal in multichannel image data by a parametric maximum noise fractions estimator. In Proceedings of the 24th International Symposium on Remote Sensing of Environment, ERIM (Ed.), Rio de Janeiro, Brazil, pp. 403–416.
 Conradsen, K., Nielsen, B.K., and Thyrsted, T. 1985. A comparison of min/max autocorrelation factor analysis and ordinary factor analysis. In Proceedings from Symposium in Applied Statistics, Lyngby, Denmark, pp. 47–56.
 Crippen, R.E. and Bloom, R.G. 1999. Unveiling the lithology of vegetated terrains in remotely sensed imagery via forced decorrelation. In Proceedings of the Thirteenth International Conference on Applied Geologic Remote Sensing, Vol. I, Vancouver, British Columbia, Canada, ERIM (Ed.), p. 150.
 Dempster, A., Laird N., and Rubin, D. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39:1–38.
 Dixon, W.J. (Ed.) 1985. BMDP Statistical Software. University of California Press, p. 734.
 Dongarra, J.J., Bunch, J.R., Moler, C.B., and Stewart, G.W. 1979. LINPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia.
 Ersbøll, B.K. 1989. Transformations and classifications of remotely sensed data: Theory and geological cases. Ph.D. thesis, Institute of Mathematical Statistics and Operations Research, Technical University of Denmark, Lyngby, p. 297.
 Flesche, H., Nielsen, A.A., and Larsen, R. 2000. Supervised mineral classification with semiautomatic training and validation set generation in scanning electron microscope energy dispersive spectroscopy images of thin sections. Mathematical Geology, 32(3): 337–366.
 Gill, P.E., Hammarling, S.J., Murray, W., Saunders, M.A., and Wright, M.H. 1986. User's guide for LSSOL (Version 1.0): A FORTRAN package for constrained linear leastsquares and convex quadratic programming, Technical Report 86–1, Department of Operations Research, Stanford University, CA.
 Green, A.A., Berman, M., Switzer, P., and Craig, M.D. 1988. Transformation for ordering multispectral data in terms of image quality with implications for noise removal. IEEE Transactions on Geoscience and Remote Sensing, 26(1):65–74.
 Harsanyi, J.C. and Chang, C.I. 1994. Hyperspectral image classification and dimensionality reduction: An orthogonal subspace projection approach. IEEE Transactions on Geoscience and Remote Sensing, 32(4):779–785.
 Hastie, T.J. and Tibshirani, R.J. 1990. Generalized Additive Models. Chapman and Hall: London.
 Jacobsen, A., Heidebrecht, K.B., and Nielsen, A.A. 1998. Monitoring grasslands using convex geometry and partial unmixing— A case study. In Proceedings of the First EARSeL Workshop on Imaging Spectroscopy, M. Schaepman, D. Schläpfer, and K. Itten (Eds.), Zürich, Switzerland, pp. 309–316.
 Jacobson, A.S., Berkin, A.L., and Orton, M.N. 1994. LinkWinds: Interactive scientific data analysis and visualization. Communications of the ACM, 37(4):42–52. http://linkwinds.jpl.nasa.gov/.
 Kent, J.T. and Mardia, K.V. 1988. Spatial classification using fuzzy membership models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(5):659–671.
 Kruse, F.A., Lefkoff, A.B., Boardman, J.B., Heidebrecht, K.B., Shapiro, A.T., Barloon, P.J., and Goetz, A.F.H. 1993. The spectral image processing system (SIPS)Interactive visualization and analysis of imaging spectrometer data. Remote Sensing of Environment, 44:145–163.
 Landy, M.S. 1993. HIPS2 software for image processing: Goals and directions. In Proceedings of the SPIE 1964 Applications of Artificial Intelligence 1993: Machine Vision and Robotics, K.L. Boyer and L. Stark (Eds.), pp. 382–391. http://www.cns.nyu.edu/home/msl/hipsdescr.cgi/.
 Landy, M.S., Cohen, Y., and Sperling, G. 1984a. HIPS: A UNIX based image processing system. Computer Vision, Graphics and Image Processing, 25(3):331–347. http://www.cns.nyu.edu/home/msl/hipsdescr.cgi/.
 Landy, M.S., Cohen, Y., and Sperling, G. 1984b. HIPS: Image processing under UNIX. Software and applications. Behavior Research Methods, Instrumentation, and Computers, 16(2):199–216. http://www.cns.nyu.edu/home/msl/hipsdescr.cgi/.
 Larsen, R., Nielsen, A.A., and Conradsen, K. 1997. Restoration of hyperspectral pushbroom scanner data. In Proceedings of the 17th EARSeL Symposium on Future Trends in Remote Sensing, P. Gudmandsen (Ed.), Lyngby, Denmark, pp. 157–162.
 Larsen, R., Nielsen, A.A., and Flesche, H. 1999. Sensitivity study of a semiautomatic supervised classifier applied to minerals from Xray mapping images. In Proceedings of the Scandinavian Image Analysis Conference (SCIA'99), Vol. 2, B.E. Ersbøll and P. J ohansen (Eds.), Kangerlussuaq, Greenland, pp. 785–792.
 Larsen, R., Nielsen, A.A., and Flesche, H. 2000. Sensitivity study of a semiautomatic training set generator. Pattern Recognition Letters, 21(13/14):1175–1182.
 Lee, J.B., Woodyatt, A.S., and Berman, M. 1990. Enhancement of high spectral resolution remotesensing data by a noiseadjusted principal components transform. IEEE Transactions on Geoscience and Remote Sensing, 28(3):295–304.
 Marsh, S.E., Switzer, P., Kovalik, W.S., and Lyon, R.J.P. 1980. Resolving the percentage of component terrains within single resolution elements. Photogrammetric Engineering and Remote Sensing, 46:1079–1086.
 Maselli, F. 1998. Multiclass spectral decomposition of remotely sensed scenes by selective pixel unmixing. IEEE Transactions on Geoscience and Remote Sensing, 36(5):1809–1820.
 Miller, J.W.V., Farison, J.B., and Shin, Y. 1992. Spatially invariant image sequences. IEEE Transactions on Image Processing, 1(2): 148–161.
 Nielsen, A.A. 1994. Analysis of regularly and irregularly sampled spatial, multivariate, and multitemporal data. Ph.D. Thesis, Department of Mathematical Modelling, Technical University of Denmark, Lyngby. http://www.imm.dtu.dk/∼aa/phd/.
 Nielsen, A.A. 1998. Linear mixture models and partial unmixing in multiand hyperspectral image data. In Proceedings from the 1st EARSeL Workshop on Imaging Spectroscopy, M. Schaepman, D. Schläpfer, and K. Itten (Eds.), Zürich, Switzerland, pp. 165–172.
 Nielsen, A.A. 1999a. Linear mixture models, full and partial unmixing in multiand hyperspectral image data. In Proceedings of the Scandinavian Image Analysis Conference (SCIA'99), Vol. 2, B.E. Ersbøll and P. Johansen (Eds.), Kangerlussuaq, Greenland, pp. 898–902.
 Nielsen, A.A. 1999b. Multichannel remote sensing data and orthogonal transformations for change detection. In Machine Vision and Advanced Image Processing in Remote Sensing, I. Kanellopoulos, G.G. Wilkinson, and T. Moons (Eds.), Springer.
 Nielsen, A.A. 1999c. Partial unmixing in hyperspectral image data. In Proceedings from the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II, ERIM (Ed.), Ottawa, Ontario, Canada, pp. 535–542.
 Nielsen, A.A., Conradsen, K., Pedersen, J.L., and Steenfelt, A. 1997. Spatial factor analysis of stream sediment geochemistry data from South Greenland. In Proceedings of the Third Annual Conference of the International Association for Mathematical Geology (IAMG'97), V. PawlowskyGlahn (Eds.), Barcelona, Spain, pp. 955–960.
 Nielsen, A.A., Conradsen, K., Pedersen, J.L., and Steenfelt, A. 2000. Maximum autocorrelation factorial kriging. In Proceedings of the Sixth International Geostatistics Congress (Geostats 2000), W.J. Kleingeld and D.K. Krige (Eds.). Cape Town, South Africa, paper no. E13 on CD Rom.
 Nielsen, A.A., Conradsen, K., and Simpson, J.J. 1998a. Multivariate alteration detection (MAD) and MAF postprocessing in multispectral, bitemporal image data: New approaches to change detection studies. Remote Sensing of Environment, 64:1–19.
 Nielsen, A.A., Ersbøll, B., Pälchen, W., and Rank, G. 1996. Spatial analysis of multivariate, (Ir) regularly sampled data: Geochemistry from the eastern Erzgebirge. In Geostatistics Wollongong '96, E.Y. Baafi and N.A. Schofield (Eds), Wollongong, Australia, pp. 1173–1184.
 Nielsen, A.A., Flesche, H., Larsen, R., Rykkje, J.M., and Ramm, M. 1998b. Semiautomatic supervised classification of minerals from Xray mapping images. In Proceedings of the Fourth Annual Conference of the International Association of Mathematical Geology (IAMG'98), A. Buccianti, G. Nardi, and R. Potenza (Eds.), Ischia, Italy, pp. 473–478.
 Nielsen, A.A. and Larsen, R. 1994. Restoration of GERIS data using the maximum noise fractions transform. In Proceedings from the First International Airborne Remote Sensing Conference and Exhibition, Vol. II, ERIM (Ed.), Strasbourg, France, pp. 557–568.
 Pendock, N. and Nielsen, A.A. 1993. Multispectral image enhancement neural networks and the maximum noise fraction transform. In Proceedings of the Fourth South African Workshop on Pattern Recognition, P. Cilliers (Ed.), Simon's Town, South Africa, pp. 2–13.
 Ren, H. and Chang, C.I. 2000. A targetconstrained interferenceminimized filter for subpixel detection in hyperspectral imagery. In Proceedings of the IEEE 2000 IGARSS, Honolulu, HI.
 Resmini, R.G., Kappus, M.E., Aldrich, W.S., Harsanyi, J.C., and Anderson, M. 1997. Mineral mapping with hyperspectral digital imagery collection experiment (HYDICE) sensor data at cuprite, Nevada, U.S.A. International Journal of Remote Sensing, 18(7): 1553–1570.
 Sadegh, P., Nielsen, H.A., and Madsen, H. 1999. A semiparametric approach for decomposition of absorption spectra in the presence of unknown components. Technical Report 1999–17, Department of Mathematical Modelling, Technical University of Denmark. http://www.imm.dtu.dk/documents/ftp/tr99/tr17 99.abstract.html.
 Settle, J.J. 1996. On the relationship between spectral unmixing and subspace projection. IEEE Transactions on Geoscience and Remote Sensing, 34(4):1045–1046.
 Settle, J.J. and Drake, N.A. 1993. Linear mixing and the estimation Spectral Mixture Analysis 37 of ground cover proportions. International Journal of Remote Sensing, 14(6):1159–1177.
 Stan, S.S. 1997. Mineral identification and mapping by imaging spectroscopy data analysis. Ph.D. thesis, Computational and Applied Mathematics Department, University of the Witwatersrand, Johannesburg, South Africa.
 Strobl, P., Richter, R., Müller, A., Lehmann, F., Oertel, D., Tischler, S., and Nielsen, A.A. 1996. DAIS system performance, first results from the 1995 evaluation campaigns. In Proceedings from the Second International Airborne Remote Sensing Conference and Exhibition, Vol. II, ERIM (Ed.), San Francisco, California, USA, pp. 325–334.
 Switzer, P. and Green, A.A. 1984. Min/max autocorrelation factors for multivariate spatial imagery. Technical Report 6, Department of Statistics, Stanford University.
 Tu, T.M., Chen, C.H., and Chang, C.I. 1998. A noise subspace projection approach to target signature detection and extraction in an unknown background for hyperspectral images. IEEE Transactions on Geoscience and Remote Sensing, 36(1):171–181.
 van der Meer, F. 1999. Iterative spectral unmixing. International Journal of Remote Sensing, 20(17):3431–3436.
 Vane, G. and Goetz, A.F.H. 1988. Terrestrial imaging spectroscopy. Remote Sensing of Environment, 24:1–29.
 Vane, G., Green, R.O., Chrien, T.G., Enmark, H.T., Hansen, E.G., and Porter, W.M. 1993. The airborne/infrared imaging spectrometer (AVIRIS). Remote Sensing of Environment, 44:127–143.
 Venables, W.N. and Ripley, B.D. 1999. Modern Applied Statistics with SPLUS, 3rd ed. Springer: New York.
 Title
 Spectral Mixture Analysis: Linear and Semiparametric Full and Iterated Partial Unmixing in Multi and Hyperspectral Image Data
 Journal

International Journal of Computer Vision
Volume 42, Issue 12 , pp 1737
 Cover Date
 20010401
 DOI
 10.1023/A:1011181216297
 Print ISSN
 09205691
 Online ISSN
 15731405
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 least squares regression
 spectral angle mapping (SAM)
 orthogonal subspace projection (OSP)
 matched filtering
 iterated constrained energy minimization (CEM)
 generalized eigenvalue problem
 target constrained interference minimized filter (TCIMF)
 nonlinear semiparametric unmixing (SPU)
 Industry Sectors
 Authors

 Allan Aasbjerg Nielsen ^{(1)}
 Author Affiliations

 1. IMM, Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, Richard Petersens Plads, DK2800, Kgs. Lyngby, Denmark