Abstract
Hyperspectral unmixing, as a blind source separation (BSS) problem, has been intensively studied from independence aspect in the last few years. However, independent component analysis (ICA) can not totally unmix all the materials out because the sources (abundance fractions) are not statistically independent. In this paper a complexity constrained nonnegative matrix factorization (CCNMF) for simultaneously recovering both constituent spectra and correspondent abundances is proposed. Three important facts are exploited: First, the spectral data are nonnegative; second, the variation of the material spectra and abundance images is smooth in time and space respectively; third, in most cases, both of the material spectra and abundances are localized. Experimentations on real data are provided to illustrate the algorithm’s performance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Keshava, N., Mustard, J.F.: Spectral unmixing. IEEE Signal Processing Mag. 19(3), 44–57 (2002)
Keshava, N.: A survey of spectral unmixing algorithms. Lincoln Lab. J. 14(1), 55–73 (2003)
Parra, L., Spence, C., Sajda, P., Ziehe, A., Müller, K.R.: Unmixing hyperspectral data. In: Adv. Neural Inform. Process. Syst. 12, Denver, Colorado, USA, pp. 942–948. MIT Press, Cambridge (1999)
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons, Chichester (2002)
Chiang, S.-S., Chang, C.-I., Smith, J.A., Ginsberg, I.W.: Linear spectral random mixture analysis for hyperspectral imagery. IEEE Trans. Geosci. Remote Sensing 40(2), 375–392 (2002)
Chang, C.-I: Hyperspectral Imaging: Techniques for Spectral Detection and Classification. Kluwer Academic/Plenum Publishers, New York (2003)
Nascimento, J.M.P., Dias, J.M.B.: Does independent component analysis play a role in unmixing hyperspectral data? IEEE Trans. Geosci. Remote Sensing 43(1), 175–187 (2005)
Stone, J.V.: Blind source separation using temporal predictability. Neural Comput. 13(7), 1559–1574 (2001)
Jia, S., Qian, Y.T.: Spectral and spatial complexity based hyperspectral unmixing. IEEE Trans. Geosci. Remote Sensing (to appear)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. Adv. Neural Inform. Process. Syst. 13, 556–562 (2000)
Paura, V.P., Piper, J., Plemmons, R.J.: Nonnegative matrix factorization for spectral data analysis. Linear Algebra and Applications 416(1), 29–47 (2006)
Miao, L.D., Qi, H.R.: Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sensing 45(3), 765–777 (2007)
Ferrara, C.F.: Adaptive spatial/spectral detection of subpixel targets with unknown spectral characteristics. In: Proc. SPIE, vol. 2235, pp. 82–93 (1994)
Green, P.J.: Bayesian reconstructions from emission tomography data using a modified em algorithm. IEEE Trans. Med. Imag. 9(1), 84–93 (1990)
Montano, A.P., Carazo, J.M., Kochi, K., Lehmann, D., P.-Marqui, R.D.: Nonsmooth nonnegative matrix factorization (nsNMF). IEEE Trans. Pattern Anal. Machine Intell. 28(3), 403–415 (2006)
Chang, C.-I, Du, Q.: Estimation of number of spectrally distinct signal sources in hyperspectral imagery. IEEE Trans. Geosci. Remote Sensing 42(3), 608–619 (2004)
Plaza, A., Martinez, P., Perez, R., Plaza, J.: A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data. IEEE Trans. Geosci. Remote Sensing 42(3), 650–663 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jia, S., Qian, Y. (2007). A Complexity Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-74494-8_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74493-1
Online ISBN: 978-3-540-74494-8
eBook Packages: Computer ScienceComputer Science (R0)