Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization

ABSTRACT

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

KEYWORDS

Hyperspectral Image; Spectral Unmixing; Area-Correlation; Bayesian Nonnegative Matrix Factorization

Hyperspectral Image; Spectral Unmixing; Area-Correlation; Bayesian Nonnegative Matrix Factorization

Cite this paper

X. Chen, J. Yu and W. Sun, "Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization,"*Open Journal of Applied Sciences*, Vol. 3 No. 1, 2013, pp. 41-46. doi: 10.4236/ojapps.2013.31B009.

X. Chen, J. Yu and W. Sun, "Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization,"

References

[1] N. Keshava and J. F. Mustard, “Spectral Unmixing,” Signal Processing Magazine, IEEE, 2002. 19(1): p. 44-57. doi:10.1109/79.974727

[2] J. Nascimento and J. Dias, “Vertex Component Analysis: A Fast Algorithm to???? Unmix Hyperspectral Data,” IEEE Transactions on Geoscience and Remote Sensing, 2005. 43(4): p. 898-910. doi:10.1109/TGRS.2005.844293

[3] J. W. Boardman, F. A. Kruse and R. O. Green, “Mapping Target Signatures via Partial Unmixing of AVIRIS Da-ta,” 1995: Pasadena, CA.

[4] M. E. Winter, “N-FINDR: An Algorithm for Fast Autonomous Spectral End-member Determination in Hyperspectral Data,” Proceedings of SPIE, 1999. p. 266-275. doi:10.1117/12.366289

[5] L. Sun, Y. Zhang and B. Guindon, “Improved Iterative Error Analysis for Endmember Extraction from Hyperspectral Imagery,” Proceedings of SPIE, 2008. doi:10.1117/12.799232

[6] D. D. Lee and H. S. Seung, “Algorithms for Non-negative Matrix Factorization,” Advances in Neural Information Processing Systems, 2001: p. 556-562.

[7] V. P. Pauca, J. Piper and R. J. Plemmons, “Nonnegative Matrix Fac-torization for Spectral Data Analysis,” Linear Algebra and Its Applications, 2006. 416(1SI): p. 29-47. doi:10.1016/j.laa.2005.06.025

[8] A. Plaza, P. Martinez, R. Perez and J. Plaza, “Spatial/spectral Endmember Extrac-tion by Multidimensional morphological Operations,” IEEE Transactions on Geoscience and Remote Sensing, 2002. 40(9): p. 2025- 2041. doi:10.1109/TGRS.2002.802494

[9] M. Zortea and A. Plaza, “Spatial Preprocessing for Endmember Extrac-tion,” IEEE Transactions on Geoscience and Remote Sensing, 2009. 47(8): p. 2679-2693. doi:10.1109/TGRS.2009.2014945

[10] B. Zhang, “Hyper-spectral Data Mining Supported by Temporal and Spatial Information,” PH.D. Thesis, Institute of Remote Sensing Applications, Chinese Academy of Sciences, 2002.

[11] N. Dobigeon, J. Y. Tourneret and C. Chein-I, “Semi-supervised Linear Spectral Unmixing Using a Hierarchical Bayesian Model for Hyperspectral Im-agery,” IEEE Transactions on Signal Processing, 2008. 56(7): p. 2684-2695. doi:10.1109/TSP.2008.917851

[12] M. N. Schmidt, “Linearly Constrained Bayesian Matrix Factorization for Blind Source Separation,” Advances in Neural Information Processing Systems, 2009.22: p. 1624-1632.

[13] M. N. Schmidt, O. Winther and L. K. Hansen, “Bayesian Non-negative Matrix Factorization,” Independent Component Analysis and Signal Separation, 2009. p. 540-547.

[14] G. Casella and E. I. George, “Explaining The Gibbs Sampler,” American Statistician, 1992. 46(3): p. 167-174. doi:10.1080/00031305.1992.10475878

[15] R. M. Neal, “Slice Sampling,” Annals of Statistics, 2003. 31(3): p. 705-767. doi:10.1214/aos/1056562461

[16] M. Arngren, M. N. Schmidt and J. Larsen, “Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images,” Proceedings of the 2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2009), 2009: p. 6 pp.-6 pp. doi:10.1109/MLSP.2009.5306262

[17] C. I. Chang and Q. Du, “Estimation of Number of Spectrally Distinct Signal Sources in Hyperspectral Imagery,” IEEE Transactions on Geoscience and Remote Sensing, 2004. 42(3): p. 608-619. doi:10.1109/TGRS.2003.819189

[18] J. M. Bio-ucas-Dias and J. M. P. Nascimento, “Hyperspectral Sub-space Identification,” IEEE Transactions on Geoscience and Remote Sensing, 2008. 46(8): p. 2435-2445. doi:10.1109/TGRS.2008.918089

[1] N. Keshava and J. F. Mustard, “Spectral Unmixing,” Signal Processing Magazine, IEEE, 2002. 19(1): p. 44-57. doi:10.1109/79.974727

[2] J. Nascimento and J. Dias, “Vertex Component Analysis: A Fast Algorithm to???? Unmix Hyperspectral Data,” IEEE Transactions on Geoscience and Remote Sensing, 2005. 43(4): p. 898-910. doi:10.1109/TGRS.2005.844293

[3] J. W. Boardman, F. A. Kruse and R. O. Green, “Mapping Target Signatures via Partial Unmixing of AVIRIS Da-ta,” 1995: Pasadena, CA.

[4] M. E. Winter, “N-FINDR: An Algorithm for Fast Autonomous Spectral End-member Determination in Hyperspectral Data,” Proceedings of SPIE, 1999. p. 266-275. doi:10.1117/12.366289

[5] L. Sun, Y. Zhang and B. Guindon, “Improved Iterative Error Analysis for Endmember Extraction from Hyperspectral Imagery,” Proceedings of SPIE, 2008. doi:10.1117/12.799232

[6] D. D. Lee and H. S. Seung, “Algorithms for Non-negative Matrix Factorization,” Advances in Neural Information Processing Systems, 2001: p. 556-562.

[7] V. P. Pauca, J. Piper and R. J. Plemmons, “Nonnegative Matrix Fac-torization for Spectral Data Analysis,” Linear Algebra and Its Applications, 2006. 416(1SI): p. 29-47. doi:10.1016/j.laa.2005.06.025

[8] A. Plaza, P. Martinez, R. Perez and J. Plaza, “Spatial/spectral Endmember Extrac-tion by Multidimensional morphological Operations,” IEEE Transactions on Geoscience and Remote Sensing, 2002. 40(9): p. 2025- 2041. doi:10.1109/TGRS.2002.802494

[9] M. Zortea and A. Plaza, “Spatial Preprocessing for Endmember Extrac-tion,” IEEE Transactions on Geoscience and Remote Sensing, 2009. 47(8): p. 2679-2693. doi:10.1109/TGRS.2009.2014945

[10] B. Zhang, “Hyper-spectral Data Mining Supported by Temporal and Spatial Information,” PH.D. Thesis, Institute of Remote Sensing Applications, Chinese Academy of Sciences, 2002.

[11] N. Dobigeon, J. Y. Tourneret and C. Chein-I, “Semi-supervised Linear Spectral Unmixing Using a Hierarchical Bayesian Model for Hyperspectral Im-agery,” IEEE Transactions on Signal Processing, 2008. 56(7): p. 2684-2695. doi:10.1109/TSP.2008.917851

[12] M. N. Schmidt, “Linearly Constrained Bayesian Matrix Factorization for Blind Source Separation,” Advances in Neural Information Processing Systems, 2009.22: p. 1624-1632.

[13] M. N. Schmidt, O. Winther and L. K. Hansen, “Bayesian Non-negative Matrix Factorization,” Independent Component Analysis and Signal Separation, 2009. p. 540-547.

[14] G. Casella and E. I. George, “Explaining The Gibbs Sampler,” American Statistician, 1992. 46(3): p. 167-174. doi:10.1080/00031305.1992.10475878

[15] R. M. Neal, “Slice Sampling,” Annals of Statistics, 2003. 31(3): p. 705-767. doi:10.1214/aos/1056562461

[16] M. Arngren, M. N. Schmidt and J. Larsen, “Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images,” Proceedings of the 2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2009), 2009: p. 6 pp.-6 pp. doi:10.1109/MLSP.2009.5306262

[17] C. I. Chang and Q. Du, “Estimation of Number of Spectrally Distinct Signal Sources in Hyperspectral Imagery,” IEEE Transactions on Geoscience and Remote Sensing, 2004. 42(3): p. 608-619. doi:10.1109/TGRS.2003.819189

[18] J. M. Bio-ucas-Dias and J. M. P. Nascimento, “Hyperspectral Sub-space Identification,” IEEE Transactions on Geoscience and Remote Sensing, 2008. 46(8): p. 2435-2445. doi:10.1109/TGRS.2008.918089