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Abundance Estimation of Hyperspectral Data with Low Compressive Sampling Rate

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Abstract

Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation, and I/O throughputs. In this paper, a compressive sensing framework with low sampling rate is described for hyperspectral imagery. It is based on the widely used linear spectral mixture model. Abundance fractions can be calculated directly from compressively sensed data with no need to reconstruct original hyperspectral imagery. The proposed abundance estimation model is based on the sparsity of abundance fractions and an alternating direction method of multipliers is developed to solve this model. Experiments show that the proposed scheme has a high potential to unmix compressively sensed hyperspectral data with low sampling rate.

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References

  1. Bioucas-Dias, J. M., Plaza, A., Dobigeon, N., Parente, M., Qian, D., Gader, P., et al. (2012). Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5(2), 354–379. doi:10.1109/jstars.2012.2194696.

    Article  Google Scholar 

  2. Pu, H., Xia, W., Wang, B., & Jiang, G. M. (2013). A fully constrained linear spectral unmixing algorithm based on distance geometry. IEEE Transactions on Geoscience and Remote Sensing. doi:10.1109/tgrs.2013.2248013.

    Google Scholar 

  3. Heinz, D. C., & Chein, I. C. (2001). Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery. IEEE Transactions on Geoscience and Remote Sensing, 39(3), 529–545. doi:10.1109/36.911111.

    Article  Google Scholar 

  4. Winter, M. E. N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data. In Proceedings of the 1999 imaging spectrometry, Denver, CO, USA, 1999 (Vol. 3753, pp. 266-275, Proceedings of SPIE—The International Society for Optical Engineering). Bellingham: SPIE.

  5. Nascimento, J. M. P., & Dias, J. M. B. (2005). Vertex component analysis: A fast algorithm to unmix hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 43(4), 898–910. doi:10.1109/tgrs.2005.844293.

    Article  Google Scholar 

  6. Chein, I. C., Chao-Cheng, W., Wei-min, L., & Yen-Chieh, O. (2006). A new growing method for simplex-based endmember extraction algorithm. Geoscience and Remote Sensing, IEEE Transactions on, 44(10), 2804–2819. doi:10.1109/tgrs.2006.881803.

    Article  Google Scholar 

  7. Xuetao, T., Bin, W., Liming, Z., & Jian Qiu, Z. (2007). A new scheme for decomposition of mixed pixels based on nonnegative matrix factorization. In Geoscience and remote sensing symposium, 2007. IGARSS 2007. IEEE International, 2328 July 2007 (pp. 1759–1762). doi:10.1109/igarss.2007.4423160.

  8. Li, J., & Bioucas-Dias, J. M. (2008). Minimum volume simplex analysis: A fast algorithm to unmix hyperspectral data. In Geoscience and remote sensing symposium, 2008. IGARSS 2008. IEEE international, 711 July 2008 (Vol. 3, pp. III-250–III-253). doi:10.1109/igarss.2008.4779330.

  9. Bioucas-Dias, J. M. (2009). A variable splitting augmented Lagrangian approach to linear spectral unmixing. In Hyperspectral image and signal processing: Evolution in remote sensing, 2009. WHISPERS ‘09. First Workshop on, 2628 Aug. 2009 (pp. 1–4). doi:10.1109/whispers.2009.5289072.

  10. Heylen, R., Burazerovic, D., & Scheunders, P. (2011). Fully constrained least squares spectral unmixing by simplex projection. IEEE Transactions on Geoscience and Remote Sensing, 49(11), 4112–4122. doi:10.1109/tgrs.2011.2155070.

    Article  Google Scholar 

  11. Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. In Hyperspectral image and signal processing: Evolution in remote sensing (WHISPERS), 2010 2nd Workshop on, 1416 June 2010 (pp. 1–4). doi:10.1109/whispers.2010.5594963.

  12. Kaarna, A., Zemcik, P., Kalviainen, H., et al. (2000). Compression of multispectral remote sensing images using clustering and spectral reduction. Geoscience and Remote Sensing, IEEE Transactions on, 38(2), 1073–1082. doi:10.1109/36.841986.

    Article  Google Scholar 

  13. Jing, W., & Chein, I. C. (2006). Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis. IEEE Transactions on Geoscience and Remote Sensing, 44(6), 1586–1600. doi:10.1109/tgrs.2005.863297.

    Article  Google Scholar 

  14. Feng, Y., He, M., Song, J., & Wei, J. (2007). ICA-based dimensionality reduction and compression of Hyperspectral imagery. Journal of Electronics & Information Technology, 29(12), 2871–2875.

    Google Scholar 

  15. Duarte, M. F., Sarvotham, S., Baron, D., Wakin, M. B., & Baraniuk, R. G. (2005). Distributed compressed sensing of jointly sparse signals. In The thirty-ninth Asilomar conference on signals, systems and computers, Pacific Grove, October 28November 1, 2005 (pp. 1537–1541). doi:10.1109/acssc.2005.1600024.

  16. Golbabaee, M. Multichannel compressed sensing via source separation for hyperspectral imagery. In European signal processing conference, Aalborg, Denmark, 2010 (pp. 1326–1329). Poland: EUSIPCO.

  17. Duarte, M. F., & Baraniuk, R. G. (2012). Kronecker compressive sensing. IEEE Transactions on Image Processing, 21(2), 494–504. doi:10.1109/tip.2011.2165289.

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, Z., Yan, F., & Jia, Y. (2013). Spatial-spectral compressive sensing of hyperspectral image. In Third IEEE international conference on information science and technology, Yangzhou, Jiangsu, China, 2325 March 2013 (pp. 1256-1259).

  19. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306. doi:10.1109/tit.2006.871582.

    Article  MathSciNet  MATH  Google Scholar 

  20. Xianbiao, S., & Ahuja, N. (2011). Imaging via three-dimensional compressive sampling (3DCS). In IEEE international conference on computer vision, Barcelona, 613 Nov. 2011 (pp. 439-446). Piscataway: IEEE. doi:10.1109/iccv.2011.6126273.

  21. Liguo, W., & Xiuping, J. (2009). Integration of soft and hard classifications using extended support vector machines. IEEE Geoscience and Remote Sensing Letters, 6(3), 543–547. doi:10.1109/lgrs.2009.2020924.

    Article  Google Scholar 

  22. Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Ting, S., Kelly, K. F., et al. (2008). Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 25(2), 83–91. doi:10.1109/msp.2007.914730.

    Article  Google Scholar 

  23. Marcia, R. F., & Willett, R. M. (2008). Compressive coded aperture superresolution image reconstruction. In IEEE international conference on acoustics, speech and signal processing, March 31 2008April 4 2008 (pp. 833-836). Piscataway: IEEE. doi:10.1109/icassp.2008.4517739.

  24. Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Ting, S., Kelly, K. F., et al. (2008). Single-pixel imaging via compressive sampling. Signal Processing Magazine, IEEE, 25(2), 83–91. doi:10.1109/msp.2007.914730.

    Article  Google Scholar 

  25. Golbabaee, M. Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery. In The 37th international conference on acoustics, speech, and signal processing, Kyoto, 2012 (pp. 2741–2744). Piscataway: IEEE.

  26. Candes, E. J., Wakin, M. B., & Boyd, S. P. (2008). Enhancing sparsity by reweighted L1 minimization. Journal of Fourier Analysis and Applications, 14(5–6), 877–905. doi:10.1007/s00041-008-9045-x.

    Article  MathSciNet  MATH  Google Scholar 

  27. Xu, Z., Zhang, H., Wand, Y., Chang, X., & Yong, L. (2010). L1/2 regularization. Science in China, series F, 53(06), 1159–1169.

    Google Scholar 

  28. Chartrand, R. (2009). Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data. In IEEE international symposium on biomedical imaging: From nano to macro, June 28 2009July 1 2009 (pp. 262–265). Piscataway: IEEE. doi:10.1109/isbi.2009.5193034.

  29. Xiuping, J., & Liguo, W. (2014). Fuzzy assessment of spectral unmixing algorithms. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7(6), 1947–1955. doi:10.1109/jstars.2013.2264313.

    Article  Google Scholar 

  30. August, Y., Vachman, C., Rivenson, Y., & Stern, A. (2013). Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains. Applied Optics, 52(10), 46–54. doi:10.1364/ao.52.000d46.

    Article  Google Scholar 

  31. Vane, G., Green, R. O., Chrien, T. G., Enmark, H. T., Hansen, E. G., & Porter, W. M. (1993). Airborne visible/infrared imaging spectrometer (AVIRIS). Remote Sensing of Environment, 44(2–3), 127–143. doi:10.1016/0034-4257(93)90012-m.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Key Projects of Natural Science Research of Universities of Anhui Province under Grant KJ2016A884, Quality Engineering Project of Universities of Anhui Province under Grant 2016zy126 and the National Natural Science Foundation of China under Grant 61071171.

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Correspondence to Yan Feng.

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This article is part of the Topical Collection on Hyperspectral Imaging and Image Processing.

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Wang, Z., Feng, Y. Abundance Estimation of Hyperspectral Data with Low Compressive Sampling Rate. Sens Imaging 18, 23 (2017). https://doi.org/10.1007/s11220-017-0168-5

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