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Sparse and low-rank abundance estimation with internal variability

  • role： First author第一作者
  • Affiliation：

    Department of Electrical and Engineering, Tsinghua University, Beijing 100084, China

    Institute of Disaster Prevertion, Langfang 065201, China

  • Email：yuanjing20110824@sina.com
  • Introduction：袁静，1981年生，女，博士研究生，研究方向为高光谱解混。E-mail：yuanjing20110824@sina.com
YUAN Jing12,  
  • Affiliation：

    Department of Electrical and Engineering, Tsinghua University, Beijing 100084, China

ZHANG Yujin1

résumé

Abundance estimation (AE) plays an important role in the processing and analysis of hyperspectral images. Constrained linear regression is usually developed to estimate abundance matrix due to its simplicity and mathematical tractability. However, this approach only focuses on the fitness between the estimated and ground-truth data without considering the internal variability such as the similarity among the first-order gradients and among the second-order gradients. To improve the accuracy of the AE, a novel method of adding internal variability to sparse low-rank AE was proposed. First, first- and second-order gradient constraint terms were used to modify the traditional mathematical model of sparse and low-rank AE. Second, norm inequality and optimization theory were applied to demonstrate the validity of the novel model. The model has been proven applicable to other related fields under constraint conditions. Third, auxiliary variables were utilized to transform the mathematic model to the enhanced Lagrange function (ELF). Finally, the ELF was solved by the alternating direction method of multipliers to estimate the abundance of hyperspectral images. In general, the traditional method of sparse and low-rank AE is the alternating direction sparse and low-rank unmixing (ADSpLRU). In this study, ADSpLRU-FOG refers to the method that adds the first-order gradient to the sparse and low-rank AE, whereas ADSpLRU-FSOG refers to the method that adds first- and second-order gradients to the sparse and low-rank AE. Experiment carried on the USUG library showed that, (1) in the convergent experiment, ADSpLRU-FOG and ADSpLRU-FSOG algorithms converged to a slightly lower NMSE than ADSpLRU. ADSpLRU-FSOG algorithm converged to the lowest NMSE among the three methods. (2) In the robust experiment, ADSpLRU-FOG and ADSpLRU-FSOG algorithms reached higher estimation accuracy than ADSpLRU in terms of SRE under white and colored noises. Among them, ADSpLRU-FSOG achieved remarkably higher SRE value than the other methods. (3) In the visual experiment, ADSpLRU-FOG algorithm could maintain the first-order gradient structure of the data more than ADSpLRU. Meanwhile, the ADSpLRU-FSOG algorithm could preserve the second-order gradient structure of the data better than ADSpLRU-FOG and ADSpLRU algorithms. Experiment based on the Urban and Jasper actual hyperspectral database showed that the accuracy of abundance matrix estimation from ADSpLRU-FSOG was better than those from ADSpLRU and ADSpLRU-FOG. Experimental results suggest that the novel method of adding the internal variability to the abundance matrix estimation can improve convergent behavior, maintain the structure of information of first-order and second-order gradients, obtain comparable estimation accuracy, and enhance robust performance for AE.

mots-clés

abundance estimation;CLR;internal variability;sparse and low-rank;ADMM

References

  1. 1.
    Babacan S D, Luessi M, Molina R and Katsaggelos A K. 2012. Sparse Bayesian methods for low-rank matrix estimation. IEEE Transactions on Signal Processing, 60(8): 3964–3977
  2. 2.
    Bach F R. 2008. Consistency of trace norm minimization. The Journal of Machine Learning Research, 9: 1019–1048
  3. 3.
    Bioucas-Dias J M, Plaza A, Dobigeon N, Parente M, Du Q, Gader P and Chanussot J. 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
  4. 4.
    Boyd S, Parikh N, Chu E, Peleato B and Eckstein J. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine Learning, 3(1): 1–122
  5. 5.
    Candès E J, Romberg J and Tao T. 2006. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2): 489–509
  6. 6.
    Chen F and Zhang Y. 2013. Sparse hyperspectral unmixing based on constrained L p-L 2 optimization. IEEE Geoscience and Remote Sensing Letters, 10(5): 1142–1146
  7. 7.
    Chen L S and Huang J Z. 2012. Sparse reduced-rank regression for simultaneous dimension reduction and variable selection. Journal of the American Statistical Association, 107(500): 1533–1545
  8. 8.
    Clark R N, Swayze G A, Wise R, Livo E, Hoefen T, Kokaly R F and Sutley S J. 2007. USGS digital spectral library splib06a. Reston, VA: U. S. Geological Survey
  9. 9.
    Feng R Y, Zhong Y F and Zhang L P. 2016. Adaptive spatial regularization sparse unmixing strategy based on joint MAP for hyperspectral remote sensing imagery. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9(12): 5791–5805
  10. 10.
    Giampouras P V, Themelis K E, Rontogiannis A A and Koutroumbas K D. 2016. Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing. IEEE Transactions on Geoscience and Remote Sensing, 54(8): 4775–4789
  11. 11.
    Golbabaee M and Vandergheynst P. 2012. Compressed sensing of simultaneous low-rank and joint-sparse matrices. eprint arXiv: 1211. 5058
  12. 12.
    Iordache M D, Bioucas-Dias J M and Plaza A. 2011. Sparse unmixing of hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 49(6): 2014–2039
  13. 13.
    Iordache M D, Bioucas-Dias J M and Plaza A. 2012. Total variation spatial regularization for sparse hyperspectral unmixing. IEEE Transactions on Geoscience and Remote Sensing, 50(11): 4484–4502
  14. 14.
    Iordache M D, Bioucas-Dias J M and Plaza A. 2014. Collaborative sparse regression for hyperspectral unmixing. IEEE Transactions on Geoscience and Remote Sensing, 52(1): 341–354
  15. 15.
    Lu T X. 1986. Solution of the matrix equation AX-XB = C. Computing, 37(4): 351–355
  16. 16.
    Negahban S and Wainwright M J. 2011. Estimation of (near) low-rank matrices with noise and high-dimensional scaling. The Annals of Statistics, 39(2): 1069–1097
  17. 17.
    Oymak S, Jalali A, Fazel M, Eldar Y C and Hassibi B. 2015. Simultaneously structured models with application to sparse and low-rank matrices. IEEE Transactions on Information Theory, 61(5): 2886–2908
  18. 18.
    Qian Y T, Jia S, Zhou J and Robles-Kelly A. 2011. Hyperspectral unmixing via L1/2 sparsity-constrained nonnegative matrix factorization. IEEE Transactions on Geoscience and Remote Sensing, 49(11): 4282–4297
  19. 19.
    Qu Q, Nasrabadi N M and Tran T D. 2014. Abundance estimation for bilinear mixture models via joint sparse and low-rank representation. IEEE Transactions on Geoscience and Remote Sensing, 52(7): 4404–4423
  20. 20.
    Richard E, Obozinski G and Vert J P. 2014. Tight convex relaxations for sparse matrix factorization//Advances in Neural Information Processing Systems 27. Montreal, Canada: Curran Associates, Inc.: 3284-3292
  21. 21.
    Richard E, Savalle P A and Vayatis N. 2012. Estimation of simultaneously sparse and low rank matrices//Proceedings of the 29th International Conference on International Conference on Machine Learning. Edinburgh, Scotland: ACM: 51-58
  22. 22.
    Rontogiannis A A, Themelis K, Sykioti O and Koutroumbas K. 2013. A fast variational Bayes algorithm for sparse semi-supervised unmixing of OMEGA/Mars Express data//2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing. Gainesville, FL, USA: IEEE: 1-4 [DOI: 10.1109/WHISPERS.2013.8080749]
  23. 23.
    Rosin P L. 2001. Robust pixel unmixing. IEEE Transactions on Geoscience and Remote Sensing, 39(9): 1978–1983
  24. 24.
    Sigurdsson J, Ulfarsson M O and Sveinsson J R. 2014. Hyperspectral unmixing with Lq regularization. IEEE Transactions on Geoscience and Remote Sensing, 52(11): 6793–6806
  25. 25.
    Sun L, Jeon B, Zheng Y H and Chen Y J. 2016. Hyperspectral unmixing based on L1-L2 sparsity and total variation//2016 IEEE International Conference on Image Processing. Phoenix, AZ, USA: IEEE: 4349-4353 [DOI: 10.1109/lelP.2016.7533181]
  26. 26.
    Tang W, Shi Z W and Duren Z. 2014. Sparse hyperspectral unmixing using an approximate L0 norm. Optik, 125(1): 31–38
  27. 27.
    Themelis K E, Rontogiannis A A and Koutroumbas K. 2010. Semi-supervised hyperspectral unmixing via the weighted lasso//IEEE International Conference on Acoustics, Speech, and Signal Processing. Dallas, Texas, USA: IEEE: 1194–1197
  28. 28.
    Themelis K E, Rontogiannis A A and Koutroumbas K D. 2012. A novel hierarchical Bayesian approach for sparse semisupervised hyperspectral unmixing. IEEE Transactions on Signal Processing, 60(2): 585–599
  29. 29.
    Yang J X, Zhao Y Q, Chan J C W and Kong S G. 2016. Coupled sparse denoising and unmixing with low-rank constraint for hyperspectral image. IEEE Transactions on Geoscience and Remote Sensing, 54(3): 1818–1833
  30. 30.
    Yi C, Zhao Y Q, Yang J X, Chan J C W and Kong S G. 2017. Joint hyperspectral superresolution and unmixing with interactive feedback. IEEE Transactions on Geoscience and Remote Sensing, 55(7): 3823–3834
  31. 31.
    Yuan J and Zhang Y J. 2017. Application of sparse denoising auto encoder network with gradient difference information for abnormal action detection. Acta Automatica Sinica, 43(4): 604–610
  32. 32.
    Yuan J, Zhang Y J and Yang D H. 2018. Sparse and low-rank abundance estimation with structural information. Journal of Infrared and Millimeter Waves, 37(2): 144–153
  33. 33.
    Zhang X D. 2013. Matrix Analysis and Applications. 2nd ed. Beijing: Tsinghua University Press: 44
  34. 34.
    Zhu F Y, Wang Y, Fan B, Xiang S M, Meng G F and Pan C H. 2014a. Spectral unmixing via data-guided sparsity. IEEE Transactions on Image Processing, 23(12): 5412–5427
  35. 35.
    Zhu F Y, Wang Y, Fan B, Meng G F and Pan C H. 2014b. Effective spectral unmixing via robust representation and learning-based sparsity. eprint arXiv: 1409. 0685

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