Total variation spatial regularization for sparse hyperspectral unmixing

IEEE Transactions on Geoscience and Remote Sensing

Volumn 50, Issue 11 PART1, 2012, Pages 4484-4502

  Iordache, Marian Daniel ^a   Bioucas Dias, José M ^b   Plaza, Antonio ^c  

^a FLEMISH INSTITUTE FOR TECHNOLOGICAL RESEARCH VITO   (Belgium)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^c UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

Hyperspectral imaging; sparse regression; sparse unmixing; spectral unmixing; total variation (TV) regularization

Indexed keywords

REGRESSION ANALYSIS; REMOTE SENSING;

HYPERSPECTRAL IMAGING; SPARSE REGRESSION; SPECTRAL UNMIXING; TOTAL VARIATION REGULARIZATION; UNMIXING;

SPECTROSCOPY;

ALGORITHM; DATA SET; EXPERIMENTAL STUDY; IMAGE ANALYSIS; IMAGERY; PIXEL; REGRESSION ANALYSIS; REMOTE SENSING; SPATIAL ANALYSIS;

EID: 84869498082     PISSN: 01962892     EISSN: None     Source Type: Journal    
DOI: 10.1109/TGRS.2012.2191590     Document Type: Article

References (70)

1. J. Adams, M. Smith, and P. Johnson, "Spectral mixture modeling: A new analysis of rock and soil types at the Viking Lander 1 site," J. Geophys. Res., vol. 91, pp. 8098-8112, Jul. 1986.
2. J. Settle and N. Drake, "Linear mixing and the estimation of ground cover proportions," Int. J. Remote Sens., vol. 14, no. 6, pp. 1159-1177, Apr. 1993. (Pubitemid 23384230)
3. A. Plaza, P. Martinez, R. Perez, and J. Plaza, "A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 42, no. 3, pp. 650-663, Mar. 2004.
4. Q. Du, N. Raksuntorn, N. Younan, and R. King, "End-member extraction for hyperspectral image analysis," Appl. Opt., vol. 47, no. 28, pp. 77-84, Jul. 2008.
5. D. Heinz and C.-I. Chang, "Fully constrained least squares linear mixture analysis for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens., vol. 39, no. 3, pp. 529-545, Mar. 2001. (Pubitemid 32400422)
6. C.-I. Chang and D. Heinz, "Constrained subpixel target detection for remotely sensed imagery," IEEE Trans. Geosci. Remote Sens., vol. 38, no. 3, pp. 1144-1159, May 2000.
7. C.-I. Chang, Hyperspectral Imaging: Techniques for Spectral Detection and Classification. New York: Kluwer/Plenum, 2003.
8. C. Borel and S. Gerstl, "Nonlinear spectral mixing model for vegetative and soil surfaces," Remote Sens. Environ., vol. 47, no. 3, pp. 403-416, Mar. 1994.
9. W. Liu and E. Wu, "Comparison of non-linear mixture models," Remote Sens. Environ., vol. 18, pp. 1976-2003, 2004.
10. N. Raksuntorn and Q. Du, "Nonlinear spectral mixture analysis for hyperspectral imagery in an unknown environment," IEEE Geosci. Remote Sens. Lett., vol. 7, no. 4, pp. 836-840, Oct. 2010.
11. A. Plaza, G. Martin, J. Plaza, M. Zortea, and S. Sanchez, "Recent developments in spectral unmixing and endmember extraction," in Optical Remote Sensing, S. Prasad, L. M. Bruce, and J. Chanussot, Eds. Berlin, Germany: Springer-Verlag, 2011, ch. 12, pp. 235-267.
12. J. Harsanyi and C.-I. Chang, "Hyperspectral image classification and dimensionality reduction: An orthogonal subspace projection," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 4, pp. 779-785, Jul. 1994.
13. J. Boardman, F. Kruse, and R. Green, "Mapping target signatures via partial unmixing of AVIRIS data," in Proc. JPL Airborne Earth Sci. Workshop, 1995, pp. 23-26.
14. J. Bowles, P. Palmadesso, J. Antoniades, M. Baumback, and L. Rickard, "Use of filter vectors in hyperspectral data analysis," in Proc. SPIE Infrared Spaceborne Remote Sens. III, 1995, vol. 2553, pp. 148-157.
15. R. Neville, K. Staenz, T. Szeredi, J. Lefebvre, and P. Hauff, "Automatic endmember extraction from hyperspectral data for mineral exploration," in Proc. 21st Can. Symp. Remote Sens., 1999, pp. 21-24.
16. A. Ifarraguerri and C.-I. Chang, "Multispectral and hyperspectral image analysis with convex cones," IEEE Trans. Geosci. Remote Sens., vol. 37, no. 2, pp. 756-770, Mar. 1999.
17. M. Winter, "N-FINDR: An algorithm for fast autonomous spectral endmember determination in hyperspectral data," in Proc. SPIE, 1999, vol. 3753, pp. 266-277.
18. Q. Du, H. Ren, and C.-I. Chang, "A comparative study for orthogonal subspace projection and constrained energy minimization," IEEE Trans. Geosci. Remote Sens., vol. 41, no. 6, pp. 1525-1529, Jun. 2003.
19. M. Berman, H. Kiiveri, R. Lagerstrom, A. Ernst, R. Dunne, and J. Huntington, "ICE: A statistical approach to identifying endmembers in hyperspectral images," IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, pp. 2085-2095, Oct. 2004.
20. J. Nascimento and J. Bioucas-Dias, "Vertex component analysis: A fast algorithm to unmix hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 43, no. 4, pp. 898-910, Apr. 2005. (Pubitemid 40476033)
21. A. Plaza and C.-I. Chang, "Impact of initialization on design of endmember extraction algorithms," IEEE Trans. Geosci. Remote Sens., vol. 44, no. 11, pp. 3397-3407, Nov. 2006. (Pubitemid 44711681)
22. C.-I. Chang and A. Plaza, "A fast iterative algorithm for implementation of pixel purity index," IEEE Geosci. Remote Sens. Lett., vol. 3, no. 1, pp. 63-67, Jan. 2006. (Pubitemid 43131898)
23. D. Rogge, B. Rivard, J. Zhang, and J. Feng, "Iterative spectral unmixing for optimizing per-pixel endmember sets," IEEE Trans. Geosci. Remote Sens., vol. 44, no. 12, pp. 3725-3736, Dec. 2006.
24. J. Wang and C.-I. Chang, "Applications of independent component analysis in endmember extraction and abundance quantification for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens., vol. 44, no. 9, pp. 2601-2616, Sep. 2006. (Pubitemid 44321553)
25. C.-I. Chang, C.-C. Wu, W. Liu, and Y.-C. Ouyang, "A new growing method for simplex-based endmember extraction algorithm," IEEE Trans. Geosci. Remote Sens., vol. 44, no. 10, pp. 2804-2819, Oct. 2006.
26. A. Zare and P. Gader, "Sparsity promoting iterated constrained endmember detection for hyperspectral imagery," IEEE Geosci. Remote Sens. Lett., vol. 4, no. 3, pp. 446-450, Jul. 2007. (Pubitemid 47117457)
27. A. Zare and P. Gader, "Hyperspectral band selection and endmember detection using sparsity promoting priors," IEEE Geosci. Remote Sens. Lett., vol. 5, no. 2, pp. 256-260, Apr. 2008.
28. M. Zortea and A. Plaza, "A quantitative and comparative analysis of different implementations of N-FINDR: A fast endmember extraction algorithm," IEEE Geosci. Remote Sens. Lett., vol. 6, no. 4, pp. 787-791, Oct. 2009.
29. X. Tao, B. Wang, and L. Zhang, "Orthogonal bases approach for the decomposition of mixed pixels in hyperspectral imagery," IEEE Geosci. Remote Sens. Lett., vol. 6, no. 2, pp. 219-223, Apr. 2009.
30. A. Zare and P. Gader, "PCE: Piecewise convex endmember detection," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 6, pp. 2620-2632, Jun. 2010.
31. C.-I. Chang, C.-C. Wu, C.-S. Lo, and M.-L. Chang, "Real-time simplex growing algorithms for hyperspectral endmember extraction," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 4, pp. 1834-1850, Apr. 2010.
32. F. Schmidt, A. Schmidt, E. Treandguier, M. Guiheneuf, S. Moussaoui, and N. Dobigeon, "Implementation strategies for hyperspectral unmixing using Bayesian source separation," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 11, pp. 4003-4013, Nov. 2010.
33. O. Duran and M. Petrou, "Robust endmember extraction in the presence of anomalies," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 6, pp. 1986-1996, Jun. 2011.
34. B. Zhang, X. Sun, L. Gao, and L. Yang, "Endmember extraction of hyperspectral remote sensing images based on the ant colony optimization (ACO) algorithm," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 7, pp. 2635-2646, Jul. 2011.
35. M. Shoshany, F. Kizel, N. Netanyahu, N. Goldshlager, T. Jarmer, and G. Even-Tzur, "An iterative search in end-member fraction space for spectral unmixing," IEEE Geosci. Remote Sens. Lett., vol. 8, no. 4, pp. 706-709, Jul. 2011.
36. C.-I. Chang, C.-C. Wu, and H.-M. Chen, "Random pixel purity index," IEEE Geosci. Remote Sens. Lett., vol. 7, no. 2, pp. 324-328, Apr. 2010.
37. S. Dowler and M. And rews, "On the convergence of N-FINDR and related algorithms: To iterate or not to iterate?" IEEE Geosci. Remote Sens. Lett., vol. 8, no. 1, pp. 4-8, Jan. 2011.
38. M. Craig, "Minimum-volume transforms for remotely sensed data," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 3, pp. 542-552, May 1994.
39. L. Miao and H. Qi, "Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization," IEEE Trans. Geosci. Remote Sens., vol. 45, no. 3, pp. 765-777, Mar. 2007. (Pubitemid 46375748)
40. J. Li and J. Bioucas-Dias, "Minimum volume simplex analysis: A fast algorithm to unmix hyperspectral data," in Proc. IEEE Int. Geosci. Remote Sens. Symp., 2008, vol. 3, pp. 250-253.
41. T.-H. Chan, C.-Y. Chi, Y.-M. Huang, and W.-K. Ma, "A convex analysisbased minimum-volume enclosing simplex algorithm for hyperspectral unmixing," IEEE Trans. Signal Process., vol. 57, no. 11, pp. 4418-4432, Nov. 2009.
42. J. Bioucas-Dias and J. Nascimento, "Hyperspectral unmixing based on mixtures of Dirichlet components," IEEE Trans. Geosci. Remote Sens., vol. 50, no. 3, pp. 863-878, Mar. 2012.
43. X. Chen, J. Chen, X. Jia, B. Somers, J. Wu, and P. Coppin, "A quantitative analysis of virtual endmembers' increased impact on the collinearity effect in spectral unmixing," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 8, pp. 2945-2956, Aug. 2011.
44. D. Iordache, J. Bioucas-Dias, and A. Plaza, "Sparse unmixing of hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 6, pp. 2014-2039, Jun. 2011.
45. J. Bioucas-Dias and M. Figueiredo, "Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing," in Proc. 2nd Workshop Hyperspectr. Image Signal Process.-Evol. Remote Sens., 2010, vol. 1, pp. 1-4.
46. J. Eckstein and D. Bertsekas, "On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators," Math. Program. Ser. A/B, vol. 55, no. 3, pp. 293-318, Jun. 1992.
47. M. Afonso, J. Bioucas-Dias, and M. Figueiredo, "A fast algorithm for the constrained formulation of compressive image reconstruction and other linear inverse problems," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2010, vol. 1, pp. 4034-4037.
48. M. Figueiredo, J. Bioucas-Dias, and M. Afonso, "Fast frame-based image deconvolution using variable splitting and constrained optimization," in Proc. IEEE Workshop Stat. Signal Process., 2009, vol. 1, pp. 109-112.
49. A. Castrodad, Z. Xing, J. Greer, E. Bosch, L. Carin, and G. Sapiro, "Learning discriminative sparse representations for modeling, source separation, and mapping of hyperspectral imagery," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 11, pp. 4263-4281, Nov. 2011.
50. A. Charles, B. Olshausen, and C. Rozell, "Learning sparse codes for hyperspectral imagery," IEEE J. Sel. Topics Signal Process., vol. 5, no. 5, pp. 963-978, Sep. 2011.
51. Y. Qian, S. Jia, J. Zhou, and A. Robles-Kelly, "Hyperspectral unmixing via L1/2 sparsity-constrained nonnegative matrix factorization," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 11, pp. 4282-4297, Nov. 2011.
52. A. Huck, M. Guillaume, and J. Blanc-Talon, "Minimum dispersion constrained nonnegative matrix factorization to unmix hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 6, pp. 2590-2602, Jun. 2010.
53. X. Liu, W. Xia, B. Wang, and L. Zhang, "An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 2, pp. 757-772, Feb. 2011.
54. M. Zortea and A. Plaza, "Spatial preprocessing for endmember extraction," IEEE Trans. Geosci. Remote Sens., vol. 47, no. 8, pp. 2679-2693, Aug. 2009.
55. A. Plaza, P. Martinez, R. Perez, and J. Plaza, "Spatial/spectral endmember extraction by multidimensional morphological operations," IEEE Trans. Geosci. Remote Sens., vol. 40, no. 9, pp. 2025-2041, Sep. 2002. (Pubitemid 35458399)
56. D. Rogge, B. Rivard, J. Zhang, A. Sanchez, J. Harris, and J. Feng, "Integration of spatial-spectral information for the improved extraction of endmembers," Remote Sens. Environ., vol. 110, no. 3, pp. 287-303, Oct. 2007. (Pubitemid 47285207)
57. A. Bruckstein, M. Elad, and M. Zibulevsky, "On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 4813-4820, Nov. 2008.
58. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
59. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, Nonlinear Phenom., vol. 60, no. 1-4, pp. 259-268, Nov. 1992.
60. Z. Guo, T. Wittman, and S. Osher, "L1 unmixing and its application to hyperspectral image enhancement," in Proc. SPIE Conf. Algorithms Technol. Multispectr., Hyperspectr., Ultraspectr. Imagery XV, Orlando, FL, 2009, vol. 7334, pp. 73 341-73 449.
61. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol. 20, no. 1/2, pp. 89-97, Jan.-Mar. 2004.
62. M. Afonso, J. Bioucas-Dias, and M. Figueiredo, "An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems," IEEE Trans. Image Process., vol. 20, no. 3, pp. 681-695, Mar. 2011.
63. A. Zymnis, S. Kim, J. Skaf, M. Parente, and S. Boyd, "Hyperspectral image unmixing via alternating projected subgradients," in Proc. Asilomar Conf. Signals, Syst., Comput., Nov. 2007, pp. 1164-1168.
64. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., vol. 43, no. 1, pp. 129-159, Jan. 2001. (Pubitemid 32406896)
65. E. Esser, "Applications of Lagrangian-based alternating direction methods and connections to Split-Bregman," Univ. California, Berkeley, CA, Tech. Rep. 09-31, 2009.
66. B. He and S. Wang, "Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities," J. Optim. Theory Appl., vol. 106, no. 2, pp. 337-356, Aug. 2000.
67. S. L. Wang and L. Z. Liao, "Decomposition method with a variable parameter for a class of monotone variational inequality problems," J. Optim. Theory Appl., vol. 102, no. 2, pp. 415-429, May 2001. (Pubitemid 33383277)
68. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1-122, 2011.
69. R. Clark, G. Swayze, K. Livo, R. Kokaly, S. Sutley, J. Dalton, R. McDougal, and C. Gent, "Imaging spectroscopy: Earth and planetary remote sensing with the USGS Tetracorder and expert systems," J. Geophys. Res., vol. 108, no. E12, p. 5131, Dec. 2003.
70. P. Combettes and V. Wajs, "Signal recovery by proximal forwardbackward splitting," SIAM J. Multiscale Model. Simul., vol. 4, no. 4, pp. 1168-1200, 2005. (Pubitemid 44932287)