A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing

IEEE Transactions on Signal Processing

Volumn 57, Issue 11, 2009, Pages 4418-4432

  Chan, Tsung Han ^a   Chi, Chong Yung ^a   Huang, Yu Min ^a   Ma, Wing Kin ^b  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Convex analysis; Convex optimization; Hyperspectral unmixing; Linear programming; Minimum volume enclosing simplex

Indexed keywords

CONVEX ANALYSIS; ENDMEMBERS; HYPERSPECTRAL; HYPERSPECTRAL UNMIXING; LINEAR PROGRAMS; MINIMIZATION ALGORITHMS; MINIMUM-VOLUME ENCLOSING SIMPLEX; MIXED DATA; MONTE CARLO SIMULATION; PROBLEM FORMULATION; PURE PIXEL; SIMPLEX ALGORITHM; SPECTRAL SIGNATURE; SUFFICIENT CONDITIONS; UNMIXING;

ALGORITHMS; COMPUTER SIMULATION; CONVEX OPTIMIZATION; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; MONTE CARLO METHODS; OPTIMIZATION;

PIXELS;

EID: 70350488509     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2025802     Document Type: Article

References (46)

1. T. M. Lillesand, R. W. Kiefer, and J. W. Chipman, Remote Sensing and Image Interpretation, 2nd ed. New York: Wiley, 2004.
2. J. A. Richards, "Analysis of remotely sensed data: The formative decades and the future," IEEE Trans. Geosci. Remote Sens., vol. 43, no. 2, pp. 422-432, Mar. 2005.
3. B. A. Campbell, Radar Remote Sensing of Planetary Surfaces. New York: Cambridge Univ. Press, 2002.
4. R. N. Clark, G. A. Swayze, K. E. Livo, R. F. Kokaly, S. Sutley, J. B. Dalton, R. R. McDougal, and C. A. Gent, "Imaging spectroscopy: Earth and planetary remote sensing with the USGS tetracorder and expert systems," J. Geophys. Res., vol. 108, no. 12, pp. 5-44, Dec. 2003.
5. G. Shaw and D. Manolakis, "Signal processing for hyperspectral image exploitation," IEEE Signal Process. Mag., vol. 19, no. 1, pp. 12-16, Jan. 2002.
6. D. Landgrebe, "Hyperspectral image data analysis," IEEE Signal Process. Mag., vol. 19, no. 1, pp. 17-28, Jan. 2002.
7. N. Keshava and J. Mustard, "Spectral unmixing," IEEE Signal Process. Mag., vol. 19, no. 1, pp. 44-57, Jan. 2002.
8. D. Stein, S. Beaven, L. Hoff, E. Winter, A. Schaum, and A. Stocker, "Anomaly detection from hyperspectral imagery," IEEE Signal Process. Mag., vol. 19, no. 1, pp. 58-69, Jan. 2002.
9. N. Keshava, "A survey of spectral unmixing algorithms," Lincoln Lab. J., vol. 14, no. 1, pp. 55-78, Jan. 2003.
10. M. O. Smith, P. E. Johnson, and J. B. Adams, "Quantitative determination of mineral types and abundances from reflectance spectra using principal component analysis," J. Geophys. Res., vol. 90, no. 2, pp. C797-C804, Oct. 1985.
11. A. A. Green, "A transformation for ordering multispectral data in terms of image quality with implications for noise removal," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 1, pp. 65-74, May 1988.
12. C.-I. Chang and Q. Du, "Estimation of number of spectrally distinct signal sources in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens., vol. 42, no. 3, pp. 608-619, Mar. 2004.
13. J. M. Bioucas-Dias and J. M. P. Nascimento, "Hyperspectral subspace identification," IEEE Trans. Geosci. Rem. Sens., vol. 46, no. 8, pp. 2435-2445, 2008.
14. J. W. Boardman, F. A. Kruse, and R. O. Green, "Mapping target signatures via partial unmixing of AVIRIS data," in Proc. Summ. JPL Airborne Earth Sci. Workshop, Pasadena, CA, Dec. 9-14, 1995, vol. 1, pp. 23-26.
15. M. E. Winter, "N-findr: An algorithm for fast autonomous spectral end-member determination in hyperspectral data," in Proc. SPIE Conf. Imaging Spectrometry, Pasadena, CA, Oct. 1999, pp. 266-275.
16. M. E. Winter and U. Imagery, "A proof of the N-FINDR algorithm for the automated detection of endmembers in a hyperspectral image," in Proc. SPIE Conf. Algorithms and Technol. Multispect., Hyperspect. Data Aug. 2004, vol. 5425, pp. 31-41.
17. J. M. P. Nascimento and J. M. 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.
18. 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.
19. 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.
20. A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, "Hyperspectral image unmixing via alternating projected subgradients," in Proc. 41st Asilomar Conf. Signals, Syst., Pacific Grove, CA, Nov. 4-7, 2007.
21. M. Berman, H. Kiiveri, R. Lagerstrom, A. Ernst, R. Dunne, and J. F. 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.
22. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature, vol. 401, pp. 788-791, Oct. 1999.
23. V. P. Pauca, J. Piper, and R. J. Plemmons, "Nonnegative matrix factorization for spectral data analysis," Linear Algebra Appl., vol. 1, no. 416, pp. 29-47, 2006.
24. N. Dobigeon, S. Moussaoui, M. Coulon, J.-Y. Tourneret, and A. O. Hero, "Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery," IEEE Trans. Signal Process., 2009, to be published.
25. M. D. Craig, "Minimum-volume transforms for remotely sensed data," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 3, pp. 542-552, May 1994.
26. 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.
27. J. W. Boardman, "Automating spectral unmixing of AVIRIS data using convex geometry concepts," in Proc. Summ. 4th Annu. JPL Airborne Geosci. Workshop, Dec. 9-14, 1993, vol. 1, pp. 11-14.
28. J. W. Boardman, "Geometric mixture analysis of imaging spectrometry data," in Proc. IEEE Int. Geosci. Remote Sens. Symp., Pasadena, CA, Aug. 8-12, 1994, vol. 4, pp. 2369-2371.
29. T.-H. Chan, W.-K. Ma, C.-Y. Chi, and Y. Wang, "A convex analysis framework for blind separation of non-negative sources," IEEE Trans. Signal Process., vol. 56, pp. 5120-5134, Oct. 2008.
30. 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., Boston, MA, Aug. 8-12, 2008, vol. 4, pp. 2369-2371.
31. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing New York: Wiley, 2002.
32. J. M. P. Nascimento and J. M. Bioucas-Dias, "Does independent component analysis play a role in unmixing hyperspectral data?," IEEE Trans. Geosci. Remote Sens., vol. 43, pp. 175-187, Jun. 2005.
33. 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, 2006.
34. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
35. P. Gritzmann and V. Klee, "On the complexity of some basic problems in computational convexity: I.: Containment problems," Discrete Math. vol. 136, no. 1-3, pp. 129-174, Dec. 1994.
36. Y. Zhou and S. Suri, "Algorithms for a minimum volume enclosing simplex in three dimensions," SIAM J. Comput., vol. 31, no. 5, pp. 1339-1357, 2002.
37. G. Strang, Linear Algebra and Its Applications, 4th ed. San Diego, CA: Thomson, 2006.
38. F.-Y.Wang, C.-Y. Chi, T.-H. Chan, and Y.Wang, "Non-negative least-correlated component analysis for separation of dependent sources by volume maximization," IEEE Trans. Pattern Anal. Mach. Intell., 2009, to be published.
39. I. J. Lustig, R. E. Marsten, and D. F. Shanno, "Interior point methods for linear programming: Computational state of the art," ORSA J. Comput., vol. 6, no. 1, pp. 1-14, 1994.
40. J. F. Sturm, "Using sedumi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimiz. Methods Software, vol. 11-12, pp. 625-653, 1999.
41. H. W. Kuhn, "The Hungarian method for the assignment method," Naval Res. Logist. Quart., vol. 2, pp. 83-97, 1955.
42. Tech. Rep [Online]. Available: http://speclab.cr.usgs.gov/cuprite.html
43. AVIRIS Free Standard Data Products [Online]. Available: http:// aviris.jpl.nasa.gov/html/aviris.freedata.html
44. G. Swayze, R. Clark, S. Sutley, and A. Gallagher, "Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada," in Proc. Summer 4th Annu. JPL Airborne Geosci. Workshop, 1992, vol. 2, pp. 47-49.
45. G. Swayze, "The hydrothermal and structural history of the cuprite mining district, southwestern Nevada: An integrated geological and geophysical approach," Ph.D. dissertation, Univ. Colorado, Boulder, 1997.
46. R. N. Clark, G. A. Swayze, A. Gallagher, T.V. King, and W. M. Calvin, "The U.S. geological survey digital spectral library: Version 1: 0.2 to 3.0 μm," U.S. Geol. Surv., Open File Rep. 93-592, 1993.