Compressive-projection principal component analysis

IEEE Transactions on Image Processing

Volumn 18, Issue 10, 2009, Pages 2230-2242

  Fowler, James E ^a  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Hyperspectral data; Principal component analysis (PCA); Random projections; Rayleigh Ritz theory

Indexed keywords

A-TRANSFORM; COMPRESSED SENSING; COMPRESSION PERFORMANCE; COMPUTATIONAL BURDEN; DECODER SYSTEM; DIMENSIONAL SUBSPACE; DIMENSIONALITY REDUCTION; EIGEN DECOMPOSITION; EIGENVECTORS; HYPERSPECTRAL DATA; ITS DATA; PRINCIPAL COMPONENT ANALYSIS (PCA); RANDOM PROJECTIONS; RAYLEIGH; RAYLEIGH-RITZ THEORY; RECONSTRUCTION PROCESS; RESOURCE-CONSTRAINED; RITZ VECTOR;

DECODING; REPAIR; SENSORS;

PRINCIPAL COMPONENT ANALYSIS;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; IMAGE ENHANCEMENT; INFORMATION PROCESSING; METHODOLOGY; PRINCIPAL COMPONENT ANALYSIS; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING;

ALGORITHMS; DATA COMPRESSION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; PRINCIPAL COMPONENT ANALYSIS; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 70349469297     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2025089     Document Type: Article

References (40)

1. Q. Du and J. E. Fowler, "Hyperspectral image compression using JPEG2000 and principal component analysis," IEEE Geosci. Remote Sens. Lett. vol. 4, no. 2, pp. 201-205, Apr. 2007.
2. B. Penna, T. Tillo, E. Magli, and G. Olmo, "A new low complexity KLT for lossy hyperspectral data compression," in Proc. Int. Geoscience and Remote Sensing Symp., Denver, CO, Aug. 2006, vol. 7, pp. 3525-3528.
3. J. C. Harsahyi and C.-I. Chang, "Hyperspectral image classification and dimensionality reduction: An orthogonal subspace projection approach," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 4, pp. 779-785, Jul. 1994.
4. J. B. Lee, S. Woodyatt, and M. Berman, "Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform," IEEE Trans. Geosci. Remote Sens., vol. 28, no. 3, pp. 295-304, May 1990.
5. X. Jia and J. A. Richards, "Segmented principal components transformation for efficient hyperspectral remote-sensing image display and classification," IEEE Trans. Geosci. Remote Sens., vol. 37, no. 1, pp. 538-542, Jan, 1999.
6. B. N. Parlett, The Symmetric Eigenvalue Problem. Philadelphia, PA: SIAM, 1998.
7. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty, principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
8. E. Candès and T. Tao, "Near-optimal signal recovery from random projections: Universal incoding strategies?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
9. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
10. E. J. Clindès and M. B, Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 21-30, Mar. 2008.
11. V. K. Goyal, A. K. Fletcher, and, S. Rangan, "Compressive sampling and lossy compression," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 48-56, Mar. 2008.
12. J. E. Fowler, "Compressive-projection principal component analysis for the compfession of hyperspectral signatures in Proc. IEEE Data Compression Conf., J.A. Storer and M.-W. Marcellin, Eds-Snowbird, UT, Mar. 2008, pp. 93-92.
13. J. E. Fowler, "Compressive-projection principal component analysis and the first eigenvector," in Proc. IEEE Data Compression-Conf., J. A., Storer and M, W. Marcellin, Eds., Snowbird, UT, Mar. 2009. pp. 223-232.
14. Z. Jia and G. W. Stewart, "An analysis of the Rayleigh-Ritz method for approximating eigenspaces," Math. Comput., vol. 70, no. 234, pp. 637-647, Apr. 2001.
15. I. T. Jolliffe, Principal Component Analysis. New York: Springer-Verlag, 1986.
16. J. E. Jackson, A User's Guide to Principal Component Analysis. New York: Wiley, 1991.
17. R. B. Cattell, "The scree test for the number of factors," Multivariate Behav. Res., vol. 1, no. 2, pp. 245-276, Apr. 1966.
18. J. M. Craddock and C. R. Flood, "Eigenvectors for representing the 500 mb geopotential surface over the northern hemisphere," Quart. J. Roy. Meteorol. Soc., vol. 95, no. 405, pp. 576-593, Jul. 1969.
19. S. A. Farmer, "An investigation into the results of principal component analysis of data derived from random numbers," The Statistician, vol. 20, no. 4, pp. 63-72, Dec. 1971.
20. P. L. Combettes, "The foundations of set theoretic estimation," Proc. IEEE, vol. 81, no. 2, pp. 182-208, Feb. 1993.
21. Q. Du and J. E. Powler, "Low-complexity principal component analysis for hyperspectral image compression," Int. J. High Performance Comput. Appl., vol. 22, no. 4, pp. 438-448, Nov. 2008.
22. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression Norwell, MA: Kluwer, 1992.
23. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
24. S. Ji, D. Dunson. and L. Carin. "Multitask compressive sensing," IEEE Trans. Signal Process., vol. 57, no. 1, pp. 92-106, Jan. 2009.
25. D. Baron, M. B. Wakin, M. F. Duarte, S. Savrvotham, and R. G. Baranuik, Distributed Compressed Sensing 2005, submitted.
26. M. Fornasier and H. Rauhut, "Recovery algorithms for vector-valued data with joint sparsity constraints," SIAM J. Numer. Anal., vol. 46, no. 2, pp. 577-613, 2008.
27. M. Mishali and Y. C. Eldar, "Reduce and boost: Recovering arbitrary sets of jointly sparse vectors," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4692-4702, Oct. 2008.
28. D. P. Wipf and B. D. Rao, "An empirical Bayesian strategy for solving the simultaneous sparse approximation problem," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 3704-3716, Jul. 2007.
29. J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process., vol. 86, no. 3, pp. 572-588, March 2006.
30. J. A. Tropp, "Algorithms for simultaneous sparse approximation. Part II: Convex relaxation," Signal Process., vol. 86, no. 3, pp. 589-602, Mar. 2006.
31. W. B. Johnson and J. Lindenstrauss, "Extensions of Lipschitz mappings into a Hilbert space," Contemporary Math., vol. 26, pp. 189-206, 1984.
32. S. Dasgupta and A. Gupta, "An elementary proof of a theorem of Johnson and Lindenstraus," Random Structures and Algorithms, vol. 22, no. 1, pp. 60-65, Jan. 2003.
33. D. Achlioptas, "Database-friendly random projections: Johnson-Lin-denstrauss with binary coins," J. Comput. Syst. Sci., vol. 66, no. 4, pp. 671-687, June 2003.
34. R. M. Willett, M. E. Gehm, and D. J. Brady, "Multiscale reconstruction for computational spectral imaging," in Computational Imaging V, C. A. Bouman, E. L. Miller, and I. Pollak, Eds. San Jose, CA: SPIE, Jan. 2007, vol. 6498, p. 64980L.
35. N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy., M. R. Feldman, and R. D. TeKolste, "Compressive imaging sensors," in Intelligent Integrated Microsystems, R. A. Athale and J. C. Zolper, Eds. Kissimmee, FL: SPIE, Apr. 2006, vol. 6232, p. 62320A.
36. D. J. Brady, "Micro-optics and megapixels," Opt. Photon. News, vol. 17, no. 11, pp. 24-29, Nov. 2006.
37. I. Johnstone and A. Y. Lu, "Sparse principal component analysis," J. Amer. Statist. Assoc., to appear.
38. G. Strang, Linear Algebra and its Applications, 3rd-ed. San Diego, CA: Harcourt Prace, 1988.
39. N. K. Johnson, S. Kotz, and N. Balakristman, Continuous Univariate Distributions, 2nd ed. New York: Wiley, 1994, vol. 1.
40. N. K. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions, 2nd ed. New York: Wiley, 1995, vol. 2.