Rank estimation and redundancy reduction of high-dimensional noisy signals with preservation of rare vectors

IEEE Transactions on Signal Processing

Volumn 55, Issue 12, 2007, Pages 5579-5592

  Kuybeda, Oleg ^a   Malah, David ^a   Barzohar, Meir ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Anomaly detection; Dimensionality reduction; Hyperspectral images; Hyperspectral imaging; Minimum description length (MDL); Noise; Redundancy reduction; Signal subspace rank; Singular value decomposition (SVD)

Indexed keywords

ALGORITHMS; NOISE ABATEMENT; SINGULAR VALUE DECOMPOSITION; TARGET TRACKING; VECTORS;

DIMENSIONALITY REDUCTION; EXTREME VALUE THEORY; HYPERSPECTRAL IMAGING; MINIMUM DESCRIPTION LENGTH; REDUNDANCY REDUCTION; SIGNAL-SUBSPACE RANK;

IMAGE PROCESSING;

EID: 36749083452     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2007.901645     Document Type: Article

References (34)

1. M. Tipping and C. Bishop, "Probabilistic principal component analysis," J. Roy. Statist. Soc.: Series B (Statist. Method. , vol. 61, no. 3, pp. 611-622, 1999.
2. Y. P. Hong and C. T. Pan, "Rank-revealing QR factorizations and the singular value decomposition," Mathem. Computat., vol. 58, no. 197, pp. 213-232, Jan. 1992.
3. L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Reading, MA: Addison-Welsey, 1993.
4. G. W. Stewart and J. G. Sun, Matrix Perturbation Theory. Boston, MA: Academic, 1990.
5. Q. Du and C. I. Chang, "A signal-decomposed and interference-annihilated approach to hyperspectral target detection," IEEE Trans. Geosci. Remote Sens., vol. 42, no. 4, pp. 892-906, Apr. 2004.
6. Q. Du and C. I. Chang, "Noise subspace projection approaches to determination of intrinsic dimensionality of hyperspectral imagery," Proc. Image and Signal Processing for Remote Sensing, SPIE, vol. 3871, pp. 34-44, Dec. 1999.
7. P. V. Overshee and B. D. Moor, "Subspace algorithms for the stochastic identification problem," Automatica, vol. 29, pp. 649-660, 1993.
8. E. Moulines, P. Duhamel, J. Cardoso, and S. Mayrargue, "Subspace methods for the blind identification of multichannel FIR filters," IEEE Trans. Signal Process., vol. 43, no. 2, pp. 516-526, Feb. 1995.
9. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
10. M. Viberg, "Subspace-based methods for the identification of linear time-invariant systems," Automatica, vol. 31, no. 12, pp. 1835-1853, 1995.
11. M. Wax and T. Kailath, "Detection of signals by information theoretic criteria," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 387-392, Apr. 1985.
12. J. Rissanen, "Modeling by shortest data description," Automatica vol. 14, no. 5, pp. 465-471, 1978.
13. J. Rissanen, "Estimation of structure by minimum description length," Circuits, Syst. Signal Process., vol. 1, no. 4, pp. 395-406, 1982.
14. P. Stoica and Y. Selen, "Model-order selection: A review of information criterion rules," IEEE Signal Process. Mag., vol. 21, no. 4, pp. 36-47, Jul. 2004.
15. E. Moulines, P. Duhamel, J. F. Cardoso, and S. Mayrargue, "Subspace methods for the blind identification of multichannel FIR filters," IEEE Trans. Signal Process., vol. 43, no. 2, pp. 516-525, Feb. 1995.
16. G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process., vol. 43, no. 12, pp. 2982-2993, Dec. 1995.
17. D. Slock, "Blind fractionally-spaced equalization, perfect reconstruction filterbanks, and multilinear prediction," presented at the ICASSP, Adelaide, Australia, Apr. 1994.
18. Y. Wu and K. W. Tam, "On determination of the number of signals in spatially correlated noise," IEEE Trans. Signal Process., vol. 46, no. 11, pp. 3023-3029, Nov. 1998.
19. K. M. Wong, Q. T. Zhang, J. P. Reilly, and P. Yip, "A new criterion for the determination of the number of signals in high-resolution array processing," in Proc. Meeting Advanced Algorithms and Architectures for Signal Processing III, San Diego, CA, Aug. 15-17, 1988, pp. 352-357.
20. A. P. Liavas, P. A. Regalia, and J. P. Delmas, "Blind channel approximation: Effective channel order determination," IEEE Trans. Signal Process., vol. 47, no. 12, pp. 3336-3344, Dec. 1999.
21. A. HyvÄarinen, J. Karhunen, and E. Oja, Independent Component Analysis, ser. Adaptive and Learning Systems for Signal Processing, Communications, and Control. New York: Wiley, 2001.
22. S. A. Kassam and H. V. Poor, "Robust techniques for signal processing: A survey," Proc. IEEE, vol. 73, no. 3, pp. 433-481, Mar. 1985.
23. N. A. Campbell, "Robust procedures in multivariate analysis I: Robust covariance estimation," Appl. Statist., vol. 29, no. 3, pp. 231-2137, Jan. 1980.
24. M. E. Winter and E. M. Winter, "Comparison of approaches for determinig end-members in hyperspectral data," in Proc. IEEE Aerospace Conf. Mar. 2000, vol. 3, pp. 305-313.
25. M. Leadbetter, Extremes and Related Properties of Random Sequences and Processes. New York: Springer-Verlag, 1982.
26. S. I. Resnick, Extreme Values, Regular Variation, and Point Process New York: Springer-Verlag, 1987.
27. S. Coles, An Introduction to Statistical Modeling ofExtreme Values New York: Springer-Verlag, 2001.
28. E. J. Gumbel, Statistics of Extremes. New York: Columbia Univ. Press, 1958.
29. A. Hyväarinen, "Survey on independent component analysis," Neural Comput. Surveys 2, pp. 94-128, 1999.
30. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions National Bureau of Standards, Applied Mathematics Series-55, Dec. 1972.
31. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
32. N. Johson and S. Kotz, Distributions in Statstics: Continuous Univariate Distributions-2. New York: Wiley, 1970, pp. 130-148.
33. I. K. Fodor, "A survey of dimension reduction techniques," LLNL Tech. Rep. UCRL-ID-148494, Jun. 2002.
34. E. Fishler and H. V. Poor, "Estimation of the number of sources in unbalanced arrays via information theoretic criteria," IEEE Trans. Signal Process., vol. 53, no. 9, pp. 3543-3553, Sep. 2005.