Recursive implementation of the distributed Karhunen-Love transform

IEEE Transactions on Signal Processing

Volumn 58, Issue 10, 2010, Pages 5320-5330

  Amar, Alon ^a   Leshem, Amir ^a,b   Gastpar, Michael ^a,c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b BAR ILAN UNIVERSITY   (Israel)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Distributed compression; distributed Karhunen Love transform; distributed transforms; principal component analysis; source coding; transform coding

Indexed keywords

DISTRIBUTED COMPRESSION; DISTRIBUTED TRANSFORMS; KARHUNEN-LOVE TRANSFORM; PRINCIPAL COMPONENTS; SOURCE-CODING; TRANSFORM CODING;

ALGORITHMS; BLOCK CODES; ENCODING (SYMBOLS); MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; MEAN SQUARE ERROR; REAL TIME CONTROL; SENSOR DATA FUSION; SENSORS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 77956756277     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2056922     Document Type: Article

References (28)

1. I. F. Akyildiz, S.Weilian, Y. Sankarasubramaniam, and E. Cayirci, "A survey on sensor networks," IEEE Commun. Mag., vol.40, no.8, pp. 102-114, Aug. 2002.
2. A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson, "Wireless sensor networks for habitat monitoring," in Proc. 1st ACM Int. Workshop on Wireless Sens. Netw. Appl., Atlanta, GA, 2002, pp. 88-97.
3. D. Estrin, L. Girod, G. Pottie, and M. Srivastava, "Instrumenting the world with wireless sensor networks," in IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP 2001), Salt Lake City, UT, May 7-11, 2001, pp. 2033-2036.
4. A. Milenkovic, C. Otto, and E. Jovanov, "Wireless sensor networks for personal health monitoring: Issues and an implementation," Comput. Commun., vol.29, no.13-14, pp. 2521-2533, Aug. 2006.
5. J. C. Chen, Y. Kung, and R. E. Hudson, "Source localization and beamforming," IEEE Signal Process. Mag., vol.19, no.2, pp. 30-39, Mar. 2002.
6. D. Slepian and J. K.Wolf, "Noiseless coding of correlated information sources," IEEE Trans. Inf. Theory, vol.19, no.4, pp. 471-480, Jul. 1973.
7. A. D.Wyner and J. Ziv, "The rate-distortion function for source coding with side information at the decoder," IEEE Trans. Inf. Theory, vol.22, no.1, pp. 1-10, Jan. 1976.
8. V. K. Goyal, "Theoretical foundations of transform coding," IEEE Signal Process. Mag., vol.18, no.5, pp. 9-21, Sep. 2001.
9. M. Gastpar, P. L. Dragotti, and M. Vetterli, "The distributed Karhunen-Loève transform," IEEE Trans. Inf. Theory, vol.52, no.12, pp. 5177-5196, Dec. 2006.
10. H. I. Nurdin, R. R. Mazumdar, and A. Bagchi, "Reduced dimension linear transform coding of distributed correlated signals with incomplete observations," IEEE Trans. Inf. Theory, vol.55, no.6, pp. 2848-2858, Jun. 2009.
11. O. Roy and M. Vetterli, "Dimensionality reduction for distributed estimation in the infinite dimensional regime," IEEE Trans. Inf. Theory, vol.54, no.4, pp. 1655-1669, Apr. 2008.
12. N. Goela and M. Gastpar, "Distributed Karhunen-Loève transform with nested subspaces," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2009), Taipei, Taiwan, Apr. 19-24, 2009, pp. 2405-2408.
13. N. Goela and M. Gastpar, "Linear compressive networks," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2009), Seoul, Korea, Jun. 28-Jul. 3 2009, pp. 159-163.
14. A. Wiesel and A. O. Hero, "Principal component analysis in decomposable Gaussian graphical models," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2009), Taipei, Taiwan, Apr. 19-24, 2009, pp. 1537-1540.
15. X. Jin-Jun, A. Ribeiro, Z. Q. Luo, and G. B. Giannakis, "Distributed compression-estimation using wireless sensor networks," IEEE Signal Process. Mag., vol.23, no.4, pp. 27-41, Jul. 2006.
16. K. Zhang, X. R. Li, P. Zhang, and H. Li, "Optimal linear estimation fusion-Part IV: Sensor data compression," in Proc. 6th Int. Conf. Inf. Fusion, Australia, Jul. 2003.
17. K. Zhang, "Best linear unbiased estimation fusion with constraints," Ph.D. dissertation, Univ. New Orleans, New Orleans, LA, 2003.
18. I. D. Schizas, G. B. Giannakis, and Z. Q. Luo, "Distributed estimation using reduced-dimensionality sensor observations," IEEE Trans. Signal Process., vol.55, no.8, pp. 4284-4299, Aug. 2007.
19. A. Amar, A. Leshem, and M. Gastpar, "A greedy approach for the distributed Karhune-Loeve transform," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP 2010), Dallas, TX, Mar. 14-19, 2010.
20. Y. Yamashita and H. Ogawa, "Relative Karhunen-Loeve transform," IEEE Trans. Signal Process., vol.44, no.2, pp. 371-378, Feb. 1996.
21. Y. Hua and W. Liu, "Generalized Karhunen-Loeve transform," IEEE Signal Process. Lett., vol.5, no.6, pp. 141-142, Jun. 1998.
22. L. Scharf, "The SVD and reduced rank signal processing," Signal Process., vol.25, no.2, pp. 113-133, Nov. 1991.
23. A. Torokhti, S. Friedland, and P. Howlet, "Towards generic theory of data compression," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 24-29, 2007, pp. 291-295.
24. D. P. Oleary, G. W. Stewart, and J. S. Vandergraft, "Estimating the largest eigenvalue of a positive definite matrix," Math. Computat., vol.33, no.148, pp. 1289-1292, Oct. 1979.
25. B. N. Parlett, H. Simon, and L. M. Stringer, "On estimating the largest eigenvalue with Lanczos algorithm," Math. Computat., vol.38, no.157, pp. 153-165, Jan. 1982.
26. P. Common and G. H. Golub, "Tracking a few extreme singular values and vectors in signal processing," Proc. IEEE, vol.78, no.8, pp. 1327-1343, Aug. 1990.
27. J. W. Demmel, Applied Numerical Linear Algebra. Philadelphia, PA: Soc. Indust. Appl. Math., 1997.
28. H. L. Van Trees, Detection, Estimation, and Modulation Theory-Part IV. New York: Wiley, 2002.