Extrapolation and Spectral Estimation with Iterative Weighted Norm Modification

IEEE Transactions on Signal Processing

Volumn 39, Issue 4, 1991, Pages 842-851

  Cabrera, Sergio D ^a   Parks, Thomas W ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--ALGORITHMS; MATHEMATICAL TRANSFORMATIONS--FOURIER TRANSFORMS;

EXTRAPOLATION ALGORITHMS;

SIGNAL PROCESSING;

EID: 0026140141     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.80906     Document Type: Article

References (35)

1. S. D. Cabrera and T. W. Parks, “Estimation of sequences in a signal class determined from the data,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (Tampa FL), Mar. 1985, pp. 1348–1351.
2. A. Papoulis, “A new algorithm in spectral analysis and bandlimited extrapolation,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 735–742, Sept. 1975.
3. R. W. Gerchberg, “Superresolution trough error energy reduction,” Opt. Acta, vol. 21, no. 9, pp. 709–720, 1974.
4. A. K. Jain and S. Ranganath, “Extrapolation algorithms for discrete signals with application in spectral estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 830–845, Aug. 1981.
5. D. P. Kolba and T. W. Parks, “Optimal estimation for bandlimited signals including time domain considerations,” IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-31, pp. 113–122, Feb. 1983.
6. T. W. Parks and D. P. Kolba, “Time domain considerations in optimal estimation for bandlimited signals,” in Applied Time Series Analysis II, D. F. Findley, Ed. New York: Academic, 1981.
7. J. L. C. Sanz and T. S. Huang, “A unified approach to noniterative linear signal restoration,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 2, pp. 403–409, Apr. 1984.
8. J. L. C. Sanz and T. S. Huang, “Discrete and continuous bandlimited signal extrapolation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, no. 5, pp. 1276–1285, Oct. 1983.
9. J. L. C. Sanz and T. S. Huang, “Some aspects of band-limited signal extrapolation: Models, discrete approximation, and noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, no. 6, pp. 1492–1501, Dec. 1983.
10. J. L. C. Sanz and T. S. Huang, “Unified Hilbert space approach to iterative least-squares linear signal restoration,” J. Opt. Soc. Amer., vol. 73, no. 11, pp. 1455–1465, Nov. 1983.
11. D. Slepian, “Prolate spheroidal wave functions, Fourier analysis, and uncertainty—V: The discrete-case,” Bell Syst. Tech. J., vol. 57, pp. 1371–1430, May 1978.
12. L. C. Potter and K. S. Arun, “Energy concentration in bandlimited extrapolation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-37, pp. 1027–1041, July 1989.
13. C. L. Byrne and R. M. Fitzgerald, “Reconstruction from partial information with applications to tomography,” SIAM J. Appl. Math., vol. 42, no. 4, pp. 933–940, Aug. 1982.
14. C. L. Byrne and R. M. Fitzgerald, “Spectral estimators that extend the maximum entropy and maximum likelihood methods,” SIAM J. Appl. Math., vol. 44, no. 2, pp. 425–442, Apr. 1984.
15. C. L. Byrne, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, and A. M. Darling, “Image restoration and resolution enhancement,” J. Opt. Soc. Amer., vol. 73, no. 11, pp. Nov. 1983.
16. C. L. Byrne and M. A. Fiddy. “Images as power spectra; Reconstruction as a Wiener filter approximation,” Inverse Problems, vol. 4, pp. 399–409, 1988.
17. M. Z. Nashed and G. Wahba, “Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations,” SIAM J. Math. Anal., vol. 5, no. 6, Nov. 1974.
18. B. J. Sullivan and B. Liu, “On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 1201–1212, Dec. 1984.
19. H. Lee, Z.-C. Lin, and T. S. Huang, “Performance and limitations of discrete band-limited signal extrapolation,” in Proc. IEEE Int. Conf. ASSP (Tokyo, Japan), 1986, pp. 1645–1648.
20. C. C. Chamzas, and W. Y. Xu, “An improved version of Papoulis-Gerchberg algorithm on band-limited extrapolation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 2, pp. 437–440, Apr. 1984.
21. A. Papoulis and C. Chamzas, “Detection of hidden periodicities by adaptive extrapolation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, no. 5, pp. 492–500, Oct. 1979.
22. K. Stewart, T. S. Durrani, and J. B. Abbiss, “The effects of bandwidth misestimation in bandlimited signal extrapolation,” in Proc. IEEE Int. Conf. ASSP (Tampa, FL), Mar. 1985, pp. 1497–1500
23. S. M. Kay and S. L. Marple, Jr., “Spectrum analysis—a modern perspective,” Proc. IEEE, vol. 69, no. 11, pp. 1380–1419, Nov. 1981.
24. C. L. Byrne and R. M. Fitzgerald, “Fourier transform estimation using prior knowledge,” unpublished manuscript.
25. H. Lee, D. P. Sullivan, and T. S. Huang, “Improvements of discrete bandlimited extrapolation by iterative subspace modification,” in Proc. IEEE Int. Conf. ASSP (Dallas, TX). Apr. 1987, pp. 1569–1572.
26. A. A. Melkman and C. A. Micchelli, “Optimal estimation linear operators in Hilbert spaces from inaccurate data,” SIAM J. Numer. Anal., vol. 16, no. 1, pp. 87–105, Feb. 1979.
27. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications. New York: Wiley, 1974.
28. P. J. Davis, Circulant Matrices. New York: Wiley, 1979.
29. S. D. Cabrera, “Optimal recovery of signals from linear measurements and prior knowledge,” Ph.D. dissertation, Dep. Elec. Comput. Eng., Rice University, Houston, TX, May 1985.
30. S. Kay, Modern Spectral Estimation: Theory Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.
31. S. L. Marple, Jr., Digital Spectral Analysis. Englewood NJ: Prentice-Hall, 1987.
32. C.-H. Chi, “Autoregressive and sinusoidal spectral estimation based on adaptive extrapolation algorithms,” M.S. thesis, Dep. Elec. Comput. Eng., Pennsylvania State Univ., June 1989.
33. S. D. Cabrera and C. H. Chi, “Frequency estimation by reduced order adaptive extrapolation,” in Proc. 1989 Johns Hopkins Conf. Inform. Sci. Syst. (Baltimore, MD), Mar. 1989.
34. S. D. Cabrera, J. T. Yang, and C. H. Chi, “Estimation of nusoids by adaptive minimum norm extrapolation,” in Proc. Fifth ASSP Workshop Spectrum Estimation, Modeling (Rochester, NY), Oct. 1990, pp. 35-39.
35. S. D. Cabrera and C. Chen, “Phase retrieval by optimal weighted norm extrapolation,” in Advances in Communications and Signal Processing, W. A. Porter and S. C. Kak, Eds. Heidelberg: Springer, 1989, pp. 303-314.