Finite Prolate Spheroidal Sequences and Their Applications I: Generation and Properties

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn PAMI-9, Issue 6, 1987, Pages 787-795

  Wilson, Roland ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Eigenvalue analysis; feature description; quency filtering; spatial fre ; uncertainty principle

Indexed keywords

MATHEMATICAL TECHNIQUES - EIGENVALUES AND EIGENFUNCTIONS; SAMPLING;

EIGENVALUE PROBLEM; EXTREMAL ENERGY CONCENTRATIONS; FINITE PROLATE SPHEROIDAL SEQUENCES; SAMPLING THEOREM;

IMAGE PROCESSING;

EID: 0023456351     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.1987.4767985     Document Type: Article

References (25)

1. D. Slepian and H. O. Pollak, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty I,'” Bell Syst. Tech. J., vol. 40, pp. 43–64, 1961.
2. H. J. Landau and H. O. Pollak, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty II,'” Bell Syst. Tech. J., vol. 40, pp. 65–84. 1961.
3. 1, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty III, Bell Syst. Tech. J. vol. 41, pp. 1295–1336, 1962.
4. D. Slepian, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty IV: Extensions to many dimensions,” Bell Syst. Tech. J., vol. 43, pp. 3009–3057, 1964.
5. —. “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty V: The discrete case,” Bell. Syst. Tech. J., vol. 57, pp. 1317– 1430. 1430. 1978.
6. “On bandwidth,” Proc. IEEE. vol. 64, no. 3. pp. 292–300, 1976.
7. D. W. Tufts, and J. T. Francis, “Designing digital filters—Comparison of methods and criteria,” IEEE Trans. Audio Electroacoust., vol. AU-18. pp. 487–494, 1970.
8. A. Papoulis and M. S. Bertran, “Digital filtering and prolate functions,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 674–681, 1972.
9. D. J. Thomson, “Spectrum estimation and harmonic analysis,” Proc. IEFEE, vol. 70, pp. 1055–1096, 1982.
10. [101 R. Wilson, H. Knutsson, and G. H. Granlund, “Anisotropic nonstationary tionary image estimation and its applications II -Predictive image coding,” IEEE Trans. Commun., vol. COM-31, pp. 398–406, 1983.
11. D. Gabor, “Theory of communication.” Proc. IEE, vol. 93, no. 26, pp. 429–441, 1946.
12. K. Shanmugam. F. M. Dickey and J. A. Green, “An optimal frequency domain filter for edge detection in digital pictures,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-I, pp. 37–69, 1979.
13. R. Wilson, “Uncertainty, eigenvalue problems and filter design,” in Proc. IEEE ICASSP-84. San Diego, CA, 1984.
14. R. Wilson, and G. H. Granlund, “The uncertainty principle in image processing,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI- 66 pp. 758–767, 1984.
15. G. H. Granlund, “In search of a general picture processing operator,” Comput. Graphics Image Processing, vol. 8, pp. 155–173, 1978.
16. L. Jacobson,and H. Wechsler, “The Wigner distribution and its usefulness in 2-D image processing,” in Proc. 6th Int. Conf. Pattern Recognition, Munich, 1982.
17. S. Marcelja, “Mathematical description of the responses of simple cortical cells,” J. Opt. Soc. Amer., vol. 70, pp. 1297–1300, 1980.
18. D. A. Pollen and S. F. Ronner “Visual cortical neurons as localized spatial frequency filters,” IEEE Trans. Syst., Man, Cybern. vol. SMC-13, pp. 907–916, 1983.
19. E. D. Nering, Linear Algebra and Matrix Theory. New York: Wiley, 1970.
20. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
21. R. Wilson, “The uncertainty principle in image coding,” Linkoping Univ., Tech. Rep. LiTH-ISY-1-0579, 1983.
22. J. H. Wilkinson, The Algebraic Eigenvalue Problem. New York: Clarendon Press, Oxford, 1965.
23. H. Knutsson, “Filtering and reconstruction in image processing.” Ph.D. dissertation, Linkoping Univ., 1982.
24. H. Knutsson, and G. H. Granlund. “Texture analysis using two dimensional quadrature filters,” in Proc. IEEE CAPAIDM Workshop, CA, 1983.
25. H. Knutsson, R. Wilson, and G. H. Granlund, “Estimating the local orientation of anisotropic 2-D signals,” in Proc. IEFE Workshop Spect. Estim., FL, 1983.