A generalized sampling theory without band-limiting constraints

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

Volumn 45, Issue 8, 1998, Pages 959-969

  Unser, Michael ^a,b   Zerubia, Josiane ^a  

^a EPFL   (Switzerland)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; NOTCH FILTERS;

GENERALIZED SAMPLING THEORY;

SIGNAL FILTERING AND PREDICTION;

EID: 0032139798     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.718806     Document Type: Article

References (25)

1. A. Aldroubi, M. Unser, and M. Eden, "Cardinal spline filters: Stability and convergence to the ideal sine interpolator," Signal Processing, vol. 28, no. 2, pp. 127-138, 1992.
2. A. Aldroubi and M. Unser, "Families of multiresolution and wavelet spaces with optimal properties," Numer. Function. Anal. Optimiz., vol. 14, nos. 5-6, pp. 417-4446, 1993.
3. __, "Sampling procedures in function spaces and asymptotic equivalence with Shannon's sampling theory," Numer. Function. Anal. Optimiz., vol. 15, nos. 1-2, pp. 1-21, 1994.
4. A. Aldroubi, "Oblique projections in atomic spaces," in Proc. Amer. Math. Soc., 1996, vol. 124, no. 7, pp. 2051-2060.
5. T. Blu and M. Unser, "Approximation error for quasiinterpolators and (multi-)wavelet expansions," Appl. Computation. Harmonie Anal., to be published.
6. J. L. Brown, "Multi-channel sampling of lowpass-pass signals," IEEE Trans. Circuit Syst., vol. 28, pp. 101-106, 1981.
7. I. Djokovic and P. P. Vaidyanathan, "Generalized sampling theorems in multiresolution subspaces," IEEE Trans. Signal Processing, vol. 45, pp. 583-599, 1997.
8. A. J. E. M. Janssen, "The Zak transform and sampling theorems for wavelet subspaces," IEEE Trans. Signal Processing, vol. 41, pp. 3360-3364, 1993.
9. A. J. Jerri, "The Shannon sampling theorem-Its various extensions and applications: A tutorial review," Proc. IEEE, 1997, vol. 65, no. 11, pp. 1565-1596.
10. D. A. Linden, "A discussion of sampling theorems," in Proc. IRE, 1959, vol. 47, pp. 1219-1226.
11. S. G. Mallat, "A theory of multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Machine Intel!., vol. PAMI-11, pp. 674-693, 1989.
12. R. J. Marks, II, Introduction to Shannon Sampling Theory. New York: Springer-Verlag, 1991.
13. A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst., vol. 24, pp. 652-654, 1977.
14. I. J. Schoenberg, Cardinal Spline Interpolation. Philadelphia, PA: SIAM, 1973.
15. C. E. Shannon, "Communication in the presence of noise," Proc. I.R.E., 1949, vol. 37, pp. 10-21.
16. H. Shekarforoush, M. Berthod, and J. Zerubia, "3D super-resolution using generalized sampling expansion," in Proc. Int. Conf. Image Processing, Washington, DC, Oct. 23-26, 1995, vol. II, pp. 300-303.
17. M. Unser and A. Aldroubi, "A general sampling theory for nonideal acquisition devices," IEEE Trans. Signal Processing, vol. 42, pp. 2915-2925, 1994.
18. M. Unser, A. Aldroubi, and M. Eden, "Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem," IEEE Trans. Inform. Theory, vol. 38, pp. 95-103, 1992.
19. __, "B-spline signal processing. Part II: Efficient design and applications," IEEE Trans. Signal Processing, vol. 41, pp. 834-848, Feb. 1993.
20. M. Unser and J. Zerubia, "Generalized sampling: Stability and performance analysis," IEEE Trans. Signal Processing, vol. 45, pp. 2941-2950, Dec. 1997.
21. H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," Computer Vis., Graph., Image Processing, vol. 54, no. 2, pp. 181-186, 1991.
22. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding. Engle- wood Cliffs, NJ: Prentice Hall, 1995.
23. M. J. Vrhel and B. L. Trus, "Multi-channel restoration of electron micrographs," in Proc. Int. Conf. Image Processing, Washington, DC, Oct. 23-26, 1995, vol. II, pp. 516-519.
24. G. G. Walter, "A sampling theorem for wavelet subspaces," IEEE Trans. Inform. Theory, vol. 38, pp. 881-884, 1992.
25. J. L. Yen, "On the nonuniform sampling of bandwidth limited signals," IRE Trans. Circuit Theory, vol. CT-3, pp. 251-257, 1956.