Lattice-theoretic analysis of time-sequential sampling of spatiotemporal signals - part I

IEEE Transactions on Information Theory

Volumn 43, Issue 1, 1997, Pages 190-207

  Parker Willis, N ^a,b   Bresler, Yoram ^a,c  

^a IEEE   (United States)

^b Cardiac Pathways Corp   (United States)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

Bounds; Geometry of numbers; Harmonic analysis; Optimum multidimensional sampling; Source coding

Indexed keywords

HARMONIC ANALYSIS; OPTIMIZATION; SAMPLING; SIGNAL ENCODING; SIGNAL THEORY;

LATTICE THEORY; MULTIDIMENSIONAL SAMPLING; TIME SEQUENTIAL (TS) CONSTRAINT; ZERO ALIASING ERROR;

DATA COMPRESSION;

EID: 0030826830     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.567677     Document Type: Article

References (30)

1. J. Allebach, "Analysis of sampling-pattern dependence in time-sequential sampling of spatiotemporal signals," J. Opt. Soc. Amer. A., vol. 71, pp. 99-105, jan. 1981.
2. D. P. Petersen and D. Middleton, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Inform. Contr., vol. 5, pp. 279-323, 1962.
3. J. Allebach, "Design of antialiasing patterns for time-sequential sampling of spatiotemporal signals," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 99-105, feb. 1984.
4. N. P. Willis and Y. Bresler, "Optimal scan design for tomographic imaging of time varying distributions," in Proc. IEEE Int. Symp. Circuits Syst., 1991, pp. 750-753.
5. M. A. Rahgozar and J. P. Allebach, "A general theory of time-sequential sampling," Signal Process., vol. 28, no. 3, pp. 253-268, sept. 1992.
6. N. P. Willis and Y. Bresler, "New results on time-sequential sampling," in Proc. 7th "Workshop on Multidimensional Signal Processing (Lake Placid, NY, sept. 1991).
7. Y. Bresler and N. P. Willis, "Unified theory of time-sequential sampling," in Proc. IS&T/SPIE Conf. Electron Imaging Science and Technology (San Jose, CA, feb. 1993), pp. 37-50.
8. N. P. Willis, "Optimum sampling and interpolation with applications to medical imaging," Ph.D. dissertation, Univ. of Ill. at Urbana-Champaign, 1992.
9. N. P. Willis and Y. Bresler, "Lattice-theoretic analysis of time-sequential sampling of spatiotemporal signals Part II: Large space-bandwidth product asymptotics," this issue, pp. 000-000.
10. _, "A lattice-theoretic approach to time-sequential sampling design," in preparation.
11. P. Erdos, P. M. Gruber, and J. Hammer, Lattice Points. England: Longman, 1989.
12. E. Dubois, "The sampling and reconstruction of time-varying imagery with application in video systems," Proc. IEEE, vol. 73, no. 4, pp. 502-522, Apr. 1985.
13. J. W. Cassels, An Introduction to the Geometry of Numbers. Berlin, Germany: Springer-Verlag, 1959.
14. P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, 2nd ed. Amsterdam, The Netherlands: North-Holland, 1987.
15. J. C. Lagarias, "Point lattices," in Handbook of Combinatorics. Amsterdam, The Netherlands: North-Holland, 1992.
16. I. Kluvánek, "Sampling theorem in abstract harmonic analysis," Mat.-Fyz. Časopis Sloven. Akad. Vied, vol. 15, pp. 43-418, 1965.
17. J. R. Higgins, "Five short stories about the cardinal series," Bull. Amer. Math. Soc., vol. 12, no. 1, pp. 45-89, 1985.
18. H. J. Landau, "An overview of time and frequency limiting," in Fourier Techniques and Applications, J. F. Price, Ed. New York: Plenum, 1985.
19. Y. Bresler, "Bounds on the aliasing error in multidimensional Shannon sampling," IEEE Trans. Inform. Theory, vol. 42, no. 6, pp. 2238-2241, nov. 1996.
20. M. Pohst and H. Zassenhaus, "Algorithmic algebraic number theory," in Encyclopedia of Mathematics. Cambridge, UK: Cambridge Univ. Press, 1989.
21. J. C. Lagarias Jr., H. W. Lenstra, and C. P. Schnorr, "Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice," Combinatorica, vol. 10, pp. 333-348, 1990.
22. D. Slepian, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-iv: Extensions to many dimensions; generalized prolate spheroidal functions," Bell Syst. Tech. J., pp. 3009-3057, 1964.
23. C. A. Rogers, "The closest packing of convex two-dimensional domains," Acta Math., vol. 86, pp. 309-321, 1951.
24. L. Fejes, "On the densest packing of convex discs," Mathematika, vol. 30, pp. 1-3, 1983.
25. S. K. Stein, "A symmetric star body that tiles but not as a lattice,"'in Proc. Amer. Math. Soc., 1972, vol. 36, pp. 543-548.
26. S. Szabo, "A symmetric star polyhedron that tiles but not as a fundamental domain," in Intuitive geometry, in Coll. Math Soc. J. Bolyai. Amsterdam, The Netherlands: North-Holland, 1987, vol. 48, pp. 531-544.,
27. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 2nd ed. New York: Springer-Verlag, 1993.
28. N. P. Willis and Y. Bresler, "Optimal scan design for time varying tomographic imaging I: Theoretical analysis and fundamental limitations," IEEE Trans. Image Process., vol. 4, pp. 642-653, may 1995.
29. N. P. Willis and Y. Bresler, "Optimal scan design for time varying tomographic imaging II: Efficient design and experimental validation," IEEE Trans. Image Processing, vol. 4, pp. 654-666, may 1995.
30. R. M. Haralick, S. R. Sternberg, and X. Zhuang, "Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 532-550, july 1987.