Quasi-orthogonality and quasi-projections

Applied and Computational Harmonic Analysis

Volumn 3, Issue 3, 1996, Pages 201-214

  Unser, Michael ^a  

^a NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010354240     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1996.0016     Document Type: Article

References (32)

1. A. Aldroubi, Oblique projections in atomic spaces, Proc. Amer. Math. Soc., to appear.
2. A. Aldroubi and M. Unser, Families of multiresolution and wavelet spaces with optimal properties, Numer. Func. Anal. Optim. 14, No. 5-6 (1993), 417-446.
3. A. Aldroubi and M. Unser, Sampling procedures in function spaces and asymptotic equivalence with Shannon's sampling theory, Numer. Funct. Anal. Optim. 15, No. 1 & 2 (1994), 1-21.
4. A. Aldroubi, M. Unser, and M. Eden, Cardinal spline filters: Stability and convergence to the ideal sinc interpolator, Signal Process. 28, No. 2 (1992), 127-138.
5. H. G. Burchard and J. Lei, Coordinate order of approximation by functional-based approximation operators, J. Approx. Theory 82, No. 2 (1995), 240-256.
6. S. Cambanis and E. Masry, Wavelet approximation of deterministic and random signals: Convergence properties and rates, IEEE Trans. Inform. Theory 40, No. 4 (1994), 1013-1029.
7. C. K. Chui and H. Diamond, A characterization of multivariate quasi-interpolation formulas and applications, Numer. Math. 57 (1990), 105-121.
8. I. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
9. I. Daubechies, "Ten Lectures on Wavelets," SIAM, Philadelphia, 1992.
10. C. de Boor, The polynomials in the linear span of integer translates of a compactly supported function, Const. Approx. 3 (1987), 199-208.
11. C. de Boor, Quasi-interpolation and approximation power of multivariate splines, in "Computation of Curves and Surfaces" (W. Dahmen et al., Eds.), pp. 313-345, Kluwer, Dordrecht, 1990.
12. C. de Boor and G. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 8 (1973), 19-45.
13. E. J. Halton and W. A. Light, On local and controlled approximation order, J. Approx. Theory 72 (1993), 268-277.
14. A. J. Jerri, The Shannon sampling theorem - its various extensions and applications: A tutorial review, Proc. IEEE 65, No. 11 (1977), 1565-1596.
15. R.-Q. Jia and J. Lei, Approximation by multi-integer translates of functions having global support, J. Approx. Theory 72 (1993), 2-23.
16. p-approximation by certain projection operators, J. Math. Anal. Appl. 185 (1994), 1-14.
17. W. A. Light, Recent developments in the Strang-Fix theory for approximation orders, in "Curves and Surfaces" (P. J. Laurent, A. L. Méhauté, and L. L. Schumaker, Eds.), pp. 285-292, Academic Press, Boston, 1991.
18. S. G. Mallat, A theory of multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 11, No. 7 (1989), 674-693.
19. I. J. Schoenberg, Contribution to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math. 4 (1946), 45-99, 112-141.
20. I. J. Schoenberg, Cardinal interpolation and spline functions, J. Approx. Theory 2 (1969), 167-206.
21. L. L. Schumaker, "Spline Functions: Basic Theory," Wiley, New York, 1981.
22. C. E. Shannon, Communication in the presence of noise, Proc. IRE 37 (1949), 10-21.
23. G. Strang, Wavelets and dilation equations: a brief introduction, SIAM Rev. 31 (1989), 614-627.
24. G. Strang and G. Fix, A Fourier analysis of the finite element variational method, in "Constructive Aspect of Functional Analysis," pp. 796-830, Edizioni Cremonese, Rome, 1971.
25. W. Sweldens and R. Piessens, Asymptotic error expansions for wavelet approximations of smooth functions, II, Numer. Math. 68, No. 3 (1994), 377-401.
26. W. Sweldens and R. Piessens, Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions, SIAM J. Numer. Anal. 31, No. 4 (1994), 1240-1264.
27. M. Unser and A. Aldroubi, A general sampling theory for non-ideal acquisition devices, IEEE Trans. Signal Process. 42, No. 11 (1994), 2915-2925.
28. 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 38, No. 1 (1992), 95-103.
29. M. Unser and I. Daubechies, "On the Approximation Power of Convolution-Based Least Squares Versus Interpolation," NCRR Report 53/95, National Institutes of Health, 1995.
30. M. Unser and M. Eden, FIR approximations of inverse filters and perfect reconstruction filter banks, Signal Process. 36, No. 2 (1994), 163-174.
31. M. Vetterli and J. Kovacevic, "Wavelets and Subband Coding," Prentice-Hall, Englewood Cliffs, NJ, 1995.
32. E. T. Whittaker, The Fourier theory of the cardinal functions, Proc. Math Soc. Edinburgh 1 (1929), 169-176.